AN INVESTIGATION OF COMMUNICATION ,
EFFECTS IN COGNITIVE SPACE '

- Disser’rafion for +he Degree of Ph.‘ D.
MICHIGAN STATE UNIVERSITY ”

ROBERT T, CRAIG

I976

 

This is to certify that the

thesis entitled

An Investigation of Communication Effects
in Cognitive Space

presented by

Robert T. Craig

has been accepted towards fulfillment
of the requirements for

Ph. D. degree in Communication

 

 

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ABSTRACT
AN INVESTIGATION OF COMMUNICATION EFFECTS IN COGNITIVE SPACE
By
Robert T. Craig

The working assumption of this study was that models of cognitive
structure may fruitfully be elaborated into general models of information
which describe the structure of messages and constrain theories of the
cognitive effects of communication. Because of its intuitive appeal and
mathematical convenience, and because of its prominence in several disci—
plines, the spacial model of cognitive structure was selected for study.
The spacial model views the mind as a multidimensional space in which
concepts are defined by their locations.

Several variations of the spacial model were discussed. The model
tested in this study assumed that cognitive space is Euclidean and that
cognitive change is representable as motion of concepts in cognitive
space. A theory of linear motion was mathematically derived. The theory
posits that the effect of information inputs about a pair of concepts is
to induce change in the distance between those concepts along the line
connecting them. Whenever the cognitive space comprises three or more
concepts the theory makes non—trivial predictions of "indirect" change
in distance between each "manipulated" concept (those which are the sub-
jects of information inputs) and all other concepts.

Several lines of research bearing on the theory of linear motion
were reviewed. Studies using the semantic differential (Osgood), non—

metric multidimensional scaling (Shepard and others), and metric

 

Robert T. Craig

multidimensional scaling (Woelfel and associates) have all demonstrated
that conceptual structures can be meaningfully represented by spacial
models. There is less decisive but still suggestive evidence that motion
of concepts in cognitive space is meaningful and that the effects of in-
formation may be linear. Thus the theory of linear motion has some
plausibility based on previous research.

A study was performed to test the theory of linear motion.

A pretest-manipulation-posttest, within-subjects experimental design
was used. Subjects were 64 graduate and undergraduate students in com-
munication classes at a large university.

Fifteen concepts were scaled. The concepts were Nations. The
Nations were selected by a procedure that combined random and judgmental
features.

The procedure for measuring psychological distance was a direct,
ratio judgment procedure suggested by Torgerson and developed by Woelfel.
The scaling procedure used was also developed by Woelfel and his associ—
ates, and is based on the classical metric model of Torgerson: essentially
an orthogonal decomposition of the variance-covariance matrix.

Three messages were constructed. Each message argued that a pair
of nations was either ”very similar" or "very different." The messages
were of comparable length and structure.

In the pretest the fifteen nations were scaled. The subjects made
direct, ratio judgments of the distances between all one hundred five
pairs of concepts. The subjects then read the messages, which were in-
tended to induce motion in six concepts, leaving nine concepts unmoved.

The two sets of concepts (manipulated and not) provided experimental

Robert T. Craig

control. Theory predicts that specific changes should have occurred in

69 out of the 105 distances among the fifteen concepts, while the remaining
36 distances should not change. The subjects also made estimates of the
distances between manipulated concepts ”in the message," those estimates

to be used as estimates of the content of the messages.

In the posttest (one week later) the subjects again read the three
messages, then again estimated the 105 inter-concept distances, which
distances were to be compared with those predicted by theory.

Pretest and posttest distances were aggregated across subjects and
the mean distance matrices were subjected to metric multidimensional
scaling, the second space rotated to comparability with the first by two
procedures based on different assumptions.

Reliability and validity of measurement were assessed. It was con—
cluded that the measurements and other procedures of the study were of
acceptable quality.

The fundamental hypothesis test was a correlation coefficient be-
tween predicted and observed posttest distances among concepts. There
are many bases upon which the correlation can be computed; all of them
were computed.

Zero order correlations between predicted and observed distances
were all in the .8 to .9 range. These high correlations reflect the
overall stability of the cognitive space over time.

First order partial correlations controlling the pretest distances
and computed for the sixty—six indirectly changed distances only, how-
ever, were generally small and non-significant.

These results were judged not to support the theory.

Robert T. Craig

Seven alternative explanations of the results were discussed:
(1) the experimental manipulations may have been too weak; (2) the ex—
perimental messages may have had unintended effects; (3) "noise"——
uncontrolled information from the environment——may have caused unin—
tended changes; (4) insufficient time may have been allowed for cogni—
tive equilibrium to be established; (5) the concepts may have been in
motion prior to the experiment; (6) the concepts scaled may not have
composed a domain in the functional sense; (7) the spacial model may be
radically false; the mind may be, instead, a network of concepts. In
connection with (6), motion among a subset comprising the six manipu—
lated concepts only was found to be substantially better predicted by
the theory than was motion of all fifteen concepts. The six manipu—
lated concepts might reasonably be thought to compose a domain. No

support was found for the network interpretation.

AN INVESTIGATION OF COMMUNICATION EFFECTS
IN COGNITIVE SPACE

By

‘ "L. J
u‘ I

‘0
Robert T. Craig

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Communication

1976

ACKNOWLEDGMENTS

I am happy to acknowledge the contributions of others without
whose support and advice this work could not have been done.

Dr. Joseph Woelfel, friend and Advisor, stimulated the idea for
this research and contributed valuable support and criticism.

Dr. Donald P. Cushman, friend and Teacher, has been the dominant
intellectual influence on me for over ten years. I cannot overstate my
indebtedness to this man, whose enormous dedication, creativity, critical
intelligence and personal forcefulness have captured the imaginations
and have raised and helped to realize the aspirations of so many young
scholars. He challenged and criticized my work at every step.

Dr. Gerald R. Miller and Dr. James L. Phillips, who rounded out my
doctoral committee, also deserve thanks. Dr. Miller contributed to my
intellectual development throughout my years at Michigan State. Dr.
Phillips was generous enough to spend hours with me on several occasions
during which I learned much about cognitive theory and formed many of
the ideas contained in this dissertation.

My friend Cynthia Goldstein, besides tolerating my ups and downs
and generally seeing to it that the ups predominate, has been my most
highly valued English composition teacher throughout this and other
recent writing. Walter Gantz, friend and office mate at Michigan State,

gave me valuable advice on all subjects from theory to phraseology.

ii

The students who served as subjects in this research must remain
anonymous, but their contribution is most appreciated.

Many others, teachers, colleagues and friends, have made important
contributions to my general intellectual growth. I should mention es—
pecially Dr. Lloyd Bitzer, who taught me the meaning of scholarship and
the value of philosophy, and (now) Dr. Thomas Farrell, my good friend
and companion through eight years of school and beyond, who taught me
about things generally.

My parents, Robert and June Craig, also had something to do with

all of this.

 

TABLE OF CONTENTS

ITEM
LIST OF TABLES . . . . . . . . . . . . . . . . . .
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . .

CHAPTER I. THE SPACIAL MODEL AND A THEORY OF LINEAR MOTION

Introduction: A Working Assumption . . . . . . . . .
Spacial Models of Cognition . . . . . . . . . . . . .
Assumptions of Spacial Models . . . . . . . . . . . .
Spacial Models of Messages . . . . . . . . . . . . . .

Spacial Theories of Communication Effects .

Theory: Communication Effects as Linear Motions in
Cognitive Space . . . . . . . . . .
Scope Conditions . . . . . . . . . . . .

Derivation of the General Structural Equation .

Summary of Empirical Assumptions Inherent in
the Theory . . . . . . . . . . . . . . .

CHAPTER II. PREVIOUS RESEARCH BEARING ON THE THEORY .

Spacial Cognitive Structures . . . . . . .

The Meaningfulness of Motion in Cognitive Space . . .
Linear Force Aggregation Theory . . . . . . . . . . .
Cognitive Consistency Without Awareness . . . . .
Summary . . . . . . . . . . . . . . . . . . . . . .

CHAPTER III. METHODS . . . . . . . . . . . . .

Design and Procedures . . . . . . . . . . . . . . .
Overview . . . . . . . . . . . . . .
Subjects . . . . . . . . . . . . . . . .
Cognitive Domain . . . . . . . . . . . . . .
Experimental Messages . . . . . . . . . . . .
Measurement of Variables . . . . . . . .

Loading of the Theory . . . . . . . . . .
Data Analysis . . . . . . . . . . . . . . . . . .
Preparation of Data . . . . . . . . . . .
Program GALILEO . . . . . . . . . . . . .
Program TESTLAW . . . . . . . . . .
Statistical Analyses . . . . . . . . . .
Assessment of Measurement and Procedures .
Hypothesis Tests . . . . . . . . . .

iii

vii

NH
(DJ-\OONH

23
24

27

29

29
34
41
48
50

53

53
53
54
55
56
59
65
66
66
66
69
72
72
74

iv

ITEM
CHAPTER IV. RESULTS .

Multidimensional Scaling Analysis .
Assessment of Measurement and Procedures .
Reliability .
Validity
Procedures
Hypothesis Tests . . . . . . .
Test One: Mean Changes . . . .
Test Two: Inter-concept Distances
Test Three: Coordinates . .

CHAPTER V. DISCUSSION . . . . . . . . . . .

Evaluation of Measurement and Procedures .
Evaluation of Results

Alternative Explanations .

Summary and Conclusion .

REFERENCES .

APPENDIX A: PRETEST QUESTIONNAIRE AND POSTTEST COVER LETTER .

APPENDIX B: PROGRAM TESTLAW .

APPENDIX C: COORDINATE MATRICES FROM GALILEO

Page

79

79
89
89
105
109
111
111
112
121

127
127
129
130
146
149
156
167

173

LIST OF TABLES

TABLE

1.

2.

10.

ll.

12.

Assumptions of Selected Spacial Models . . . . . . . . .

Possible Distributions of Changes of Distance in a Domain
of 15 Concepts . . . . . . . . . . . . . . . . . . . . . . .

Effects of Deletion of Extreme Values on the Posttest Mean
Inter-concept Distances . . . . . . . . . .

Effect of Rotation Procedure Upon Distances Moved by Concepts
Between Pretest and Posttest . . . . . . . . . . . . . . . .

Means and Standard Deviations of Pretest Distances, Posttest
Distances and Pretest—Posttest Changes in Distance; Pearson
Correlations of Pretest with Posttest Distances; and t—Tests
for Correlated Means . . . . . . . . . . . . . .

Means and Standard Deviations of Pretest Masses, Posttest
Masses and Pretest—Posttest Changes in Mass; Pearson Corre—
lations of Pretest with Posttest Mass, and t—Tests for
Correlated Means . . . . . . . . . . . . . . . . . . . . .

Means and Standard Deviations of Pretest Message Content
Estimates, Posttest Message Content Estimates and Pretest—
Posttest Changes in Message Content Estimates; Pearson
Correlations of Pretest with Posttest Message Values; and
t—Tests for Correlated Means . . . . . . . . .

Pearson Correlations of Mean Pretest Inter—Concept Distances
(Sij) with Mean Posttest Inter—concept Distances (s'ij)

Pretest—Posttest Pearson Correlations of MDS Coordinates . .

Pearson Correlations of 3'1, with §mi. and Si., Broken
Down by Number of Dimensions Included in Computations, by
Method of Obtaining s'ij and by Subsets of Cases . . . . . .

First Order Partial Correlations (Controlling Si.) of s'
with §mi and Si, , Broken Down by Number of Dimensions
Included in Computations, by Method of Obtaining s' ij and
by Subsets of Cases . . . . . . . . . . . . . .

11

Pearson Correlations of A5,. with A§m_. and Ag ., Broken
Down by Number of Dimensions Included in Computations, by
Method of Obtaining s'ij and by Subsets of Cases . .

57

68

81

90

101

102

106

117

119

119

vi

TABLE Page

13. Pearson Correlations of A31. with A§mi, and A§i., Asij
Computed from Actually Observed S'i" and Smi, and gij
Computed from Fifteen Dimensions, Broken Down by Subsets

of Cases . . . . . . . . . . . . . . . . . . . . . . . . . . 121

14. Pearson Correlations of f', with fmi and fik for Two

Rotations, Cases Broken Down by Cumulative Dimensions and
Experimental Groups . . . . . . . . . . . . . . . . . . . . 122

15. First Order Partial Correlations (Controlling fik) of f'ik

with fmik and fik for Two Rotations, Cases Broken Down by
Cumulative Dimensions and Experimental Groups . . . . . . . 124

16. Pearson Correlations of Af. with Afm. and Afik for Two

Rotations, Cases Broken Down by Cumulative Dimensions and
Experimental Groups . . . . . . . . . . . . . . . . . . . . 125

17. First Order Partial Correlations (Controlling Si.) of s'ij
with gm, and §., for Indirectly Changed Distances Among

Manipuleed Conddpts Only . . . . . . . . . . . . . . . . . 139

18. Pearson Correlations of Distance From Each Concept With
Absolute Change of Distance From That Concept . . . . . . . 145

19. Pretest Coordinate Matrix . . . . . . . . . . . . . . . . . 173
20. Unrotated Posttest Coordinate Matrix . . . . . . . . . . . . 175

21. Rotated Posttest Coordinate Matrix, No Stable Concepts
Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . 177

22. Pretest Coordinate Matrix Translated to Stable Concepts
Centroid . . . . . . . . . . . . . . . . . . . . . . . . . . 178

23. Unrotated Posttest Coordinate Matrix Translated to Stable
Concepts Centroid . . . . . . . . . . . . . . . . . . . . . 180

24. Rotated, Translated Posttest Coordinate Matrix, Stable
Concepts Rotation . . . . . . . . . . . . . . . . . . . . . 182

FIGURE
1. No
2. No
3. No
4.
5.
6.

LIST OF FIGURES

Stable Concepts Rotation, X—Y Plane . . . . . .
Stable Concepts Rotation, X—Z Plane . . . . . .

Stable Concepts Rotation, First Three Dimensions

Stable Concepts Rotation, X—Y Plane . . . . . .

Stable Concepts Rotation, X—Z Plane . . . . . . .

Stable Concepts Rotation, First Three Dimensions .

vii

85

86

87

88

CHAPTER I
THE SPACIAL MODEL AND A THEORY OF LINEAR MOTION

Introduction: A Working Assumption

 

It is perhaps unnecessary to remark that we would understand a
great deal more about human communication if we understood the human
mind. That in itself, however, is not sufficient justification for
communication theory to embrace cognitive theory. The working as-
sumption of this study is that there is potentially a more specific
kinship between the two fields: that formal models of structure can be
applied equally well to cognitions and messages, and that constraints
on process inherent in those structural models can shape theories of
the cognitive effects of communication. This implies that theoretical
borrowing between the fields ought to be worthwhile.

The borrowing process is illustrated and the validity of the
working assumption is put to the test in the present study. Beginning
with a general ”spacial” model of information, this Study develops a
model of message content and derives and tests a specific hypothesis
about the cognitive effects of messages. Thus the purpose of this study
is to test the general hypothesis that cognitive change brought about
by messages is spacial in character, by testing a specific hypothesis
derived from spacial assumptions. This chapter outlines the theoretical
background of the general hypothesis, and derives the specific hypothe-
sis of this study from general assumptions. Chapter II reviews the re-
search literature bearing on the theory presented in Chapter 1. Chapter
III describes the design and procedures of an experiment intended to

test the theory. Chapter IV presents the results of that study.

Chapter V, finally, discusses the findings in relation to the theory and
to the adequacy of the study as a test of the theory, and draws impli-
cations for further research.

Spacial Models of Cognition

 

Several theorists have developed more or less elaborate models of
the mind as a multidimensional space in which concepts are defined by
their locations. In order to place in context the model used in the
present study, some of the more important of these models will now be
reviewed, and their assumptions compared and contrasted.

Scott (1969) conceives of cognitive structure as a multidimensional
space spanned by attributes, in reference to which cognitive elements are

”phenomenal objects

located. The term "domain" refers to any set of
which the person treats as functionally equivalent, and the attributes
by which he comprehends those objects” (p. 262). That a "primitive” at—
tribute such as evaluation (like—dislike) may be well—nigh universal
among domains notwithstanding, the concept of domain is introduced pre-
cisely because it is assumed that the set of attributes differs from
domain to domain. Not all cognitive objects are comparable. Moreover,
not all objects even within a domain are necessarily directly comparable.
Objects are compared by reference to attributes:
An attribute is represented in the model as a line in multidi—
mensional space, divided into segments corresponding to charac—
teristics (categories of the attribute) that the person recognizes
(p. 262).
Scott does not appear to assign any particular significance to a set of
reference axes of the cognitive space, except insofar as the number of

"dimensions worth” of attributes in the space is a type of cognitive com—

plexity. He apparently does not assume that attributes pass through the

 

origin of the space, or that the origin is in any way meaningful. He
does not assume that attributes are continuous. Quite to the contrary,
he assumes that in the most common case, attributes are made up of gross
segments within which the person makes no discriminations. Finally,
Scott makes no mention of any concept of cognitive change.

The most interesting aspect of Scott's model is that not all objects
within a domain are necessarily comparable. For the geometry of cogni-
tive space, this implies that not all points in the space have projections;
on all attributes—-a peculiar geometry! "Image comparability," the
judgment of all objects in a domain on a common set of attributes, is a
variable in this model, and is only one of several possible styles of
cognitive integration. This View is well-suited to Scott's interest in
cognitive complexity, a context in which to model the mind in the Appol—
lonian idiom of Euclidian geometry might appear to beg the essential
questions. Yet one wonders whether Scott, who sacrifices the continuous,
homogeneous properties of Euclidian space without replacing them with a
similarly coherent system, has not thereby denuded the spacial model of
much of its suggestiveness. His model has no unambiguous entailments.

Several other cognitive theorists have worked with models which,
like Scott's, might be characterized as ”quasi-spacial." Zajonc (1960)

and Runkel (1963) are further examples of theorists who view cognition

as projection of a stimulus on a set of psychological dimensions, with—
out making any further assumptions about the nature of this cognitive
space. Kelly (1963, p. 146) also makes reference to a "psychological
space” whose axes are dimensions (his term is ”constructs"), but he

develops the idea no further. Schroder, Driver and Streufert (1967)

define the properties of information processing structures in dimensional

terms: differentiation is the number of psychological dimensions in a

 

structure, discrimination is the fineness of categorization along the

 

dimensions, and integration is the manner in which the dimensions are

 

interrelated in information processing. The issue of integration is
crucial for a spacial model. Whether a "set of dimensions" constitutes
a true space depends upon what one assumes about how the psychological
dimensions are integrated. Schroder gt .21- define integration in terms
of the non-spacial concept of "schemata” or "rules."

Certainly the most notorious spacial model of cognition is the
"semantic space" of Osgood and his associates (Osgood, Suci and Tannen-
baum, 1957).* More than do any of the models previously reviewed, this
one employs the full resources of the spacial paradigm in both conceptu-

alization and operationalization of cognitive structure. The essentials

 

of the semantic space are succinctly stated in The Measurement of

Meaning:

1. Semantic judgement can be completely represented in a
[Euclidian] space defined by a set of elemental semantic
factors . . .

2. Any axis or dimension placed through the origin of the
semantic space represents a potential semantic scale or
attribute of judgment . . .

3. The semantic nature of any such attribute is given by its
relations [cosines of the angles between it and] the elemental
factors . . .

 

* I should stress that it is the semantic space concept only with which
we are here concerned, and not the "representational mediation" theory

of meaning (which Osgood nevertheless sees as the more fundamental ex-
planatory principle). The representational mediation theory, in any case,
seems not to have generated much interest among communication researchers,
while the semantic space and its associated measurement and analysis
techniques have become staples of the field.

4. Every concept in semantic space may be said to be "contained"
by its characteristic attribute [the axis passing through the
concept and the origin] . . .

a. Another concept is different from this concept by virtue
of having a characteristic attribute which is independent
(not co-linear with) the concept;

b. Another concept is different by virtue of having more or
less of the same characteristic attribute.

5. Two concepts may interact [e.g. may be compared] to the extent
that they are contained by the same attribute . . . (pp. 116-
117).

The "elemental factors” are obtained by factorization of a matrix
of correlations among a representative set of seven—point bipolar adjec-
tive scales (the "semantic differential") on which subjects judge the
meanings of concepts. Research suggests that three such orthogonal
factors are EvaIuation, Potency and Activity. The meaning of a concept
can be represented as the concept's projections on these factors (the

origin being the point of neutral meaning), and the "semantic distance”

or difference in meaning between concepts is given by

_ Z 2
D11 ‘ j dil ’
where D11 is the linear distance between concepts_i and_l, and dil is the

difference between the projections of_i and_1 on factor 1, This equation
also serves as a definition of cognitive change.

While not all kinds of belief or knowledge structures covered by
the term "cognition" are representable in terms of the semantic space,
the idea of "conceptual structure" is, nevertheless, defined within the
model as a spacial configuration:

Conceptual structure . . . The distance [D] between each concept

and every other concept can be calculated and entered into an
mixim_matrix. This matrix represents the semantic structure of

 

of the set of m_concepts, giving the distance or similarity

relations among all concepts. The set of distances repre-

senting the semantic structure are "plotable" in a space having

the same (or fewer) dimensions as the number of dimensions

represented in the measuring instrument (pp. 93-94).

The final model to be reviewed here is quite different from the
others. This model has been developed by Woelfel and his associates
(references under Woelfel, Saltiel, Gillham, Barnett, Serota, Taylor, \
Danes). If the majority of cognitive theorists cited have foregone the
benefits of powerful mathematical assumptions for the sake of substantive
assumptions about the cognitive attribute space, Woelfel represents an
entirely contrary orientation. He argues for ”the restructuring of
existing theory or the creation of new theory itself designed to fit the
most powerful measurement and research models currently available”*
(Woelfel, 1974a). He argues, that is, that we should begin with the
most mathematically powerful analysis techniques available, and construct
measures and theories to fit their requirements. For cognitive theory,
this implies a spacial model.

Woelfel (1974a) postulates that cognition is ”a process of relating
objects of thought to each other. Fundamentally, this involves taking
note of similarities and differences between objects . . ." The phrase
"similarities and differences" suggests the notion of attribute, and,

indeed, this is what Woelfel has in mind. Attributes are important in

his model, however, only insofar as the aggregation of respects in which

 

two objects of thought differ is taken to underlie an overall

 

*Woelfel makes this statement in the context of a discussion of
sociological theories, but he applies its implications to cognitive
theory as well.

 

dissimilarity or distance between the two objects. Thus dissimi—

 

larity, rather than attribute, is the generating concept of Woelfel's

model.

Dissimilarities among cognitive objects may be represented

by a continuous numbering system such that two objects con-
sidered to be completely identical are assigned a paired dis-
similarity score or distance score of zero (0), and objects
of increasing dissimilarity are represented by numbers of
increasing value . . . The definition of any set of [n] con—
cepts or objects may therefore be represented in terms of

the [n x n] matrix D . . . where any entry dij represents the

dissimilarity or distance between i and j (Woelfel & Saltiel,
1974).

The distance matrix is analyzed by subjecting it to a metric
multidimensional scaling routine (Torgerson, 1958; Serota, 1974)
which yields a coordinate space of n—l or fewer dimensions in which
the concepts are "plotable." This definition of conceptual structure
is obviously similar to Osgood's, but in both its derivation and its
applications it is quite different. For Osgood, the conceptual
structure is derived from distances between concepts on a set of funda-
mental semantic factors, which are Obtained, in turn, from analysis of
the semantic differential. For Woelfel, the conceptual structure is
directly derived from an instrument which requires the subject to pro-
vide direct, metric, pairwise distance estimates. While attributional
differences are assumed to underlie these distances, there is no as—
sumption of an attribute space spanned by fundamental factors. The
dimensions of the cognitive space, that is, are not assumed to have
any psychological significance, although they may have such signifi—
cance. Whatever overall interpretability the space may exhibit is a

function of the extent to which the pairwise attributional differences

between concepts fall into interpretable patterns. These patterns might
be clusters, dimensions or other forms, depending upon the particular
set of concepts scaled-—or the patterns may not be at all interpretable.
In any case, the configuration "is" just what it "is”: it's validity is
not considered to be dependent upon its interpretability.

What is of key importance for Woelfel is not the interpretability
of cognitive space, but its dynamics. "Change in the definition of any
object may be represented as movement of the object in the space relative
to other objects" (Woelfel & Saltiel, 1974). Movement is measured by
obtaining the matrix D and its spacial representation at several points
in time, rotating the coordinate spaces to a criterion which is assumed
to make them comparable to each other, and computing changes in location.
Velocities can be calculated from locations at two points in time, ac—
celerations from locations at three points in time, and so forth. The
crucial test of Woelfel's model is whether "laws of motion" can be found
to parsimoniously account for the changes observed in the cognitive
space. If such laws cannot be found, or if more parsimonious laws can
be found in another paradigm, then the model fails.

Assumptions of Spacial Models

 

The examples of the spacial model reviewed above encompass a con-
siderable range of assumptions. Table 1 summarizes these assumptions
roughly.

The table makes it obvious that most of the models are quite crude.
In the majority of cases it is impossible to determine whether or not a
given model implies a given assumption. Why I have applied the term

”quasi-space" to all of the models except Osgood's and Woelfel's should

also be clear: The models so designated have few unambiguously spacial

properties.

Table 1. Assumptions of Selected Spacial Models.

 

Scott Zajonc Runkel Kelly Schroder Osgood Woelfel

 

3—111; e_ta_l-
Dimensional
Attributes Yes Yes Yes Yes Yes Yes No
Continuous
Attributes No ? ? ? No Yes No
All Objects
Comparable No ? ? ? ? Yes Yes
Interpretable
Reference Axes No ? ? ? ? Yes No
Interpretable
Origin No ? ? ? ? Yes No
Change = Motion
In Space ? ? ? ? ? Yes Yes
Continuous
Space ? ? ? ? ? Yes Yes
Unbounded
Space ? ? ? ? ? No Yes
Homogeneous
Space ? ? ? ? ? No Yes
Isotropic
Space ? ? ? ? ? No Yes

 

The most interesting contrast in the table is that between the
Osgood and Woelfel models, for these two are both unambiguous and very
different from each other. The differences might be summed up by saying

that, while Osgood makes strong assumptions about cognitive structure,

10

Woelfel makes strong assumptions about cognitive change. It also appears
that Woelfel's is the more general, and the more testable, of the two
models.

I have already pointed out the differences between Osgood and
Woelfel with respect to the nature of attributes and the "interpret-
ability" of the structure of cognitive space. I might add that these
differences are evidence for the greater generality of Woelfel's model.
Were Osgood's assumptions true, Woelfel's model would be no less viable;
but were Woelfel's assumptions true, Osgood's model would lose its soul.

The five assumptions at the bottom of the table are more relevant
to change than to structure. The assumption that cognitive change is
equivalent to motion in cognitive space is fairly trivial in the Osgood
model, but is a very strong assumption in the Woelfel model. The as—
sumption implies that cognitive objects can be observed to "move” in a
geometrically reasonable fashion. In general, this means that the motion
of a cognitive object does not disturb the overall structure of the
space, or the locations of other objects. This is trivial in Osgood's
model because a change in the meaning of a concept on the semantic dif—
ferential would not generally be expected to change the factor structure
of the scales or the meanings of other concepts. In Woelfel's model the
motion of an object requires that definite changes occur in the directly
measured distances between that concept and every other object in the
space, an implication which allows for rigorous tests of "laws of motion"
as in the present study.

Both models assume a continuous space, but Osgood's space is

bounded whereas Woelfel's is not. The boundedness of Osgood's space is

11

an artifact of (l) the semantic differential, which is made up of seven—
point scales, and (2) factor analysis, which normalizes (to a range of
1.1.0) the projections of concepts on the reference axes of the space.
Woelfel's is a metric model in which boundedness is a strictly empirical
question. Both models pretty much beg the question of continuity.

A homogeneous space, in contrast to a heterogeneous space, is one
whose density, or resistance to motion, is equal at all points. An iso—
tropic space, in contrast to ananisotropicspace, is one in which objects
have no "natural resting place" or natural direction of movement (Gillham,
1972). Woelfel's model assumes a homogeneous, isotropic space (Woelfel,
1971, Chap. 1). These assumptions are a pragmatic, if not a strictly
logical requirement of the assumption that the coordinate system of cogni-
tive space is entirely arbitrary. If cognitive space is heterogeneous or
anisotropiq then Woelfel's model may fail due to a failure to find ”nice”
laws of motion, because "dense regions" or "natural resting places,” if
they exist, cannot be located_a priori with respect to an arbitrary co-
ordinate system. In this case the model can be saved only by finding some
other set of antecedents which can incorporate the peculiarities of cog-
nitive space into the laws of motion.

Osgood's model appears to assume a heterogeneous, anisotropic space.
I say "appears" because, although Osgood and his associates do not comment
directly on the issue, there is considerable circumstantial evidence to
justify my inference. The evidence comes mainly from the congruity model
of cognitive consistency (Osgood & Tannenbaum, 1955). Three aspects of
the congruity model have implications for the semantic space. First, the

congruity model assumes a tendency toward "polarization” of meanings—-

12

that is, a tendency for objects to be valued 1‘3 on the semantic differ-
ential scales. Thus there appears to be a "natural resting place" at the
boundary of semantic space. (Note that this would be expected as an
artifact, were cognitive space "really” unbounded.) Second, the model
assumes that the more polarized is a concept, the more difficult it is

to change the concept (in any direction)--in effect, semantic space be-
comes "denser" as the boundary is approached. Third, there is evidence
that the congruity model applies variously to the several dimensions of
semantic space. Tannenbaum (1968) states:

. . . It is worth noting that the congruity predictions in cogni—

tive interaction studies are generally supported least (i.e., there

is a greater discrepency between predicted and obtained scores) on

the evaluative, as opposed to the activity and potency factors . . .

One suggestion (and it is only a tentative suggestion) is that Egg

same rules d2 up; apply £9 all dimensions (p. 62).

One ought to point out that any evidence for the uniqueness of
evaluative judgments not only suggests that Osgood's semantic space is
heterogeneous, but is evidence £23 that assumption as opposed to the
assumption of homogeneity in Woelfel's model. Whether Woelfel's model
will encounter empirical difficulty along these lines remains to be seen.

Woelfel's model has some shortcomings, the most severe of which
arise from the problems of measurement. The model handles measurement
very well 13 principle, but in practice it is just measurement which most
seriously limits the model's applicability. The model requires ratio
level measurements of psychological distance which, quite simply, cannot

be reliably provided by individual human subjects, at least under pro-

cedures so far devised. Thus the model, which one would like to describe

 

individual as well as aggregate phenomena, can be tested only on aggre—

gate data-—which, it has been pointed out, can be made as reliable as

l3

necessary by means of the sample size (Barnett, 1972; Woelfel, 1974b;
Danes and Woelfel, 1975).

One could also attack Woelfel's model by citing cognitive structures
which it seems unable to describe—-my knowledge of how to tie my shoes,
for example. But this sort of criticism ignores the large range of
phenomena which the model dggs seem to describe, and avoids rather than
attacks the central issues raised by the model, which are both empirical
and interesting. No claim of universal synthesis can be made for the
model. The literature of cognitive theory is a cornucopia of spaces,
networks, schemata, groups, implicational structures, psychologics,
algorithms and other paradigms (cf. Zajonc, 1968; Deese, 1969; Weick,
1968). To attempt to subsume all of those models under one model at the
present stage would be folly. It would be better, as in the present
study, to tackle the issues raised by a specific, well-formulated model,
attempting thereby to determine the range of phenomena to which it
applies.

Despite its possible shortcomings, Woelfel's model seems to be the
best\gxtantkapproximation to a general spacial model of cognition. This
is because (1) the model is very general--genera1 enough to subsume many
of its rivals; (2) the model is fully spacial——it incorporates a full
set of geometric assumptions and implications, and thus epitomizes the
spacial paradigm; and (3) the model is more empirically testable (begs
fewer questions) than the Osgood model, its closest competitor. Never—
theless, Osgood's model should be kept in mind as a viable alternative.

The model employed in this study is essentially Woelfel's. It

assumes that cognitions are representable as locations in multidimensional

14

space, that cognitive change is representable as motion in space, and
that cognitive space is continuous, unbounded, homogeneous and isotropic.
The model makes no assumption as to the psychological interpretability of
the spacial coordinate system_pg£_§e, but assumes that the coordinate
system is a stable manifold for which concepts like location, distance
and motion, and the full range of geometric implications of those con—
cepts, are valid. This model has been selected because it is operation—
alizable and permits a full and fair test of spacial assumptions.

Spacial Models of Messages

 

A spacial model of messages assumes that the content of a message
is a "scaling" or "plotting" of concepts in a message space having the
same sorts of structural properties as the cognitive space which it
reflects.

Woelfel has proposed a definition of the message in the spacial
paradigm:

Any message, whether verbal or otherwise, may be defined as a
statement of the location of some object relative to some other
object(s). To the extent that this definition differs from the
location (definition) already assigned to that object by the in-
dividual, the message may be said to contain information. Any
message, therefore, may be concisely and exactly defined as a
vector from the point in the self at which the individual himself
locates the object to the point in space at which the message
locates the same object. When the message defines the location
of the object to be the same as the individual's own definition,
the information content, and consequently the force, of the in-
coming message is zero.

. . .When the individual is in receipt of several messages at
once (as is frequently the case) the vector sum of all the
messages will constitute a resultant vector which describes

the aggregate message at an instant in time (Woelfel, 1971,
Chapter 6, pp. 11-12).

There are three directions in which I would like to extend Woelfel's

definition. First, at least one aspect of the definition can be construed

15

as ambiguous. The message is defined both as a statement of the location
of an object, and as a vector from the receiver's location of an object
to the location proposed in the message. But these are not the same——
one can be thought of as a quality of the message itself, and the other
is a relationship between the message and the receiver. While there is
some justification in communication theory for a refusal to define the
message except in relation to some receiver, that consideration must be
weighed against the pragmatic need to study messages in their own right
(as in content analysis). The two parts of the definition ought to be
distinguished.

Second, the definition ought to more explicitly recognize that a
message usually refers to several cognitive objects. This is logically
required by the assumption that an object is defined by its location with
respect to other objects (or with respect to attributes in Osgood's model).
Since it is theoretically likely that the message will, to some extent,
exert forces upon all of the objects to which it refers, the message
should be expected to create more than one vector of change in the re—
ceiver.

Third, the definition fails to recognize that messages usually
have some internal structure. A verbal message usually includes a set
of sentences organized in some fashion. The theory of argumentation
views the message as a proposition supported by arguments,which are, in
turn, comprised of evidence, warrants, etc. We often want to manipulate
or measure the internal structure of messages, and the definition of
message should allow for this.

In view of these arguments I propose the following set of defini—

tions.

l6

Assertion: The coded representation of a psychological distance
between two objects.

Message (coded form): A set of assertions.

Argument: A function defined on that subset of a message which
includes all assertions referring to either or both members of
a given pair of concepts.

Proposition : The output of an argument; the "distance in the
message" between two concepts.

Message (cannonical form): An n x n matrix of propositions,
where n is the number of objects referred to by assertions in
the coded form of the message.

Message (reduced form): An n x m matrix of coordinate values,
where n is the size, and m is the rank, of the cannonical form
of the message; a "plotting" in m—dimensional space of the set
of n objects referred to by a message.

 

Message (assimilated form): A transformation of the message as
a function of the corresponding cognitive structure in the
receiver.

 

Information in a messag : The difference between the assimilated
message and the corresponding cognitive structure of a receiver,
assuming a "best fit" rotation of the two coordinate systems; a
set of vectors from the location of an object in the cognitive
structure of a receiver to the locations of corresponding Objects
in the assimilated message.

 

These definitions are designed to suggest a spacial model of the
message, and to extend Woelfel's definition in the directions indicated
above. The definitions are, nevertheless, admittedly crude. There is
the problem of operationalization——I discuss this below, but obviously
the problem is formidable. There are further problems at the conceptual
level. Do the definitions of assertion, argument and proposition fully
specify the internal structure of messages? The definition says that an
argument is a function which operates upon the assertions in a message,
but what sort of function? This is not so much a conceptualization as a

category of conceptualizations which need to be developed. The definition

17

is general because it cannot presently be further specified. What the
definition does propose is that the assertions in a message are combined
in some manner, and that the nature of that combination is a subject for
investigation. What I have in mind is that the distance between concepts
can be derived indirectly from assertions relating each of the concepts
to "third” concepts, but this is only a hint. Similar comments could be
made about the definition of the assimilated form of the message, which
likewise is not so much a conceptualization as a subject for further
thought and research.

In order to operationalize the concept of assertion, "the coded

' we must identify rules of

representation of a psychological distancefl
transformation between linguistic and other codes, and spacial cognitive
structures. This is, at best, a far off goal. Furthermore, one wonders
whether such an enormous task is worth undertaking before we have good
evidence as to the relative usefulness of the spacial model. But how are
we to gather data for the model if we cannot operationalize it? The
answer, of course, is that when we cannot directly measure variables, we
look for indirect indices of them. There appear to be some promising
routes toward this more modest objective.

Osgood (1959) discusses two methods, one of which is closely re-
lated to the semantic space model, but the other of which is more directly
applicable to the general spacial model.

"Evaluative Assertion Analysis" is a method of measuring the evalu-
ation of concepts in a message. It does not provide an index of psycho—
logical distance, but it is an approach which could be extended to pro—

vide such an index. The method proceeds in several steps from

18

identification of the attitude objects in the message, to "translation"
of the message into a series of evaluative assertions, to assignment of
directionsenuiweights to each assertion, and finally, to averaging of
the evaluations. The result is a scaling of the concepts in the message
on an (assumed) unidimensional attitude scale. This method could be
extended by performing a similar series of steps for other semantic di—
mensions, such as Potency and Activity, and deriving a distance matrix
from the multidimensional differences between objects. This procedure
would, of course, be extremely laborious. Still worse, it would be
practically impossible to computerize. Nevertheless, the method would
yield an index of psychological distance which would have a good pre—
sumption of validity in terms of both the semantic space model and the
set of definitions given above.

"Contingency Analysis" might yield a cruder but more direct index
of psychological distance. Osgood sees this method as giving an index
of the association structure of a source, but whether one interprets the
data in terms of association or psychological distance is, at present,
purely a function of the model one prefers. Contingency analysis proceeds
by (1) dividing the message into units, (2) noting the presence or absence
of reference to each concept or category in each unit, and (3) computing
the contingencies or co—occurences among concepts. Osgood suggests that
the contingencies be tested for statistical significance (in effect,
treating the results dichotomously), but from the standpoint of the
spacial model, it would be better to treat contingency directly as an
index of proximity. The selection of units is a problem: the general
criterion is to select units which are neither so small as to preclude

co-occurence of concepts, nor so large as to insure universal

l9

co-occurence. Another potential source of problems is that a rather
large "message" may be necessary in order to obtain a complete, reliable
distance matrix. The advantages of this method (and they are strong ad-
vantages) are that (l) the whole process, from division of the message
into units to multidimensional scaling of the distance matrix, can be
made explicit enough for a computer program; and (2) the output from the
procedure has face validity as an index of psychological distance (see
Osgood, 1959, pp. 66-73, for examples). The face validity of contigency
analysis might be questioned on the grounds that, for example, ”commu—
nism" and "democracy" co-occur frequently in Western propaganda, despite
their great psychological distance. How does the method account for the
linguistic difference between comparison and contrast, both of which are
co—occurences? The answer is that is doesn't directly, and this might
indeed be a problem. One only hopes that experience will show that con—
trasts and explicit dissociations are not so frequent as to distort the

inferred cognitive space. One might find, for example, that communism”

"politicalness," but

and "democracy" are quite close on a dimension of
quite far apart on a dimension of evaluation. Such an interpretation
would be possible if the concepts co—occur only in the presence of other
"political" terms.

Smith (1974) has developed a set of computer programs, based on
principles similar to Contingency Analysis, which yield "computer gener-
ated analogues of mental structures from language data." The programs
generate multidimensional spacial representations of message content and

permit observation of changes over time. The existence of this software

opens up new possibilities for exploration of spacial models of messages.

20

Unfortunately, none of the above techniques are applicable in
situations (such as the present study) in which short messages are to be
presented to subjects as part of an experimental procedure. Two approaches
to operationalizing the spacial model of message content remain. One ap-
proach would be to infer message content from its effects on receivers.
In a study like the present one, however, such a method would beg the
essential question, since what is at issue is just what effect messages
do have on cognitions spacially conceived. The final method is to have
a sample of subjects directly estimate the distances between pairs of
concepts "in the message." This, too, has its shortcomings, insofar as
message "content" is likely to be as much a function of the judges as of
the message reflecting, in short, the "assimilated" message. However,
the use of the receivers' judgments of message content is a defensible
and practicable, if less than ideal, method of estimating message content
in an experimental situation. (One might argue that the subjects who
judge message content should be other than the experimental subjects.

One might as easily retort, however, that the judgments of "outside”
judges would be simply a less accurate estimate of the message as as—
similated by the experimental subjects.)

Thus a spacial model of messages appears to be operationalizable
in all types of situations in which it is likely to be applied, indicating
that the project of coordinating formal models of cognitive and message
structure is practical as well as theoretically interesting.

Spacial Theories of Communication Effects

 

Woelfel (1971; Woelfel and Saltiel, 1974; Saltiel and Woelfel,
1975) has proposed two hypotheses regarding communication effects in terms

of the spacial model.

 

21

The first hypothesis, which we may call the cognitive Law of
Motion, holds that cognitive objects have constant resistance to acceler—
ation in a cognitive space which is continuous, unbounded, linear, homo—
geneous and isotropic. Formally, this reduces to the classical, me—
chanical equation, F=ma. In principle, this hypothesis can be tested by
experiments analogous to experiments which confirm the mechanical law.
For example, the assumption of constant inertial mass is confirmed if the
ratios among accelerations induced in concepts by identical forces (e.g.
identical messages) are constant across experiments. A further implica—
tion of the law is that motion (velocity), once induced, remains constant
unless it is opposed by some force. In the case of human cognition, the
influence of a message would result in constant change until the force
of the message is countered by some opposing force——other messages either
internally or externally generated. The law assumes that the cognitive
space itself has no viscosity, or resistance to motion within it, but we
could be forced by data to amend this assumption and complicate the law
accordingly.

Woelfel's second hypothesis, known as the Theory of Linear Force
Aggregation (FAT), proposes that a cognition is equal to the arithmetic
mean of all information accumulated by a person. Communication effects
are thus equivalent to a change in the mean given additional values. In
this theory, the number of messages which have formed a concept may be
identified with the constant inertial mass referred to in the cognitive
law of motion. From the standpoint of FAT, the effect of communication
is to establish equilibrium points toward which concepts will tend to

move; while, from the standpoint of the Law of Motion, the effect of a

22

message is to generate force as a function of the discrepancy between
the message content and the cognitive space of the receiver.

The two theories are not entirely integrated with each other,
although Woelfel and Saltiel (forthcoming) have taken a step in that
direction. The assumption which naturally arises from FAT is that the
force generated by a message is directly proportional to its discrepency
from the belief of a receiver. Woelfel and Saltiel show, however, that
this assumption can run into problems when one attempts to explain certain
attitude change findings——boomerang effects, for example. Woelfel and
Saltiel suggest the possibility that the broadest range of findings in
the literature can be explained by supposing that the theory predicts an
equilibrium point to which the belief will converge over time, but that
the instantaneous force generated by a message is inverse to its dis—
crepancy from the receiver's position.

The present study sidesteps most of these issues, which are left
for later investigation. The study of "motion" in the strict sense can
be pursued after it has been determined that cognitive change is de-
scribable generally in spacial terms.

Thus The Linear Force Aggregation Theory is the basis for the
present study for two reasons. First, FAT is the more closely tied of
the two theories to the spacial model of message content, in that it
explicitly includes messages as the key explanatory variable. Second,
FAT is testable without necessitating the measurement of the acceler—
ation of concepts in cognitive space——a tricky procedure better not
attempted at this early stage of experimental investigation. Roloff

(1974) measured acceleration in an experimental setting; however, that

 

 

23

was acceleration of a unidimensional attitude rather than of concepts in
a multidimensional space. Gillham (1972) computed accelerations in a
multidimensional space; however, he used the accelerations only as an
index of inertial mass, and could not test any hypotheses regarding ac-
celeration, because he lacked the necessary experimental and statistical
controls.

One point concerning spacial theories of communication effects
should be made clear: the test of any particular theory is not equiva—
lent to a test of the general spacial model. Many spacial theories are
possible-—some more complicated than others. The theory to be presented
here, for example, assumes linear motion in a stable, Euclidian space.
Complications such as nonlinear motion and warpage of space could be in—
troduced later if the simpler theory fails to explain data. The general
strategy should be to test simpler theories first, and to complicate
theories only when forced to by data. It should be recognized, however,
that there is a point at which the repeated failure of ever—more-complex
theories to account for the observed phenomena would force us to con—
clude that Umegeneral spacial paradigm is unfruitful. So while no study
can provide a "crucial" test of the general spacial model (or even, for
that matter, of the specific theory under investigation), a study such
as the present one can contribute to the ultimate evaluation of the
general spacial model.

Theory: Communication Effects as Linear Motions in Cognitive Space

 

Scope Conditions
The theory predicts the time 5' distances among a set of concepts

(s'ij) given the following:

 

24

(i) The following quantities are known: the set of distances
between each pair of concepts 1 and j_at time E (Sij)’ the projection

of each concept on each dimension of cognitive space at £(fi the

k),
inertial mass of each concept (ni), the number of messages received in
the interval £_—.£' (p), and the set of assertions contained in messages
received during the interval £_- 3} (Eij).

(ii) The interval_£ —_E' is sufficient for equilibrium to be
established in the cognitive space following receipt of messages.

(iii) No change occurs during the interva1_£ — 3} except that

induced by known messages.

Derivation of the General Structural Equation

 

Woelfel's Linear Force Aggregation Theory states that a belief is
equal to the mean value of all messages received. Translated into terms

of the spacial model,

(1) n
)3

= k=l Sijk ,
ij n

Where: sij = the psychological distance between concepts i and j,

s. = the distance proposed by message k,

1jk
n = the total number of messages which have located 1 and j——

the 'inertial mass' of Sij'

A direct implication is that the effect of "new" messages on an already
established belief is equivalent to a change in a mean given additional
values.

(2) ns.. +ps.. p

 

 

25

l
ij

p = the number of new messages

Where: 5 = the new belief

sij = the mean distance proposed by the new messages

In view of the conclusions of Woelfel and Saltiel (forthcoming), we Cu;
to regard s'ij as an equilibrium value that will be approached over tir
as the messages are processed. In short, we are dealing here with whaI

"comparative statics" rather than dynamics.

strictly might be called
Assume that n, the total number of messages which have located 1

and j, can be expressed as a sum of two quantities,

= +
(3) n ni n ,

where n. and n3. are the number of messages which have located 1 and j,
1

respectively. This assumption allows us to partition the expression or

the right in equation (2) so as to reflect the relationship between in-

ertial mass and message effects.

(4) n. p ~ _ n. p ~ _
, 1 . . (sij Sij) + ._1 . . (sij Sij)

n n + p n n + p

 

.1

where the left bracketed expression is the change brought about in j ar
the right bracketed expression is the change brought about in i. The
change brought about, that is, is inversely proportional to the number
of messages which has located a concept. In still other words, the ch:
brought about by new messages is "apportioned" between i and j in inveI
proportion to their inertial masses.

Now assume that i and j are located in a multidimensional space,
and our problem is to determine the change in location of a "moved" C0]

cept i with respect to all other concepts in the space. The first ste

26

in doing this is to note that sij can be expressed in terms of the pro—
jections of i and j on a set of orthogonal reference axes of the space.

(5) = r _ 2
ij kil (fik fjk) ’

where f.
1

k and fjk are the projections of i and j, respectively, on axis

f, and r is the dimensionality of the space. Eij and s'ij can, of course,

be expressed similarly.
The general structural equation for post-message pairwise distances
among concepts in the space can now be derived in three steps. First,

we need an expression for f the projection of concept 1 on axis f as

ik’
proposed by new messages. Second, we need an expression for f'ik’ the
new equilibrium for the projection of i on f brought about by the new
messages. Third, we can write the general structural equation.

The expression for fik assumes that one—half of the change proposed
by Eij is directed toward concept 1, and that the change proposed is ap—
portioned among the dimensions of the space proportionate to the distance

between the projections of i and j on the dimensions.

2

(6) ~ = (f. — f. ) 1 ~ _ f. — f,
fik fik + __3JL___igi__ -____ - (Sij Sij) . 1k jk
(Sij) 2 lfik ' fjkl

The last factor in expression (5) is needed to determine the sign

of the changes proposed in fi The expression for f’ the post—

k' ik’

message equilibrium value of the projection of concept 1 on axis f, can

now be adapted from the appropriate parts of equation (4).

(7) f' — + zni . P (E )

ik " fik ' ik ' fik

 

 

n n + p

27

In equation (7),;1 is multiplied by 2 to take account of the fact that
the derivation of Eif has already divided the proposed change, and allo-
cated the change to concepts i and j separately. Note that if either
p=0 or §1j=sij, then equations (6) and (7) result in f'ik=fik' These
equations, that is, can be applied to any concept in the space, regard—
less of whether any messages have affected that concept.

Substitution into equation (5) now gives the general structural

equation.

(8) . = r . _. 2
Sij 1:1 (f 1k fjk) ’

where i and j are any two concepts in the space. Equation (8) is a

 

general structural equation in the sense that it gives the post-message
distances between all pairs of concepts, including pairs in which
neither, one or both concepts have been affected by messages.

Summary of Empirical Assumptions Inherent in the Theory

 

(i) The theory assumes that the variables such as ni and Eij are
stable phenomena, quantities that can be measured, and quantities which
in fact age measured by the instruments employed.

(ii) The theory assumes that all relevant messages are known, im-
plying both that messages received before time 5 have no effects during
the interval t — t' and that all information received during the interval
is included in the calculations. This assumption could be especially
dangerous if Woelfel's hypothesis that cognitive objects have constant
resistance to acceleration (but not velocity) is valid.

(iii) The theory assumes the spacial model of message content—-

that a message is composed of a set of assertions which propose distances

28

between pairs of concepts, thus setting up forces along the lines con-
necting these concepts. The theory further assumes that the force of an
assertion is divided equally between a pair of concepts, and that a con—
cept's resistance to that force is a function of the number of messages
which have located the concept.

(iv) The theory assumes that complex cognitive processes occur
out of the awareness of subjects. It seems rather unlikely, that is,
that subjects consciously make indirect changes in cognitive distances
so as to conform to the spacial model. If these processes go on, they
do so implicitly and unconsciously.

(v) Finally, the theory assumes that the pairwise distances
among cognitive objects are constrained by the stable, Euclidian charac—
ter of cognitive space, so that the pairwise distances are not indepen-
dent of each other: the motion of a concept implies precisely calculable

changes in its distance from every other concept in the space.

CHAPTER II
PREVIOUS RESEARCH BEARING ON THE THEORY

This chapter surveys research literature bearing upon the theory
of linear motion at several points. The issues discussed include (1)
the existence of cognitive structures conforming to the spacial model;
(2) the meaningfulness of motion in cognitive space; (3) Woelfel's
Theory of Linear Force Aggregation; and (4) the occurrence of complex
cognitive processes out of the awareness of subjects. Following the
review of these issues, we consider the overall status of the theory in
light of previous research.

Spacial Cognitive Structures

 

Evidence that cognitive structures exist which can be represented
in terms of a spacial model has come mainly from (1) studies of Osgood's

' and (2) studies employing nonmetric multidimensional

"semantic space]
scaling methods. Both of these lines of research tend to support the
spacial model, although the MDS studies are perhaps the more credible.
Osgood and his associates have found that at least some dimensions
of semantic space are remarkably stable and invariant across cognitive
domains. Osgood, Suci and Tannenbaum (1957) state:
The same three major factors of evaluation, otency and activity
(which were empirically rather than theoretically derived) have
reappeared in a wide variety of judgmental situations, particu-
larly where the sampling of concepts has been broad. The rela—
tive weights of these factors have been fairly consistent:
evaluation accounting for approximately double the amount of
variance due to either potency or activity, these two in turn
being approximately double the weight of any subsequent factors.
(p. 325)

This central finding has held up quite well in subsequent studies in

many cultures. Seventeen years after publication of The Measurement

29

 

3O

pf Meaning, Osgood (1974) is able to assert that the accumulated research
"is rather convincing evidence for the universality of the affective
meaning system" (pp. 33—34).

There are, however, several problems associated with the semantic
space research. First, and most significantly, Osgood's research methods
are such as to make it difficult to falsify his central assumptions. The
relative success of those methods in a massive accumulation of studies is
certainly evidence of the merit of the assumptions. On the other hand,
the question of whether cognitive space is_pgsp thought of as an attri—
bute space cannot very directly be answered by a method which involves
measuring meaning on interval attribute scales and factoring those scales.
The method begs the question. Second, there is evidence that the sort of
bipolar scales used in the semantic differential do not actually repre—
sent psychological poles. Wishner (1960) found indications that "gram—
matical antonyms do not necessarily correspond to psychological opposites"
(p. 110). Danes and Woelfel (1975) performed a multidimensional scaling
study including adjectives frequently used in the semantic differential,
and found that supposed polar opposites (l) were at substantially dif-
ferent distances from the origin and (2) were at angles to each other
through the origin substantially different from 180 degrees. Third, as
noted in Chapter I, the semantic space is bounded as a result of both
the seven step scales and the factor analysis procedure used to generate
the semantic space. Such a set of procedures must lead to ceiling ef—
fects in measurement. Thus not only the apparent boundedness of semantic
space but its apparentaniSotropimnand heterogeneity are methodological

artifacts.

 

 

31

These three difficulties are sufficiently serious to cast some
doubt on Osgood's findings, although it must be admitted that the con—
sistency of those findings and the consequent wide and successful appli—
cation of the methods of the semantic space in social science research
provide at least some support for the utility of a spacial view of cog—
nition. Thus the semantic space research is one source of evidence for
the existence of stable, spacial cognitive structures.

The basic logic of multidimensional scaling as applied in psycho-
logical research has been expressed by Helm, Messick and Tucker (1959):
. . . The fundamental concept in multidimensional scaling is
psychological distance, which is usually estimated in terms of
judgments of similarity among stimuli; i.e., two stimuli judged

to be very similar are considered to be psychologically closer

together than two stimuli judged to be very different. Given

judgments of similarity among all the stimuli in a set, mathe—
matical models exist which provide an interpretation of this
psychological distance in terms of Euclidian space, and analytical
techniques are available to obtain the dimensionality of the space
as well as stimulus scale values determined within a rotation and

translation. (p. 111)

Serota (1974) has outlined the background and history of MDS in
some detail. Within the category of MDS we can distinguish between
metric and nonmetric techniques. Metric or classical MDS was developed
as a psychological measurement technique largely by Torgerson (1958).
Metric MDS requires the input of interval or ratio level paired compari—
sons data among a set of concepts, and operates upon the data to scale
the concepts in an orthogonal vector space which retains all of the in—
formation in the original data (i.e., the distance matrix can be exactly

reproduced from the coordinate matrix by application of the Pythagorean

Theorem).

 

 

32

Serota (1974) describes the concerns about metric MDS that led to
the development of nonmetric techniques by psychometricians:

First, the notion that subjects could make reliable interval
of ratio judgments was not readily accepted. It is axiomatic that
the reliability of the judgment is inversely proportional to the
difficulty of the judgment task. Since the model was attempting
to describe individual differences in cognitive arrangement, or
psychological distance, it was believed that the technique should
be adapted to function with ordinal judgment data which simplify
the subject's task and increase the reliability of the findings
reported.

Second, the use of the "additive constant" approach was con—
sidered suspect since its use with ratio scaling violates the
assumption of absolute magnitude and its use with interval sealing
required separation of systematic and random error to get the data
to fit a Eculidian real space. Richardson (1938) made the as-,
sumption, which Torgerson defends, that the data was fallible and
represented a foreshortening of the differences which when strictly
interpreted would yield triangle inequalities and add unnecessary
dimensions. The nonmetric approach (Shepard, 1962a, 1962b;
Kruskal, 1964a, 1964b) avoided the problem rather than attempting
to deal with it by (1) eliminating the distance component from the
procedure, (2) artificially generating a configuration in a
Euclidian real space of m dimensions (m is less than n and is de-
termined from the data) which could be adjusted to fit the dis—
similarities relationship and (3) reporting the degree of mono—
tonicity between the scale distances and the reported dimensionality
(stress).

Third, the process of determining dimensionality was itself
challenged as contradictory to the goal of simplicity. Shepard
(1962a, 1972) states that the purpose of multidimensionality in
scaling should be to produce an expression of interrelationship
which is readily interpretable. Techniques built upon this view-
point tended to emphasize rank reduction at the price of iso-
morphism of the solution to the raw data . . . (pp. 48-49).
Because of its emphasis upon producing an interpretable space of

small dimensionality, nonmetric MDS can be and has been used to determine
the utility of a spacial concept of cognitive structure. A representa-
tive, indeed almost comprehensive source for the current theory and ap-
plications of nonmetric MDS in the behavioral sciences is the two volume

collection by Shepard, Romney and Nerlove (1972). A review of the papers

in those volumes tends both to further evidence the utility of the

 

33

spacial model of cognition and to justify our suspicion of Osgood's
methods of operationalizing that model. Many MDS studies, that is, have
found interpretable spacial configurations, but many of those studies
also suggest that not all interpretable multidimensional spacial repre—
sentations of cognitive structures also have interpretable dimensional
structures. Spacial structures may appear as interpretable clusters,
circumplexes or other nondimensional forms. The set of possible forms
has been somewhat systematized by Degerman (1972).

In a study that exemplifies the flexibility of MDS, Rapoport and
Fillenbaum demonstrated that color terms in American English scale as a
two dimensional circumplex corresponding quite closely to the theoretical
color circle, and that "Have" words in American English (return, steal,
take, etc.) scale as a set of clusters in space. Regarding the "Have"
words, the authors conclude (p. 121): "The two dimensions are difficult
to interpret, and as the tight clusters appearing on the plot suggest,
any attempt at a dimensional representation imposes structure on the data
that is not there . . ." Indeed, Rapoport and Fillenbaum argue that MDS
analysis is inappropriate in such a case, but their argument rests en—
tirely on the assumption that a spacial representation must yield inter—
pretable dimensions——a doubtful assumption in view of the clearly inter—
pretable clusters present in the plot of their data.

When MDS studies have found interpretable dimensions, the dimensions
are sometimes similar to the Evaluation, Potency and Activity dimensions
of the semantic space and sometimes not. The study of Nations reported
by Wish, Deutsch and Biener (1972) found the evaluation-like dimension of

Political Alignment and the potency-like dimension of Economic Development,

 

34

but also found dimensions of Geography—Population and Culture—Race which
have no correspondence with semantic space findings. Rosenberg and
Sedlak (1972) found, for personality terms, clear dimensions of good—bad
and dominance—submission. Burton (1972) found that occupation names fall
long dimensions of dependency, prestige and skill, D'Andrade, ep._al.
(1972) found that disease terms scale by seriousness and contagion.

These studies all give evidence both of the validity of the general
spacial model of cognition and the utility of MDS as a way of operation-
alizing the spacial model. Perhaps more compelling evidence, however,
comes from those studies which have related spacial representations to
human behavior assumed to depend upon the cognitive similarity of objects.
That such relations hold has been demonstrated for the substitutability
of consumer products (Stefflre, 1972) and of political candidates (Mauser,
1972): products or candidates found by MDS to be closer together are
more likely to be substituted for one another (switched among) in the
market or the electoral arena. Jones and Young (1972) found that fre—
quency of social communication could be predicted from distances among
people in a spacial representation of a social structure.

In sum, both semantic space and nonmetric MDS research tends to
confirm the utility of a spacial model of cognition, in that those
studies have shown that the spacial representation is stable, valid on
its face, and reliably related to other human behavior.

The Meaningfulness of Motion in Cognitive Space

 

If nonmetric MDS has a strength it is in the reduction of data to
interpretable spacial representations. If we take seriously Woelfel's

theoretical argument as presented in Chapter I, however, the existence

 

35

of such interpretable configurations is neither necessary nor sufficient
to support the spacial model. Interpretability is unnecessary in that a
cognitive structure might be spacial and yet display no "interpretable"
dimensions or other structures. Nor is interpretability sufficient to
support the spacial model, for the concept of space implies motion, in
terms of which the space may be described as homogeneous or hetero-
geneous and so forth.

Because the relationships it displays can be assumed, even in
principle, to be merely ordinal, nonmetric MDS may be considered unsuit—
able for the investigation of motion in cognitive space. Thus their
interest in the study of change has motivated the renewed interest of
Woelfel and his associates in metric techniques. This revived interest
has led to the development of the Galileo system——a set of measurement
and design techniques and a package of computer programs——which adapts

classical MDS to Woelfel's interest in the study of cultural processes."

The Galileo system has been described in detail by Serota (1974), but a
succinct overview of the technique is provided by Taylor, Barnett and
Serota (1975):

The subjects are given a complete (n(n—l)/2) list of pair com—
parisons for the set of concepts being scaled. They are asked to
make ratio judgments of the dissimilarity between concepts using
the form:

Iflx and y are_u units apart, how far apart are concept
a and concept p2

Such an item wording requests a distance judgment from a
respondent (" . . . how far apart are a and p?”). However, it
requests that this judgment be made as a proportion of a standard
distance provided by the researcher ("if x and y are u units
apart . . ."). This format allows the respondent to report any
positive value; the scale is thus unbounded at the high end, con-
tinuous, and grounded with a true zero (identity — two concepts
are perceived to be the same).

 

 

36

Since the data for an individual case is highly unreliable
(reliability being inversely proportional to the difficulty of
the judgment' task), and since our goal here is a measure of
social or cultural conceptions (Serota pp, 31,, 1975), we may use
aggregation techniques to improve our measurements. By applying
the Central Limits Theorem and Law of Large Numbers we find that
the arithmatic average of all responses for any cell in the matrix
will converge on the true mean for the population as the sample
grows large. . .

The mean distance matrix is further transformed to a scalar—
products matrix which has been double—centered (Torgerson, 1958)
to establish the origin at the centroid of the distribution.
This matrix is subsequently factored (using a direct iterative,
unstandardized procedure) to achieve a coordinate matrix whose
columns are orthogonal axes and whose rows are the projections
of the concept location on each of the axes . . . This space
has the property of representing the average distance judgments
for all possible pairs simultaneously. Additionally, the multi—
dimensional space is constructed from the unstandardized dis—
tance vectors between all possible pairs, and all variance in
the sample population is thus accounted for by the n—dimensional
space.

Finally, this procedure is repeated at each point in time and
the spaces are rotated about the centroid to a least-squares best
fit to provide approximations of the concept motions over time.
From these resultant cross-time coordinate matrices we can fit
curves (trajectories) of motion which describe the relational
change from the set. (PP- 4—5)
A more recent addition to the system is an alternative rotation pro—
cedure which takes account of theoretical assumptions about which con—
cepts havernuihave not ”moved" during the interval between observations
(Woelfel, et a1., 1975).

Woelfel's mathematical theories and the (in principle) precision

of the Galileo system as an operationalization of cognitive space not-

withstanding, the evidence thus far produced to support the inference

*Studies by Barnett (1972) and by Danes and Woelfel (1975) have achieved
adequate levels of reliability with samples of well under one hundred
people.

 

37

of meaningful motion in cognitive space is both sparse and rather impre—
cise. An examination of four studies bearing on the question finds that
the inference of meaningful motion rests largely on the_pg§£_hgg "inter—
pretability" of observed changes in location of concepts. Even so, the
obtained results are sufficiently interesting to warrant further investi—
gation.

Gillham (1972) found that motion over two intervals (encompassing
several months) in the aggregate cognitive space of members of a soci-
ology department was "lawful” according to several criteria, including
interpretability in terms of_pg§£_hgg explanations, general stability of
the configuration over time and predictability of magnitudes of changes
of concepts from gross differences and changes in volume of information
flow about the concepts. Gillham made no specific prediction of forms
of motion; nor did he measure or control the content of information.

The study incorporated only rough indices of the amount of information
communicated about each concept. Gillham's pgsp_hgg interpretations of
motions were aided by interviews in which respondents to the study were
asked to explain specific changes in their responses. The resulting
flavor of Gillham's interpretations is given by a brief quotation:

Once again the dimensions that are used vary considerably across
respondents. The professor who has the largest changes from
time two to time three is said to be ' . . . a nicer guy than I
had thought' and 'more of an outcast' in relation to another
professor who once had much power in the department. It is
clear from personal observation that this professor whose posi—
tion changed so much has recently spent much more time talking
with graduate students than he once did. Two respondents who
were later interviewed mentioned meeting him in the graduate
lounge . . . (pp. 53-54)

In a five wave panel study of the 1972 U. S. Presidential Election,

conducted in Champaign County, Illinois, Barnett, Serota and Taylor

38

(1974) tested several qualitative hypotheses about motion of candidates
and issues in the aggregate space. These were: (1) that candidates
would converge over time with issues with which they were publicly as—
sociated; (2) that the candidates would diverge from each other over
time; (3) that the candidate whose aggregate distance from ”Me" (one of
the concepts scaled) was minimal at the time of the election would be
elected; and (4) that the overall magnitude of the space would shrink as
the election approached. The study suffered from methodological problems
--in particular, a very high rate of subject attrition. And again, as in
Gillham's study, the hypotheses could be tested only by post hoc inter—
pretations of observed changes in light of what the authors informally
knew about the events of the election campaign. By that weak criterion
the data were claimed to provide some support to the hypotheses. The
authors conclude:
These findings clearly lack the rigor necessary to test the primary
hypothesis that movement in the vector space is a function of the
amount of information the subjects receive. We can only infer this
from the results reported above. It is, however, possible to ob—
serve regular motion in the space reported here which maintains a
high level of face validity with both current political polling
practices and actual voting behavior for the population. To use—
fully apply these techniques and test our main hypothesis it will
be necessary to control the information concerning the scaled con-
cepts and/or perform a content analysis about those topics, while
utilizing the metric multidimensional scaling instrument at a
level of rigor consistent with the precision which it is able to
achieve. (p. 30)
Taylor, Barnett and Serota (1975) have since completed a trend
study of a congressional election near Detroit, Michigan. The trend
study, by observation of independent samples at several points in time,

avoids the problems of subject attrition and sensitization. Hypotheses

one, three and four of this study'were identical to those of the previous

39

study, while hypothesis two was replaced. The new hypothesis two was

that "identification of a candidate with the issues clustering closest
to the average position for the respondents (Me) will cause that candi-
date to converge with the average position for 'Me'."

The method of analysis employed—fipgsg hgg, qualitative interpre—
tation of motions in light of informal knowledge about the campaign——
was similar to that of the previous study. This time, however, the
authors appear to have had much more direct and intimate knowledge of
the Democratic candidate's campaign strategies, and, indeed, seem to
have influenced those strategies to a degree. This greater knowledge
permitted the authors to make several qualitative predictions, which
generally were confirmed.

The Democratic candidate attempted to identify himself with crime
prevention and subsequently converged with that concept in the space.
The candidate's distances from two concepts on which he did not comment,
however, remained relatively stable. This was considered to support
Hypothesis One. The new Hypothesis Two is still more interesting be—
cause it introduces a question of indirect change——whether identifying
a candidate with an issue that is ”close" to the aggregate Me will move
the candidate closer to Me. Significantly, a qualitative analysis of
the Democratic candidate's motion with respect to Bussing, Crime Preven—
tion and Me was judged to support the hypothesis. Since the prediction
of the election outcome by a formula based on the distance of the candi—
dates from Me was accurate within two percent, and was more accurate
than a prediction based on customary polling methods, Hypothesis Three

was also considered supported. Hypothesis Four, however, was not supported.

 

40

Although the study discussed above is in many ways quite impressive,
its limitations are also obvious (and readily admitted by the authors).
The most general and serious problem is that lack of control (statistical
or experimental) over information flow prevented before—the-fact pre—
diction of motion based on explicit mathematical assumptions. A second
problem is that the analysis tended to focus upon certain motions and
ignore others. In particular there was no attempt to systematically ex-
plain all observed changes, to seek out evidence contrary to theory, or
even to account for apparent anomalies (like the great motion of the
Republican Party, presumably a relatively massive concept).

A fourth study which has attempted to assess the meaningfulness of
motion in cognitive space is reported in Woelfel, gt .al. (1975). This
study was conducted in a controlled setting. Data were collected at four
points in time. Between measurements subjects received messages, attri—
buted to two sources, advocating a behavior, the CTP, the meaning of
which was left vague. As predicted, the two message sources and CTP were
observed to converge in space. This motion was especially evident when
a rotation procedure was employed which attempted to leave only those
three concepts free to vary, a result which suggests the possibility that
the results of previous studies would have been more clear—cut had they
been able to use the new rotation procedure.

Just because this study was so much more controlled than the pre—
vious three its weakness as a test of theory, rather than as a piece of
research pg£_§g, become prominent. Once again, despite the mathematical
precision of Woelfel's theories and the presumed precision of the scaling

technique employed, only a qualitative prediction was made. Furthermore,

41

only some of the spacial information available was used in making and
testing the predictions. Specifically the prediction that the two sources
and CTP would converge says nothing about how those concepts would move
with respect to other concepts in the space. If the notion of "Laws of
Motion in Cognitive Space" is to have any nontrivial meaning then that
additional information must be taken into account and the corresponding
phenomena explained.

Linear Force Aggregation Theory

The hypothesis that a cognition is equal to the mean of all the
information to which a person has been exposed has been somewhat success—
fully tested from several standpoints in studies carried out by Woelfel
and his associates.

One line of research has considered whether a belief or attitude
can be predicted from estimates of the information to which the person
has been exposed. In the earliest of these studies, which predated the
theory itself, Woelfel and Haller (1971) accounted for 64 percent of the
variance in high school students' educational aspirations, and 57 per—
cent of occupational aspirations, with linear regression models which
included as predictors the means of the educational and occupational ex—

pectations for the student held by the student's designated significant

others.‘ Mettlin (1970) successfully replicated those results with a
different sample of students. Using linear regression models, Woelfel
and Hernandez (1974) accounted for about 55 percent of the variance in
college students' self—conceptions as marijuana users, and Woelfel, g;

31, (1974) accounted for about 62 percent of the variance in French—

Canadian separatism.

42

The impressive coefficients of determination reported in these
studies should be interpreted with a great deal of caution. First, as
a practical matter we will seldom be able to measure 311 messages to
which an individual has been exposed, and we certainly will not be able
to do so in field settings and for substantially interesting cognitions.
Thus FAT cannot be, and in fact has not been, strictly tested in field
studies such as those cited above. Second, the linear models tested in
studies incorporated many variables, which are only interpretable £9
varying degrees as indices of ”information." In Woelfel and Haller (1971),
for example, Educational Aspirations were about as strongly predicted by
Occupational Aspirations and Academic Performance as by Significant Other
Expectations, and all three of these variables contributed to the re—
ported R2 of .64. Academic Performance can be considered as self-
reflexive behavior and therefore as information, but to similarly inter-
pret Occupational Aspirations would be questionable. The results of
Woelfel and Hernandez (1974) and Woelfel, g; 31. (1974) are even more
dubious from this standpoint. Information exposure in these studies was
measured by subjective reports, which over twenty years of cognitive
consistency research (Abelson, et al., 1968) suggests may correlate with
attitude quite independently of actual communication content. Further—
more each study included over thirty variables in the multiple regression
models, and in each case demographic ("structural") and "related atti-
tude” variables independently explained significant proportions of vari—
ance. Again, demographic variables may incorporate location in the
societal communication network, but "related attitudes” seem entirely

indefensible as information measures. Third, these studies actually

43

contradict the simple mathematical formulation of the theory insofar as
they have found indications that not all sources ”count" equally in
attitude formation. This is evident to some extent from the varying
regression weights of the exposure variables. More directly, Woelfel
and Hernandez (1974) estimated the "inertial masses" of various sources
and found them to vary considerably.

Woelfel, however, has always regarded the theory as oversimplified
in this respect (see, for example, Saltiel and Woelfel, 1975); and the
necessity, under some circumstances, of differentially weighting messages
from different sources does not seriously compromise the principle of a
linear force aggregation theory. Nor is the above critique intended to
assert that the available evidence denies the predictive utility of FAT.
It asserts only that the available evidence, while suggestive, falls far
short of ”proof."

A second line of research into FAT comprises two studies which test
the implication that the more information upon which a cognition is based
the more resistant to change is that cognition. First, Gillham (1972)
examined the hypothesis that motion of a concept in multidimensional
cognitive space is inversely proportional to the amount of information
composing it. The concepts in his study were members of a sociology
faculty, and the amount of information was indexed by such variables as
the number of graduate assistants working with the professor and the
mean number of hours respondents reported talking with the professor.

All correlations between these indices and the ”inertial mass" (relative
stability) of the concepts were in the predicted direction, although

most of the correlations were quite low. Second, Saltiel and Woelfel

44

(1975) found that attitude change in a sample of high school students
over a six month interval inversely correlated (r=.l9, p<.05) with an
index of "number of messages." The index was computed for each respon—
dent by multiplying the number of people with whom the respondent re—
ported (specifically named) having talked about the attitude issues by
the average amount of communication the respondent reported having with
these "significant others." Thus two very different studies have both
found absolutely low but directionally consistent correlations supporting
the FAT implication that information accumulates as the inertial mass of
concepts.

Saltiel and Woelfel (1975) report additional results bearing on
the theory. Most interesting among these are the negative findings that
attitude change was BEE related to heterogeneity of significant other
opinions (as measured by the variance of attitude responses directly ob—
tained from respondents' nominated significant others), nor to an index
of psychological stress, nor to self-reported strength or certainty of
opinion. These negative findings tend to rule out possible competing
explanations of attitude stability.

A third and final line of research into FAT includes studies which
directly attempt to assess the theory's utility for predicting the cog—
nitive effects of information inputs. The study reported in this dis—
sertation is in this line, which may be said to have begun with Roloff
(1974).

Roloff tested the basic implication of the theory for cognitive
change: the proposition that attitude change is directly and linearly

related to the number of incoming messages and the discrepancy of those

45

messages from the old attitude, and that attitude change is inversely
related to inertial mass (accumulated information). In a multiple—
message experiment Roloff found significant correlations between dis—
crepancy and attitude change at different times, for two of three topics.
For the third topic discrepancy and attitude change were correlated at
one time but not at the other time. The deviant issue was later iden—
tified as having the highest inertial mass of the three. Roloff also
found that the maximum attitude change on each topic occurred with the
delivery of the first message. Subsequent messages induced significantly
smaller change increments. Again, this is consistent with the idea that
information accumulates as inertial mass. Although these are not precise
tests of the mathematical theory, they do lend the theory some support.
The political study by Taylor, Barnett and Serota (1975) also at—
tempted to test the cognitive change implications of FAT. The authors
grant at the outset that in
. . . field studies such as the research described here, however,
lack of experimental controls prevents adequate empirical exami—
nation of these [FAT] equations. Attitude change, then, is
treated as a simple quantitative function of the number of mes-
sages an individual has received about a given attitude object.
Thus, the greater the information history about an attitude ob—
ject the more difficult it becomes to foster attitude change.
(p. 2)
By this weaker test findings such as that the less known Democratic
challenger moved more in cognitive space than did the more known Repub—
lican incombant, and that the Democratic candidate moved more with
respect to issues on which he campaigned than issues which he didn't
mention, may provide some support for the theory. On the other hand,

how are we to explain the fact that among the concepts that underwent

the greatest change were the Republican Party, the Democratic Party and

 

46

Me—-presumably highly massive concepts? The support given FAT by this
study is weak at best.

Finally, Woelfel 3;, 31., (1975) report a laboratory experiment in
which three low mass concepts associated with each other by means of
messages converged toward each other in cognitive space. These results
conform generally to the theory; although again no direct test is made
of the mathematical theory, and the relative motions are not entirely
consistent with what one might reasonably suppose to be the relative
masses of the concepts.

Considered together these three studies are rather weak evidence
for the utility of FAT for predicting the cognitive effects of messages.
In fact, the present study is the first to attempt a direct test of FAT
as a mathematical theory of the cognitive effects of communication.

Two very substantial lines of research in addition to the three
sets of studies discussed above might be interpreted as bearing on FAT.
These are studies of the relation between advocated and obtained atti—
tude change and studies of information integration.

FAT quite unambiguously predicts a positive linear relation be—
tween attitude change advocated and obtained. A summary of the research
literature by Greenberg and Roloff (1975), however, makes clear that non—
linear and even negative relations frequently have been found. Ulti-
mately either the conflicting studies will have to be reinterpreted to
fit the theory or the theory itself will have to be changed or restricted
in scope. The last choice is taken by Greenberg and Roloff, who suggest
that the relation is linear and positive (thus FAT may apply) only for

low mass concepts. Greenberg and Roloff report data showing a linear

 

47

relation between attitude change advocated and obtained on a set of topics
relatively unknown to the experimental subjects. This is consistent with
their interpretation, but does not, of course, demonstrate the proposition,
fatal to FAT as a general theory, that the relation is nonlinear for high
mass topics.

The main event in the information integration literature has been a
bout between models which assume that information inputs are added to form
an overall impression and models which assume that information inputs are
averaged. Considered as an information integration model, FAT is quite
definitely an averaging model. Reviewing the literature on "summative"
versus averaging models of information integration, Wyer (1974) concludes:

It is undoubtedly clear by now that 'critical' tests of summative

and averaging models, and the identification of the psychological

processes to which they pertain, are very difficult to construct.

The data usually interpreted as evidence for a summative process

(e.g., the 'set size' effect) can be accounted for by an averaging

model such as Anderson's. On the other hand, the 'averaging—like'

effects when moderately polarized information is added to highly
polarized information could in principle be predicted by a summa—
tive model, suchzfi;Fishbein's, which takes into account the influ—
ence of attributes other than those specified in the information

presented. (p. 300)

Wyer goes on to present further data which he argues support a summative
over an averaging model. However, he goes still further to suggest that
both models may be false or may apply only in limited circumstances.

All considered, the research evidence bearing on FAT must be re—
garded as equivocal. Clearly there are many issues to be resolved. As
is frequently the case in the behavioral sciences, resolution of these
issues is made more difficult by the fact that competing theories are
applied in different research paradigms which are not always easily com—

parable. How do we relate Gillham's results to the information inte—

gration literature, for example? Still unless a theory succeeds pp its

48

pyp ground it is not at all worthy of consideration. In the present case
the "home ground" of FAT is the set of studies by Woelfel and his associ—
ates which seem generally consistent with the theory, although the sup—
port is weak and the studies unrigorous. Research is called for to test
the theory more rigorously.

Cognitive Consistency Without Awareness

 

At least one aspect of the theory of linear motion presented in
Chapter I may be quite counter—intuitive. As we previously have noted,
the theory assumes a total integration of cognitive structure in terms
of a "consistency" principle which is representable as the stable,
Euclidian character of cognitive space. Thus motion of a concept with
respect to_§py other concept implies motion of that concept with respect
to_gll other concepts in accordance with a straightforward application
of the Pythagorean Theorem. Not only does such a consistency principle
imply exceedingly complex cognitive processes, but those processes must
operate entirely outside of the subject's awareness. Does psychological
research lend any plausibility to such a hypothesis?

Brock (1968) has considered this issue from the standpoint of con—
sistency theories in social psychology. Brock cites several examples of
studies in which dissonance reduction (or a corresponding consistency
process in terms of some other theory) has apparently taken place with—
out the conscious awareness of subjects. Lack of awareness is assumed
on diverse grounds, including young age of subjects (three—year—olds,
Brock, 1963), assessment of awareness of response-reinforcement con—
tingency in a verbal conditioning setting (Cohen, Greenbaum and Mansson,
1963), and use of hypnosis (Brock and Grant, 1963; Blum, 1961; Rosenberg,

1960).

49

Perhaps the most impressive evidence, however, comes from studies
of consistency models which are both complex and unfamiliar to subjects
but to which subjects' behavior nevertheless conforms, thus presumably
unconsciously. Brock cites one such study in which McGuire (1960) found,
among a sample of below average achievement high school students, in—
direct attitude change as required by the multiplicative probability rule
on propositions syllogistically related to propositions which were the
targets of persuasive messages. McGuire comments:

In the present study several procedures were employed in an at—

tempt to minimize the degree of conscious awareness. (For example,

no mention was made to the 35 that their consistency was being
assessed; the related propositions were widely separated from one
another in the questionnaire; a quantitative expression of opinion
was required and the assessment of inconsistency involved a mathe-

matical model unfamiliar to the Ss.) (p. 352)

McGuire's main finding was replicated in two experiments reported
by Dillehay, Insko and Smith (1966), who conclude that ”it is unlikely
that a conscious effort toward logical consistency is operating: the
properties of the model are far too complex to be understood and applied
by even the most astute subjects” (pp. 653-654).

A somewhat similar line of reserach has been pursued using the
congruity model (Osgood and Tannenbaum, 1955) as the criterion of con—
sistency. Tannenbaum and Gengel (1966) established three source—concept
linkages, and, in a separate message, made the concept attitude positive
or negative. Congruity predictions of subsequent attitude changes
toward the sources (which were not mentioned in connection with the per—
suasive messages) were generally supported, although there were some con-

trary findings. The subjects were college students. Tannenbaum (1966)

extended the logic of the first study to a situation in which linkages

50

were established between a single source and two concepts, and attitude
toward one of the concepts was then changed by a persuasive message. The
congruity model prediction that change in the first concept would influ—
ence the source attitude, and that this source change would, in turn,
produce appropriate changes in the second concept, was strongly supported
in the results. The subjects were high school males. Although it is not
mentioned in the original report, Tannenbaum (1968) adds:

When subjects were queried for their reasons for showing fairly

substantial attitude change toward one concept as a result of

reading a 300 word message on another concept, a considerable
number first indicated surprise and doubt that they had changed.

When their pre— and post—test scores were made available and they

were convinced that they had indeed changed their beliefs, they

voiced considerable resentment and were clearly upset with them—

selves. (p. 434)

The accumulated evidence impressively supports the proposition that
complex consistency processes can occur without the conscious awareness
of subjects. None of this, of course, directly bears on the theory
tested in the present study, except that it generally lends plausibility
to theories of a certain type; i.e., theories which postulate complex,
unconscious cognitive processes. Whether the maintenance of relation—
ships as required by the theory of linear motion is a process that
actually goes on is an unanswered empirical question. The point is that
the evidence suggests the question is worthy of serious study: it is not
on its face absurd.

Summary

This chapter has reviewed research literature bearing upon (1)

the utility of a spacial representation of cognitive structure; (2) the

meaningfulness of motion in cognitive space; (3) Woelfel's Theory of

Linear Force Aggregation; and (4) the occurrence of complex and

51

unconscious consistency processes in the human mind. What, in general,
is the status of the theory of linear motion in light of the literature?

First the literature strongly supports the inference that spacial
models can be meaningful and useful representations of cognitive structures.
This is not to say that all cognitive structures can be represented spac—
ially, but is to say that a broad range of structures can be so repre-
sented, and that such representations have won an important place in
behavioral research.

Second, however, the evidence for the meaningfulness of motion in
cognitive space, while suggestive, is far from conclusive. The research
so far has not been very rigorous; and in fact the accumulated evidence
largely consists of pg§5.hgg interpretations of selected features of the
observed changes in spacial locations of concepts. The theoretical work
in this area is rather highly developed. Needed is research of com—
parable quality, research that will test g priori hypotheses derived
from explicit assumptions.

Third, the evidence bearing on FAT is quite equivocal. Despite
its conceptual simplicity the theory is very difficult to operational—
ize. All evidence, both positive and negative, can be attacked, for
example, on the ground that it fails to take account of all information
to which the subject has been exposed. While studies by Woelfel and
his associates have generally been interpreted as at least consistent
with the theory, little effort has been made to explain the apparently
contradictory findings of research on message—attitude discrepency and
information integration. There is a presumption that the theory is over—

simple and will ultimately have to be complicated. Here the need is for

 

52

research of precision sufficient to suggest the necessary complications.
Attention must be directed particularly to operationalizing the con—
cepts in the theory and testing numerical predictions.

Fourth, plenty of evidence points to the occurrence of complex,
unconscious consistency processes. Thus our theory of linear motion
cannot be rejected out of hand merely because it assumes that such pro—
cesses occur. Of course the theory may well be rejected because the
specific processes it posits happen not to occur——but that is a matter
to be settled by empirical investigation.

This dissertation was conceived in View of the above. Building
upon the secure foundation of spacial models of cognitive structure,
the theory of linear motion extends those models into less—explored
territory: the explanation of cognitive change. The particular as-
sumptions made permit numerical predictions, which, in turn, permit a
more rigorous test of both the spacial model and FAT. The study re—
ported in the following chapters is an attempt at such rigorous theory—

testing.

 

CHAPTER III
METHODS

This chapter describes the methods——design, procedures and analysis
——of an empirical study intended to test the theory of linear motion pre—
sented in Chapter I in view of the research background presented in
Chapter II. The study is described under the two main headings of Design
and Procedures, and Data Analysis.

Design and Procedures
Overview

A pretest-manipulation-posttest, within—subjects experimental de—
sign was employed. The study was conducted at Michigan State University
on two successive Mondays, June 23 and 30, 1975.

In the pretest a cognitive domain of 15 concepts was scaled using
the Woelfel technique of direct, ratio judgments of inter—concept dis—
tances (see below "Measurement of Variables"). Subjects then read three
messages, each intended to change the distance between a pair of concepts.
Thus motion should have been induced in six concepts, leaving nine con—
cepts which were not manipulated. The two sets of concepts (manipulated
nad not) provided experimental control. As a result of this procedure,
theory predicts that specific changes should have occurred in 69 of the
105 pairwise distances among the 15 concepts, while the remaining 36
distances should not have changed.

In the posttest the actual post-message inter—concept distances
were measured, these to be compared with those predicted by theory. Pre—
test and posttest were separated by one week. Messages were presented
pgph immediately following the pretest and immediately before the post—
test. The purpose of this procedure was to allow for a period of time

53

 

54

sufficient for complex cognitive changes to occur, while also taking
account of the tendency for the effects of messages to "wear off” over
time.

In sum, the pretest consisted of a printed packet containing the
following: (1) a cover letter explaining the purpose of the experiment,
(2) an instrument for obtaining estimates of the inertial masses of the
15 concepts, (3) the 105 distance estimates, (4) the three messages, and
(5) questions following each message for obtaining estimates of the dis—
tance proposed by the message. The posttest, administered one week later,
consisted of a printed packet containing the following: (1) a cover
letter, (2) the three messages, (3) questions following each message for
obtaining estimates of the distance proposed by the message (in order to
assess reliability of those items), (4) the measures of inertial mass
(in order to assess reliability and validity of those items and provide
a filler following the message), and (5) the 105 distance estimates.
Subjects

The participants in the study were students in communication
classes at Michigan State University. The questionnaires were admin-
istered during classes, and the students were informed that participa—
tion was strictly voluntary.

A total of 93 students participated. Of those, 64 provided usable
data. Fourteen subjects were present at the pretest but not at the post—
test, while ten subjects were present at the posttest but not at the pre—
test. Four subjects, although they were present at both administrations,
failed to complete one or both questionnaires. Thus 28 subjects had to

be excluded from the data analysis because they provided insufficient data.

55

The data of one additional subject were excluded. The posttest
data of this subject displayed a pattern which the experimenter inter—
preted as intentional non—cooperation with the experiment. 102 of the
105 distance estimates of this subject were identical (all were 100).
The remaining three estimates were sharply changed from the pretest in
the direction opposite to that suggested by the experimental messages.
Whatever may explain the behavior of this subject it is not the hypothe—
sis under investigation.

Thus 64 subjects were included in the data analysis. Of these, 36
were students in one graduate course and 28 were students in two under—
graduate courses. 38 of the subjects were males and 26 were females.
The mean age of the subjects was 26 and the median age was 24. In
general, then, the subjects tended to be advanced college students,

people who are capable of performing complex cognitive tasks.

Cognitive Domain

”nations" was selected for study. The

The cognitive domain of
domain seemed suitable for spacial modelling because it consists mainly
of a set of discrete entities (nations) to which we attribute various
characteristics. The domain also has previously been studied——for
example, by Wish, Deutsch and Biener (1972). The spacial representation
of the domain should, therefore, be somewhat predictable. Fifteen
nations were studied. The number 15 was considered to be the approxi~
mate upper limit possible for the subjects and setting of the study.

The specific nations to be included in the study were selected by
a three-stage procedure that combined random and judgmental features.
First, a set of six nations judged to be diverse and relatively familiar

to most people was selected from the list used by Wish, Deutsch and

56

Biener. The six are U.S.A., U.S.S.R., China, Brazil, West Germany and
India. The purpose of this procedure was to provide a stable framework
for the cognitive space and to make the structure of the space somewhat
predictable (Wish, Deutsch and Bierner found clear dimensions of Poli—
tical Alignment and Economic Development). Second, a pool of 18 countries
was selected by means of a table of random numbers from the roster of the
United Nations (Office of Public Information, 1972). Third, 9 of the 18
countries were discarded based on three criteria: (1) eliminate countries
duplicated in the six chosen from the Wish, Deutsch and Bierner study, (2)
retain pairs of countries which seem promising for message construction,
and (3) retain countries so as to maintain a roughly even spacial dis—
tribution in terms of the expected dimensional structure. The nine coun—
tries chosen by this procedure were: Singapore, Mexico, Portugal, Poland,
Fiji, Central African Republic, Congo, Greece and Guyana.

The 15 countries to be included in the study were assigned numbers
from a table of random numbers. These numbers determined the order of
appearance of the countries on the questionnaires and were used as iden—
tification numbers in the data analysis. Thus the final list of nations
was: (1) China, (2) Singapore, (3) Mexico, (4) U.S.A., (5) Portugal,

(6) Poland, (7) India, (8) Fiji, (9) West Germany, (10) Brazil, (11)
Central African Republic (C.A.R.), (12) Greece, (13) U.S.S.R., (14)
Congo and (15) Guyana.
Experimental Messages

The decision to use three messages was constrained by several con—

siderations. A "message" is conceived of as a set of arguments bearing

upon the distance between a single pair of concepts. With respect to a

57

message the whole set of distances among concepts in a cognitive domain
can be divided into three subsets: (l) the single distance ”directly"
changed by the message, (2) the set of distances "indirectly" changed by
the message, and (3) the set of distances not at all changed by the mes—
sage. "Direct" change in distance means simply that the manipulated con—
cepts move either toward or away from each other. ”Indirect" change in
distance means that the manipulated concepts, as they move toward or away
from each other, each also move with respect to all of the remaining con—
cepts in cognitive space. Distances neither directly nor indirectly af—
fected by a message are assumed not to change at all. In a domain of 15
concepts there are 105 distances. If one message is processed the spacial
theory predicts one directly changed distance, 26 indirectly changed dis—
tances and 78 unchanged distances. Table 2 gives the whole set of pos-
sible distributions of types of changes in a 15-concept cognitive domain.

Table 2. Possible Distributions of Changes of Distance in a Domain of
15 Concepts.

 

 

No. of No. of Distances No. of Distances No. of Distances
Messages Directly Changed Indirectly Changed Unchanged

0 0 O 105

l l 26 78

2 2 48 55

3 3 66 36

4 4 80 21

5 5 90 10

6 6 96 3

7 7 98 O

 

All three types are theoretically important in that the theory pur—

ports to exactly predict them. A failure with respect to any type would

58

constitute a failure of the theory. The "indirect" changes, however, are
particularly crucial because they alone are a unique consequence of the
spacial model. The "direct" and "no change" types are predicted by many
other possible theories and thus do not distinguish among theories. In
light of this the number of messages should be selected so as to provide
for some of each type of change, but should emphasize the theoretically
crucial "indirect" changes.

Another general consideration is the practical limitations imposed
by the subjects and the experimental setting. Both of these factors sug-
gest that the smallest possible number of messages be used, as each mes-
sage exacts a price in time and in the information processing capacities
and the good will of subjects.

Three messages seemed to be an optimal number, all of the above
considered.

Three pairs of concepts were selected for inclusion in messages.
The selection was based on both theoretical and practical grounds. The
theoretical grounds were that the nations be Of no greater than moderate
inertial mass and that the members of each pair be at a moderate dis-
tance from each other. The former criterion was established to facili-
tate manipulation of the concepts with a single message, while the latter
criterion was established to maximize flexibility in message construction
and minimize the possibility of regression artifacts in the results.
Nations were measured against these criteria by the judgment of the ex-
perimenter. The practical ground for selecting pairs of nations was that
the mere presentation of factual information by a moderately high credi-

bility source could be expected to imply a substantial change in the

59

distances between the concepts. This test also was applied by the judg—
ment of the experimenter.

The pairs of countries selected were (1) Singapore and Fiji, (2)
Congo and Guyana, and (3) Portugal and Brazil.

Information about the six countries was obtained from the Encyclo—
paedia Britannica (1974: "Brazil, History of”; Fu—kiau kia Bunseki—L.;
"Guyana"; Ho; Honeybone; Perez de Amaral). Information was selected
based on its judged interest and relevance to a consistent theme of
similarity or difference between the pairs. The information was used in
composing three messages. The first message developed the theme that
"Fiji and Singapore are remarkably similar"; the second message argued
that "Congo and Guyana are very different”; and the third message pro—
posed that "Portugal and Brazil are closely related.”

The messages are included with the questionnaire in Appendix A.
The messages are of similar length. The Fiji—Singapore message is 204
words long, the Congo—Guyana message is 204 words and the Portugal—
Brazil message is 178 words. The structure of the first and third mes-
sages differs somewhat from that of the second. In the former cases the
countries are compared point by point; whereas in the latter case the
countries are discussed in separate but parallel parts of the message.
This structural difference was intended to reinforce the content em—
phases of the messages by associating the similar countries and dis—
sociating the dissimilar countries.

Measurement of Variables
The measurement of variables in this study was throughout based on

the principle of direct, ratio estimation advocated by Woelfel (see

60

Woelfel, 1974; Danes and Woelfel, 1975). In brief, the rationale for
this method holds that the measurement of any cognitive variable can be
thought of as the measurement of conceptual separations, or distances
between entities. Given this assumption the problem of measurement be-
comes just a practical one of establishing a unit of measurement in terms
of which all values of the variable may be expressed as ratios. Danes
and Woelfel (1975) reason:

Let's suppose for a moment that no standardized metric existed

for the measurement of distance, a problem that our ancestors

were faced with years ago. Then could the distance between A

and B be measured? Yes. But a metric and a rule for doing so

must initially be created before measurement could proceed.

That is, some arbitrary distance, say the distance between x

and y, must first be generated, and the distance between A and

B could then be given in relation to that arbitrary distance . .

With respect to the measurement of conceptual separations, the

identical logic could be used, and measurement of the conceptual

domain could then be given by a two-staged procedure: the speci-

fication of a metric and a request to use ratios of that metric

for the measurement of the separations among other conceptions.

As an example, the following kind of question could be asked:

If NIXON and AGNEW are one hundred (100) units apart, then in

relation to NIXON and AGNEW how far apart are NIXON and McGOVERN?

From the experience of the authors, most persons would report a

number considerably larger than one hundred. (p. 3)

The technique proposed by Danes and Woelfel is not entirely new.
The technique was recommended by Torgerson (1958), who suggested: "The
subject might be told to assume that on some scale the distance (amount
of difference) between stimuli A and B is ten units. His task would then
be to report the distance (amount of difference) between stimuli A and C
on the same scale" (p. 293). Torgerson also warned, however, " . . . the
task may ordinarily be too difficult for the subject, since it involves
judgments of a fairly high level of complexity" (p. 293). The difficulty
of the task would be expected to produce unreliability of measurement.

Anyone who proposes to use the technique, then, must confront and deal

with the problem of unreliability.

61

Woelfel (1974, p. 12) accepts that unreliability seriously limits
the technique's utility for measuring individual subjects (though he
suggests, without much basis, that the diffusion of the technique through
the scientific community and the general culture would improve precision
in the task because of practice and familiarity).* Woelfel argues, how—
ever, that the reliability problem disappears when attention is focused
upon measurement of aggregate variables rather than individual variables.
In the aggregate case one can use large samples of people, taking advan—
tage of the statistical principle that the sample mean converges toward
the true population mean as sample size increases. Thus the problem of
unreliability becomes essentially one of cost. Given unlimited resources
and a large population from which to sample, the reliability of aggre-
gate measurement (the sample mean) can be made as high as one might wish.

Two papers have systematically investigated the reliability of
Woelfel's technique of aggregate measurement.

Barnett (1972) reports two studies which tested the reliability of
a metric multidimensional scale for which direct ratio judgments were
used to obtain the distance matrices. In the first study he tested re-
liability by correlating time 1 with time 2 projections of 17 concepts
on the first three dimensions of the space. Before calculation of the
correlations, the time 2 coordinate matrix was rotated to least squares
best fit with the time 1 matrix. The analysis was performed separately

upon random subsamples of sizes 25, 50, 75 and 100 subjects. Findings

 

*Woelfel (personal communication) has proposed the additional argument
that the apparent unreliability of the technique in many situations

may result not from the faultiness of the technique but from the true
instability of the phenomena supposedly measured. This argument, how-
ever, only redefines the problem as one of invalidity-—trying to measure
something that doesn't actually exist.

 

62

were that the larger the sample the greater the reliability, that the
first dimension was more reliable than the second and the second more
reliable than the third, and that reliability ranged from a low of .23
for the third dimension and 25 cases to a high of .80 for the first
dimension and 100 cases. In a second study Barnett examined 15 concepts
at three points in time (four weeks and then three weeks apart) for sub—
samples of 25, 50 and 61 subjects. Here again the reliability increased

"size" of the dimension, but the corre-

with both size of the sample and
lations in this case were somewhat higher, ranging from .13 to .86 with
25 cases, from .44 to .97 with 50 cases and from .45 to .95 with 67
cases. Barnett attributes the greater reliability of the second scale
to several factors, including greater homogeneity of the subject popula-
tion, better data preparation, shorter time interval between administra—
tions, fewer concepts and a more homogeneous conceptual domain. Barnett
conducted a third analysis with random data and found correlations of
.21, .01 and .38 for the first three dimensions. These numbers suggest
the order of magnitude at or below which one should question whether the
data reflect real phenomena.

Danes and Woelfel (1975) obtained judgments of separation among 17
concepts from 50 respondents at two administrations with an interval of
five weeks between measurements. The researchers evaluated reliability
by three methods. First the test—retest correlation computed over the
136 cells of the inter-concept distance matrix was .86, indicating good
reliability of the aggregate separations. Second the technique of cor—

relating test-retest coordinates in the multidimensional space generated

by a metric MDS procedure with rotation of the second space to least

 

63

squares best fit with the first space——the technique used previously by
Barnett-—yielded correlations of .97, .81 and .87 for the first three
coordinates. Thus this study found slightly better reliability than did
Barnett's. Third the absolute amount of reliable variance was computed
by multiplying the total variance for all items on each coordinate by the
reliability of that coordinate. This was compared by several procedures
to the reliable variance of a set of seven—step Likert-type items that
correlated highly with the first (evaluative) dimension of the multidi—
mensional scale. The procedures involved transformation of the Likert
items to make them comparable in range to the MDS coordinates. All com—
parisons were said to indicate that the multidimensional scale had
greater reliable variance than the set of Likert—type items.

In sum, research on the reliability of aggregate, direct, ratio
judgments of separation indicates that adequate reliability 2gp be
achieved with a relatively homogeneous sample of about 50 people and a
relatively homogeneous set of 17 or less concepts. Although it must
still be regarded as experimental, the technique is not without basis.

Three sorts of variables were measured in the present study: con-
cept inertial masses, inter—concept distances and message contents. The
questionnaire referred to in the following text is included as Appendix
A.

The inertial mass of a concept is defined by Woelfel as the con—
cept's resistance to acceleration, which is theoretically a function of
the total information about the concept accumulated by a subject or aggre—
gate. A set of items was devised based on this conceptualization and
the technique of direct, ratio estimation. The subject was asked to

estimate "how much information you have——how much you know—~about each

 

64

of fifteen countries. Consider all that you know about each country,
from whatever source." The unit for the scale was established by anchor—
ing zero as "the complete absence of knowledge" and 100 as ”an average
amount of information.” Thus the mass of each nation was estimated as a
ratio of an ”average” amount of information.

Inter—concept distance is conceptualized in the spacial model as
psychological distance or total attributional difference. Accordingly,
the inter—concept distances were measured by direct, ratio estimation of
"how different (or in other words 'far apart') you perceive the countries
to be." The unit was established by stipulating that "Italy and England
are 100 units apart.” The value of zero was said to mean that the pair
of countries was "exactly the same." Each subject estimated all 105
inter-concept distances in this fashion. The items were listed system-
atically in order of concept numbers (1—2, 1—3, . . . , 2—3, 2—4, . . .).
The items were grouped in clusters of eight on the page in order to en—
hance readibility.

Message content is conceptualized in the spacial model as an as—
sertion about the distance between a pair of concepts. Its theoretical
function necessitates that message content be measured on the same scale
as the inter—concept distances. Thus the subjects were asked to estimate,
for each message and the corresponding pair of nations, "how different
the two countries are according to the message." The unit of measurement
was again established by stipulating that "Italy and England are 100
units apart." The instructions for the items were placed on a separate
page preceding the messages. Each message was placed on a separate page,

with the items measuring message content at the bottom of the page.

65

Loading of the Theory

 

The theory of linear motion requires that the following quantities
be estimated: 5,, S',. f, f', s,, n, and for all conce ts i
13’ 13’ 1k’ 1k’ 1], 1 p p -—’
pairs of concepts i,‘j and spacial coordinates_k.
sij and S'ij’ the pretest and posttest inter—concept distances,
were taken from the means (across subjects) of the direct, ratio judgments

of inter-concept separations. fik and f' the pretest and posttest

ik’
spacial coordinates, were obtained by metric multidimensional scaling
analysis of the mean distance matrices S and S', with rotation of the
posttest coordinate space to congruence with the pretest space. This
procedure is described below (see "Program Galileo"). The Eij, the inter—
concept distances as proposed by messages, were assumed equal to the
corresponding sij’ except for the three distances intended to be mani—
pulated by the messages. These three Eij were taken from the three items
for measuring message content. The grand means of the pretest and post—
test sample means were used as the most stable estimates available. The
ni were estimated by the grand means of the pretest and posttest sample
means of the inertial mass items discussed above. Finally, p was assumed
equal to unity for each of the six concepts directly affected by the
three messages and zero for all other concepts.
Hypothesis

The hypothesis tested in this study was that the observed, post—
test, mean inter-concept distances and the observed, posttest spacial
coordinates would correlate highly with those predicted by theory. The
preceding sections describe the design and procedures upon which a test
of the hypothesis was based. The following sections describe the data

analysis procedures by which the hypothesis was tested.

 

66

Data Analysis
Preparation of Data

Data were keypunched by the author directly from the (pre—coded)
questionnaires. The data deck was cleaned by visual inspection of a list
and by tabulation and inspection of variables having restricted "legal"
values. After those procedures ten cards were selected randomly, in-
spected and found to be error—free.

Program GALILEO

GALILEO is a package of computer programs, developed by Woelfel and
his associates, which accepts as input sets of inter—concept distance
estimates, computes descriptive statistics, performs a metric multidi—
mensional scaling analysis on aggregate inter—concept distance matrices,
performs rotations to make spaces from different samples or different
time periods comparable, and outputs printed statistics, printed and
punched distance and coordinate matrices, and two—and three—dimensional,
static and dynamic plots. The inner workings of the GALILEO package have
been described in detail by Serota (1974, pp. 52-8L-87-99).

GALILEO was used in the present study in two stages. In the first
stage the raw inter—concept distance data were subjected to the "Dis—
tance Means Matrices" option, which computes descriptive statistics and
outputs printed and punched aggregate inter-concept distance matrices.
The program allows the user to specify a "maximum value” for the inter-
concept distances. Values larger than the maximum are ignored in com—
puting the aggregate matrices.

One disadvantage of unbounded scale items is that subjects who

use relatively large numbers have disproportionate influence on the

67

aggregate results. With vary large samples this problem is negligible,
but with smaller samples it can lead to serious distortions when, for
example, one subject uses extraordinarily large numbers. Gillham (1972,
pp. 40-42) encountered this problem and solved it by discarding the data
of the deviant subject. The ”maximum value" feature has been incorporated
into GALILEO to facilitate the solution of similar problems.

The raw distance data were run with the Distance Means Matrices
option twice: once with no maximum value and once with a maximum of
1000. Punched mean distance matrices were obtained from both runs. Only
the means matrices with a maximum value of 1000 were used in subsequent
runs. This involved deletion of 10 data points from the calculation of
the posttest means matrix. Eight of these were from one subject and two
were from a second subject. The effects of these values on the corres-
ponding mean distances are given in Table 3. It is evident that these
values would have had a greatly disproportionate influence on the results
of the study.

The second stage use of GALILEO involved processing of the mean
distance matrices (maximum value of 1000) by means of the ”Comparison of
Spaces" option. This option performed multidimensional scaling analyses
on both pretest and posttest mean distance matrices, rotated the posttest
coordinate system to congruence with the pretest coordinate system, out—
put printed and punched, rotated and unrotated coordinate matrices, and
prepared dynamic plots of the pretest and posttest data in a common co—
ordinate system of both two and three dimensions.

The Comparison of Spaces option of GALILEO allows the user to in-

corporate assumptions about which of a set of concepts have remained

68

Table 3. Effect of Deletion of Extreme Values on the Posttest Mean
Inter—Concept Distances.

 

Extreme Subject Mean Including Mean ExCluding

 

Concept Pair Value ID Extreme Value Extreme Value
Mexico-USSR 2184 08 211.406 180.095
Poland-Guyana 1084 08 178.203 163.825
China-Guyana 7000 62 277.141 170.429
Singapore-Mexico 7000 62 231.078 123.635
Singapore—Brazil 9000 62 288.812 150.540
Mexico—Fiji 5000 62 227.000 151.238
Mexico-W. Germany 4000 62 209.125 148.952
Mexico-Brazil 2000 62 117.891 88.016
Mexico-C.A.R. 4000 62 207.078 146.873
Brazil—Greece 9000 62 270.687 132.127

 

stable over time. The default assumption is that all concepts are stable.
Thus the posttest coordinates are rotated to least squares best fit with
the pretest coordinates. The main advantage of this procedure is that it
is based on the simplest possible assumptions. The main disadvantage of
the procedure is that it tends to distort and obscure "real" motion of
concepts by minimizing that motion and distributing it among all of the
concepts scaled. Alternatively time user may specify a set of concepts
which may be assumed to be stable. The rotation then proceeds in such a
way as to minimize the change of those concepts while allowing the others
to change. This procedure is described in detail by Woelfel,_gg .gl.

(1975). Briefly, the procedure involves translation of the coordinate

69

systems to the centroid of the specified stable concepts and rotation to
the criterion of least squares best fit of those concepts with themselves.
The main advantage of the stable concepts option is that it can yield more
accurate description of motion by taking advantage of information about
stable concepts. The main disadvantage is that it can distort and obscure
real motion if the assumptions about stable concepts happen to be false.
It also leaves the researcher open to the charge of question-begging.

The Comparison of Spaces option was run twice: once specifying no
stable concepts (the default option), and once specifying the nine unmani-
pulated nations (those not mentioned in messages) as stable. The later
procedure took advantage of what was known about the experimental pro—
cedures and their intended effects; while the former procedure allowed
for the possibility that the experimental procedures might have had un-
intended effects. All further analyses were conducted in parallel fashion
on the output of both options. Thus the researcher hedged his bets.

Program TESTLAW

 

TESTLAW is a FORTRAN IV program written by the author to perform
calculations necessary to the analysis of this experiment. The program
is included as Appendix B. The general functions of the program are to
accept as data the output from GALILEO, to compute theoretical predic-
tions, and to output predicted and observed inter-concept distances and
concept coordinates. The output may then be subjected to further sta-
tistical analysis. Although TESTLAW was written especially for the
present study, it is sufficiently general to be applicable to a range of
studies testing the same or a highly similar hypothesis. By some further
effort the program could have been made still more general (certainly

more elegant!), but those are matters for the future.

70

The punched output from GALILEO-—mean distance matrices and rotated
coordinate matrices-—may be input into TESTLAW. Additional required in-
puts include a run name, a set of parameters (number of concepts, number
of dimensions, number of real dimensions—time one, number of real dimen—
sions-time two), message content values and concept masses.

The punched output from TESTLAW consists of three decks. The first
is a deck of Coordinate Values. This deck comprises one "case'' for each
coordinate value—jg x m cases, where p = the number of concepts and m =
the number of dimensions. Each case includes, in addition to the concept
and dimension identification numbers, four variables: the pretest co—

ordinate (fik)’ the posttest coordinate (f'i ), the coordinate predicted

k

by theory including inertial mass in the computation (fmi and the co—

k),
ordinate predicted by theory excluding inertial mass from the computation

A A

(fik). fmik is computed from the theoretical equations given in Chapter

I (expressions 6 and 7); while fi is computed from the same equations

k
only excluding hi, the concept mass, from the computation. The predic-
tions are computed both ways in order to permit a check of the usefulness
of the variable mass.

The second output deck from TESTLAW is a deck of Pairwise Distances.
This deck comprises one case for each inter-concept distance—5p x 3 cases.
Each case consists of l.+ 1 cards, where l = (m/3) + 2, m is the number
of dimensions and m/3 is rounded down to the lower whole number. The di-
mensions included are the first three and every third thereafter (1, 2,
3, 6, 9, . . .). Each card begins with the two concept numbers, and each
of the first 1 cards follows those by a dimension number. The_l + 1th

card indicated 99 for the dimension number. Each of the first 1 cards

71

includes four variables. The four variables on the kth card (5.5.1) have
been computed based upon the first g coordinates. The variables are pre—

test distance (sij posttest distance (S'ijk)’ distance predicted by

k),

theory including inertial mass in the computation (§mij ), and distance

k
).

predicted by theory excluding inertial mass from the computation (gijk

Again, §mij is computed from the theoretical equations given in Chapter
I (expressions 6, 7 and 8); while gij is computed from the same equations
only excluding ni from the computation. The purpose of computing_l ver—
sions of the four variables is to allow the user to check whether, for
example, predictions based on the first few dimensions are superior to
predictions based on more dimensions which presumably include more ran—
dom error. The 1_+ 1th card includes, in addition to the two concept
numbers and the number 99, three variables. These are the two concept
inertial masses (ni, nj) and the actually observed mean posttest dis—
tance (S'i')' This last variable will differ from (s'ijm)’ the posttest
distance as computed from all m coordinates, because of distortions intro-
duced when GALILEO rotates the imaginary dimensions of the posttest co—
ordinate system. See Danes (1975, pp. 34-37) for a discussion of this
problem.

The third output deck from TESTLAW is a deck of concept variables.
This deck comprises one case for each concept—jg cases. Each case in—
cludes the following: the concept number, m values for ”the change in
concept 3F (Aik), each computed on the basis of the first g dimensions
(5 = 1, m), the pretest distance ofyi from each manipulated concept, the

change in distance of_i from each manipulated concept, the pretest dis—

tance of ;_from each unmanipulated concept, the change in distance of i

 

72

from each unmanipulated concept, the total of the pretest distances 0f.£
from all manipulated concepts, the total of the changes in distance of_i
from all manipulated concepts, the total of the pretest distances of.l
from all unmanipulated concepts, the total of the changes in distance of
g from all unmanipulated concepts, and the mass of i. All of the changes
in distance referred to above are absolute changes.

In the present study TESTLAW was run once with each of two sets of
GALILEO outputs: the set deriving from the stable concepts rotation pro—
cedure and the set deriving from the no stable concepts rotation procedure.

Statistical Analyses

 

All statistical analyses were performed using Statistical Package
for the Social Sciences (SPSS) programs (Nie, pg ‘gl., 1975). "Statis—
tical significance" of a result is taken to mean a probability of .05 or
less, as determined by the SPSS program.

AssessmentcfifMeasurement and Procedures

Several analyses were conducted to assess the measurement and pro—
cedures of the study. These include tests of reliability and validity,
and procedural and manipulation checks.

Reliability of measurement was assessed in three, distinct ways.
The first involved analysis of the raw data——the data of the 64 subjects.
Test-retest Pearson correlations were computed across subjects for each
variable——the 105 inter—concept distances, the 15 concept masses and the
three message content estimates.

The second way of assessing reliability involved analysis of ag—
gregate data. Here the reliability of the aggregate inter—concept dis—

tances was assessed by correlating pretest with posttest means across

 

the 105 distances. This correlation was computed in 60 different ways.

First, three different versions of s'ij could be used: that derived from
the no stable concepts rotation procedure, that derived from the stable
concepts rotation procedure, and that derived from the raw data. Second,
the correlation could be computed for four important subsets of the 105
inter—concept distances: the whole set of 105, the 36 unmanipulated dis—
tances, the 69 manipulated distances and the 66 indirectly manipulated

distances. Finally, for each of the two rotation procedures, s'l

could
be based on 1, 2, 3, 6, 9, 12, or 15 coordinates (these are the_l = 7

values of s'ij computed by TESTLAW for these data). Thus there were

k
((2 x 7) + l) x 4 = 60 possible ways of computing the reliability of the
aggregate inter-concept distances. All of these were computed.

The third way of assessing reliability was to use the methods of
such studies as Gillham (1972), Barnett (1974) and Danes and Woelfel
(1975). This involved correlating the pretest coordinates with the post—
test coordinates for each dimension of the multidimensional scale to
determine the stability of each dimension. This method assesses the
reliability of the structure of the multidimensional space, rather than
the reliability of the individual or aggregate inter—concept distances.

All three methods of assessing reliability, of course, confounded
unreliability and real change, although these could be sorted out some—
what at the individual level by comparing the reliabilities of manipu—
lated distances to those of unmanipulated distances.

Measurement validity was assessed by two kinds of procedures. The
first involved inspection of the data and judgment of face validity based

on such questions as whether very "close” and "distant" countries are

74

those that one would expect, and whether more prominent countries have
larger measured masses than less prominent countries. A second kind of
procedure involved comparison of the reliabilities of manipulated versus
unmanipulated variables. For the reliabilities of manipulated variables
to be lower than those of unmanipulated variables would be consistent with
the assumption of greater real change of the manipulated variables. Taken
together, these procedures could yield some, albeit imperfect indications
of the validity of measurement.

The procedural assessment of the study included three checks. The
first check was to determine whether the pairs of nations selected for in-
clusion in messages met the stated criteria of low to moderate inertial
mass and moderate distance. This was determined by comparing the masses
and distances to the means of those variables. The second check was
whether the messages, as measured by the message content estimates,
actually advocated changes in distance as intended by the experimenter.
The third check was whether the experimental manipulation worked. One
would expect to find that t-tests for correlated means performed on the
pretest-posttest changes would be significant for the three directly
manipulated distances, and for many of the 66 indirectly manipulated dis-
tances as well; while the 36 unmanipulated distances should not have
changed significantly.

Hypothesis Tests

 

The general hypothesis test was a comparison of predicted with ob-
served posttest inter-concept distances and concept coordinates. Such a
test, however, may be conducted in many different ways, each of which
contributes information from a unique point of view. Three general types

of tests were employed in this study.

 

75

The first type of test involved inspection of changes in the inter-
concept mean distances, and of the plotted results of the multidimensional
scaling analysis, to determine whether the pattern of changes from pre-
test to posttest was consistent with the hypothesis. This type of analy-
sis, admittedly, can produce no clear decision as to the merits of the
hypothesis. It can, however, at once make an overall impression and yield
up a wealth of details that might help in interpreting findings derived
from more structured procedures.

The second type of test was a correlation of predicted with observed
posttest inter-concept distances. This correlation can be and was com-
puted on 384 distinct bases. First, two different rotation procedures
were used to make the posttest space comparable to the pretest space (see
above "Program GALILEO"). Each procedure (because it involved rotation
of some imaginary coordinates) yielded a unique set of "observed" post—
test distances as computed from spacial coordinates. The actually ob-
served mean posttest distances were, of course, still a third set. Thus
at least three correlations might be computed, one for each set of post-
test distances. Second, there is some reason to believe that the theo—
retical predictions may be more accurate when restricted to the first few
dimensions of the space, since the higher (smaller) dimensions may con—
tain a larger proportion of error and the imaginary dimensions may repre-
sent some sort of cognitive inconsistency. Program TESTLAW gives, in
the present case, computations based on seven cumulative Subsets of the
dimensions: 1, 1-2, 1-3, 1-6, 1—9, 1—12, 1—15. Thus for each of the
three sets of posttest distances, seven correlations may be computed, or

21 correlations in total. Third, TESTLAW gives two sets of predicted

 

76

post—message inter-concept distances, one set computed from the exact
equations presented in Chapter I, and a second set computed from those
same equations only excluding inertial mass from the computations. The
purpose of computing both sets of predictions was to see whether the in-
clusion of masses affects the accuracy of prediction. Thus 42 correla-
tions could be computed. Fourth, these 42 correlations could each be
computed for four interesting subsets of the inter-concept distances.
These include, in addition to the whole set of 105 distances, the 36 un—
manipulated distances, the 69 manipulated distances and the 66 indirectly
manipulated distances. Thus 168 correlations could be computed. Fifth,
the theory predicts that the inter-concept distances will not change
except insofar as they are directly or indirectly affected by the input
of information. It is of great importance to separate those two compo-
nents-—the stability component and the change component-—to determine
whether the theory successfully predicts both. If the theoretical pre-
dictions are accurate only in predicting stability then the theory is
useless as a description of cognitive change. Thus the stability compo—
nent should be removed from the analysis. This can be done by statis-
tically controlling the pretest distances, which in turn can be done
either by computing partial correlations or by correlating predicted
with observed changes in distance. Thus 504 correlations in total might
be computed: the 168 correlations discussed above and their counterpart
first order partials and change score correlations. Some of these cor—
relations, however, would not be meaningful. The partials and change
score correlations need not be computed for the 36 unmanipulated dis-

tances because no change is predicted for those distances. That

77

eliminates 84 potential correlations. Nor would it be meaningful to
compute change scores consisting of the difference between pretest dis-
tances computed on the basis of less than all of the dimensions and the
actually observed posttest distances, which include, as it were, all of
the dimensions. The change scores so derived would simply not represent
any theoretically meaningful quantity. Thus 36 more potential correla—
tions are ruled out. Actually, then, 384 distinct versions of the cor-
relation of predicted with observed posttest inter-concept distances were
computed. These 384 correlations did not at all constitute an equal
number of independent tests of the theory. Quite to the contrary, the
correlations are highly interdependent. Each, however, provides a unique
point of view of the data.

A similar comment could be made regarding the third set of hypothe—
sis tests which were performed. These involved correlating predicted
with observed posttest coordinate values. Here again a large number of
possible variations of the test were all computed. Again the two rota—

"Observed" posttest coordinates.

tion procedures yielded distinct sets of
There were, however, no "actually observed" coordinates aside from those
given by the rotation procedures. Nor were there any "indirectly" mani—
pulated coordinates—~one could distinguish only between the coordinates
of the manipulated concepts and those of the unmanipulated concepts. Nor
was it meaningful to compute correlations based on less than two dimen—
sions when they would have as few as five degrees of freedom. Thus, in
short, the coordinate values yielded a much smaller set of correlations
than did the inter-concept distances. In fact 180 correlations were com-

puted. 76 of those were zero order correlations between predicted and

observed coordinates based on two rotation procedures, two predictors,

78

seven subsets of the dimensions, three subsets of the concepts (all
concepts, the manipulated concepts and the unmanipulated concepts), and
excluding eight correlations that would have had too few degrees of
freedom. 52 first order partials controlling the pretest coordinates
were computed. These corresponded to the zero order correlations except
for the 24 based on the unmanipulated concepts. Partials in those cases
would not have been meaningful. Finally, 52 correlations of predicted
with observed changes in coordinates were computed. These corresponded

to the partials.

 

CHAPTER IV
RESULTS
This chapter presents the results of the study under the general
headings of Multidimensional Scaling Analysis, Assessment of Measurement
and Procedures and Tests of Hypothesis.

Multidimensional Scaling Analysis

 

The results of the metric MDS analysis are given in Tables 19
through 24 (Appendix C) and in Figures 1 through 6.

Table 19 is the coordinate matrix for the pretest data. Table
20 is the unrotated coordinate matrix for the posttest data. Fifteen
roots were extracted from each distance matrix. This result would be
theoretically impossible since p points can always be represented in pfl
or fewer dimensions. In each case, however, one dimension accounted for
approximately none of the variance in the distance matrix. These coor-
dinates, as Serota points out (1974, p. 64), " . . . are artificial and
represent rounding error in the computer algorithm . .”

Three of the 14 valid roots extracted from the pretest matrix were
negative, while two of the 14 valid posttest roots were negative. The
negative roots accounted for about 6.7 percent of the total pretest
inter—concept distances (the total of their eigenvalues was —ll,553 as
compared to a trace of 161,713 for the matrix). The negative roots ac—
counted for about 2.7 percent of the total posttest inter-concept dis-
tances (the total of their eigenvalues was —4397 as compared to a trace
of 161,192 for the matrix). Similar shrinkage of the imaginary dimen—
sions has been noted in previous studies (e.g., Taylor, Barnett and
Serota, 1975).

79

 

 

 

80

Table 21 gives the posttest coordinates matrix rotated (so as to be
comparable to the pretest space) by the no stable concepts rotation pro—
cedure. Tables 22 and 23 give the unrotated pretest and posttest coordi-
nate matrices translated to the centroid of the nine stable (unmanipu—
lated) concepts. Table 24, finally, gives the results of the stable con—
cepts rotation performed on the translated posttest matrix to make it
comparable to the pretest space.

An examination of the coordinate matrices indicates that the two
rotation procedures give somewhat different results. The data in Table
4 make the effect of the rotation procedures much clearer still. Table
4 gives the amount of change of each concept from pretest to posttest
coordinate spaces as determined from the two rotation procedures. The
mean changes for the no stable concepts rotation were 65.29 for the un—
manipulated concepts and 53.30 for the manipulated concepts, while the
mean changes for the stable concepts rotation were 29.99 for the unmani-
pulated concepts and 110.37 for the manipulated concepts. Thus the ratio
of the mean changes of manipulated to unmanipulated concepts was about .8
for the no stable concepts rotation (the "stable" concepts changed more!),
but the ratio was about 3.7 for the stable concepts rotation.

Plots of the MDS results are given in Figures 1 through 6. In all
figures the pretest and posttest locations are plotted together, connected
by lines. The pretest locations are indicated by the concept identifica-
tion numbers. Figures 1 through 3 are of the results of the no stable
concepts rotation procedure, and Figures 4 through 6 are of the results
of the stable concepts rotation procedure. Figures 1 and 4 show the first

two dimensions: X (the abscissa) is the first dimension and Y (the

 

 

81

 

 

 

 

Table 4. Effect of Rotation Procedure Upon Distances Moved by
Concepts Between Pretest and Posttest.
Distance Moved
Concept No Stable Concepts Stable Concepts
1. China 86.421 31.025
2. Singapore# 46.534 96.377
3. Mexico 57.143 25.329
4. U.S.A. 69.008 40.956
5. Portugal# 45.951 110.364
6. Poland 68.218 27.125
7. India 38.269 17.480
8. Fiji# 82.820 119.441
9. W. Germany 65.002 46.909
10. Brazil# 40.340 113.628
11. C.A.R. 43.710 17.582
12. Greece 89.591 23.494
13. U.S.S.R. 70.270 39.977
14. Congo# 49.104 103.903
15. Guyana# 55.050 118.527

 

#Manipulated Concept.

 

 

82

ordinate) is the second dimension. Figures 2 and 5 show the first and
third dimensions: X (the abscissa) is the first dimension and Z (the
ordinate) is the third dimension. Figures 3 and 6 are three dimensional
plots: X, the first dimension, runs from left "front" to right "rear”;
Y, the second dimension, is vertical; and Z, the third dimension, runs
from right "front" to left "rear."

Regardless of rotation or point in time, the X and Y dimensions
are readily interpretable as Economic Development and Political Ide—
ology, respectively. The first dimension runs from U.S.A. and West
Germany at the high end through moderately developed European and Latin
American countries to the least developed African and Asian countries
to the low end. The second dimension runs from China and U.S.S.R. at
one end through various Asian and European countries to the American
nations at the low end-—a general, although not entirely consistent
trend from most radical to most conservative countries. These two di—
mensions are similar to the first two dimensions found in the nonmetric
MDS analysis of nations by Wish, Deutsch and Biener (1972).

The third dimension is not so readily interpretable (nor was it
in the Wish, g£_gl. study). Regional clustering, however, is evident
on the X—Z plane (Figures 2 and 5), with each quadrant corresponding
roughly to a continental zone. The single important exception--the

location of Guyana in the ”African” quadrant—~is discussed below.

 

Figure 1.

No

83

 

 

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Stable Concepts Rotation, X—Y Plane

 

 

Figure 2.

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Stable Concepts Rotation, X-Z Plane

 

 

85

 

 

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Figure 3. No Stable Concepts Rotation, First Three Dimensions

 

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Figure 5. Stable Concepts Rotation, X-Z Plane

 

88

 

 

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Figure 6. Stable Concepts Rotation, First Three Dimensions

 

 

 

89

Assessment of Measurement and Procedures

 

Reliability

Reliability was assessed in three ways, the first being test—
retest comparisons of the raw (unaggregated) data. Tables 5, 6 and 7
contain the information relevant to this assessment. Table 5 gives,
for the 105 inter-concept distances, the pretest and posttest means
and standard deviations, the means of the pretest—to—posttest changes,
the standard deviations of those changes, Pearson correlations of
pretest with posttest scores, and t-tests for correlated means. Table
6 gives the same information for the 15 concept inertial mass estimates
and Table 7 gives the same information for the three message content
estimates.

The reliabilities of the inter—concept distances, as indicated
by the Pearson correlations, were quite poor. Of the 105 correlations
only 32 were statistically significant and only 7 were greater than
.5. No correlation was negative. The concept mass reliabilities were
higher but by no means absolutely high. Fourteen of the 15 correla-
tions were significant; 11 were over .5; the highest was .64. The
three message content estimates were quite unreliable. Only two of
the three correlations were significant and none was as great as .4.

The second way of assessing reliability is by pretest—posttest
comparison of the aggregate inter—concept distances——a correlation
computed over the sample means. As was noted in Chapter III, we are
interested in 60 different versions of this correlation. The results

are given in Table 8.

 

 

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No.I amo. Amm.sONv Aoa.mmav Asw.mmav

aw.a- oa.owa om.awa .e.m.m.sIooNxmz
Nm. mmo. Amw.NNHv Aam.mNHv ANN.NNHV

MN.NH ma.msa aw.Nma muwwueIouaxmz
Ha. Nma. Amm.sNHV AeN.NNHV Ame.wmav

os.N Nm.eqa wa.asa .m.<.oIOUNxmz
NH.N« HON. Aos.mmv AeN.NsV ANN.msv

«N.ea No.ww mN.HN eNNNaENIooNxmz
40.- HNo. Aoa.swav xNa.mNHv Aoa.smav

Nm.I ma.msa NN.aqH Anagram .2Iooaxmz
wN.I mos. Ams.amav Aoe.smav Aeo.esav

ms.o- 4N.Hma NG.NmH eNmamlooaxmz
ea. oqa. Asa.sNav Ame.amav Amm.mmav

ma.N ma.wma qa.mma maeaHlooNxez
mN.- «we. Aaa.wsav Aom.mmav AHN.NNHV

NN.mI sw.mma oo.ama eawaomuooaxez

I .I . . new . . . .
A ml .mv sows .m one: m

 

Avmsawudoov m OHQNH

94

 

Ns.I amm.«« Awa.maav Ams.NAHV ANN.oAHv
Hm.oaI ee.eaa AN.GON someooI.<.m.s
Aq.HI Aas.F«« Aam.mmav Ams.awv Asw.Nmav
em.sNI aa.wma AG.N©H .m.m.m.eu.<.m.s
As.I NAm.*« AAs.msaV Aom.AoaV ANN.mqav
om.wI Aa.ama As.osa momwuoI.<.m.e
os.I wwo. ANq.ONNv AAm.AoAV Amo.mmav
GH.AHI ma.omH AA.NNH .m.<.OI.<.m.:
ms.I ANA. AAe.ooAv ANm.oAv AwA.smv
ms.eI wN.MNH mw.mNH eaaumumI.<.m.p
so.I Nam.11 Awm.omav ANH.AAV AwN.mmHv
am.- NA.ooa Hm.aoa Acmeumu .3-.<.m.:
MA.I was. AmA.mONV Aoe.Nmav Ams.HAav
sw.wa- Ns.moa AN.NwA eHmHmI.<.m.e
as.I Amm.*« ANA.oeHV Amw.mNav Amm.smAV
mA.NI Na.eAa sm.mwa «NeeHI.<.m.p
«N.AI NAH. Aoa.qAAv AHm.ONHV Aqm.asav
sw.eNI sa.mma WA.owa eemaomI.<.m.p
ma.- mes. Amm.aoav AON.HsHv ANs.mOAV
mm.NI Ns.AmH oo.oea eammsuuomI.<.m.:
I. I. A.m.mv new: A.o.mv A.m.mv
u u T.” 3 .3 ms mCOflumz mo Hfimm
A m.. .mv new: .m game m

 

Aew=ENueoov m magma

 

 

 

95

 

ma. wma. Aaa.MAav Awm.ssav Awo.wNav
wa.m em.Nea mm.mma somaOOIaammsaaoa
mo. NaN. Ams.eaav Asa.mav Awm.aaV
ma.a se.mma Nm.sma .m.m.m.eIAammaaaom
No.I Awa. Ame.aAv Ame.amv Amm.AeV
mN.I ma.moa NA.moa mommaoIAammsuaoa
ee.I oNa. AmA.amav AaA.eNav Aos.omav
mN.maI om.Ama ww.Nma .m.<.OIAamwsaaoa
ow.a- coo. Amm.amav AmN.asV Aem.ANav
ae.mNI Aa.oA wA.moa eaammamneamweaaom
am.I Nam. Aao.awv Asa.aev AGA.NAV
Aa.mI wa.maa ee.sNa Aamaame .zueamwsaaom
eo.I sea. Aaw.mmav ANo.mNaV AAw.aaav
aa.aI mm.Asa mA.waa eaaaAIAamwaaaoa
as. AoN. Aam.amav Amo.mNav Ase.NaV
mA.A Aa.oma Ne.Nsa maeeaIeamwsaaoa
Aa.a emm.aa Aam.wAV Aaw.eAv Aam.mmv
wN.aa aa.NNa ma.moa ecmaomIAammsaaoa
ma.a- oAa. Amw.saav Aso.osav Aos.aeav
se.ANI NA.aea mm.awa Amemssz.a.m.p
l | A.Q.mv one: A.m.mv A.a.mv
a a ha ha ha ha meoaamz No Name
A ml .3 Ewe: .m :wmz m

 

Aemseauaoov m magma

 

 

96

 

so. Nam.a AmN.smav Aaa.ANav AmN.maV
Ne.aa mm.mea aN.Nma Awemssu-eamaoa
eo.- wsa. Amm.mAav Aes.NmaV Awa.omav
sm.a- ea.oea om.aea eowcoo-ecmaoa
mm.m« Hom.xx« Acm.amv Am©.mmv Amm.mmv
oo.ma No.oa ma.sA .m.m.m.p-eemaoa
ma. Aeo. Awm.Naav Asm.oav Ama.mAv
oe.N mm.oNa Ae.Aaa Queens-enmaom
ma. maa. ANA.wmav Ama.Nmav ANa.omav
aa.a ee.wAa Nm.aAa .m.<.o-eemaoa
Na. Amo. Ace.eAav Aom.mNaV Aoa.sNav
oN.a ON.Ama oo.wqa eaaamam-esmaom
ON.a aoN. Ass.mwv Amm.eev AON.on
mw.Na sm.Aaa Nm.eoa sameamu .3-eemaoa
mm. waa. Aoa.mmav ANo.Amav Ama.Nmav
ow.Na om.oAa ao.mea eamam-eamaom
om. aea. Ame.meav Aom.asav Aoa.moav
mm.oa Ae.eAa ao.aea maeaa-eemaoa
Na. mmo. Amw.aAav Aam.amav Aom.wwv
ow.ma me.aea mw.aqa Amamsso-Aammsaaoa
m. m. A.m.mv new: A.Q.mv A.Q.mv waOfiumz mo mem
.a ha ha ha
A ml .mv ammz .m smoz m

 

Apmdaauaoov m OHQOH

 

 

97

 

0a.- N00. ANO.A0a0 A0a.sNav A00.mqa0
s0.aa- 00.nsa mA.0ma eaaNmam-eamaa
00.- 0Aa. AmA.swa0 Aam.sma0 AaA.Nma0
00.ma- 0a.00a 00.4Aa Asmaamo .3-aaaaa
ma.a- Asm.aa Amw.0Na0 AAa.mA0 AAO.mma0
Aa.0a- AN.ANa ss.maa emcmssu-maeaa
m0. 0mm.«« Ama.m00 A00.N00 Aes.N00
0m. Nm.mma m0.Nma sowaoo-maeaa
00.- smN.* A00.Nma0 AA0.A0a0 AaA.0ma0
04.aa- MN.ama NA.m0a .N.m.m.0-maeea
mm. mmm.a*« A00.0A0 AON.NAO Amm.NA0
mm.m mA.0ma Na.mma mommao-maeaa
ma. 0aa. Aom.Ama0 ANm.Naa0 Aos.MNa0
N0.N 00.0aa m0.msa .m.<.o-maeea
0a. 000. AAm.mAa0 Awa.ama0 Ae0.0Na0
AN.N m0.mma 00.0ma eaawmam-maeaa
0m. ANa. ANa.m0a0 Aes.mma0 A00.maa0
mm.aa am.00a 0A.Ama Aemaame .3-ma0ea
NN.- m0a. AN0.N00 A00.000 Awm.0A0
0m.N- As.NNa 00.mNa eanaa-maeaa
I. -. A.a.mv amwz A.o.mv A.o.mv
u .a 3 .3 ma 3 maoauwz mo Hanna
A mI .3 5mm: .. .m cmwz m

 

Aemscaueoov m maame

 

98

 

ms.- 00a. AsA.a0a0 AaA.sma0 AmA.mma0

00.0a- ma.mAa aa.0ma eommoo-agmagme .3
00. mmN.m Amg.0Na0 ANN.Aaa0 A00.A00

0m.0a sw.ema mm.eNa .m.m.m.3-aemaame .3
0a.- a00. Ams.Ama0 ANO.N0a0 A00.00a0

AN.m- mm.ANa 00.0ma mmmmge-Ammagmm .3
m0.- «MN. A00.0Aa0 Amm.mma0 A00.0sa0

aa.aN- Nm.00a m0.A0a .m.<.O-aemsamw .3
mN.- 000. Asm.mAa0 A40.NNa0 ANA.0ma0

0m.m- 0N.0sa mm.msa Aaammag-agmagmm .3
N0.- m00. A00.a0a0 Ams.a00 AAO.Asa0

00.0a- AA.sNa ma.mqa Ammmame-Aaaaa
A0.- mNN.m Asm.A0a0 A00.a0a0 Aam.mma0

mm.a- N0.mma a0.00a aomgoo-eaaaa
m0.a- 00m.mm Ama.00a0 A0m.mma0 A00.00a0

AN.MN- N0.m0a 0N.00N .m.m.m.0-Aaaaa
as. 0aN. AOA.mma0 ANa.0mav AA0.N0a0

s0.A AN.00a mm.0ma mmmmgu-Aaaaa
am. 0m0. AmN.m0av AON.mma0 AmA.ema0

aa.A 0m.mma 0a.0sa .m.<.0-Aaaaa

I. I. . . gmm . . . .
A ml . 3 new: . m ammz m

 

Ammmgaggomv m magma

 

99

 

00.Nm a00. A00.ama0 AsA.0aa0 A0A.smv

mm.0m NA.Nma 0N.am Ammmam0-.m.m.0
ma.Nm Asa. AAm.0ma0 A0m.mma0 A00.aA0

mm.0a 00.0aa sm.0A eomm00-.m.<.0
0N. ama. AmN.00a0 Am0.Ama0 A00.Asa0

m0.m a0.mAa 00.0Aa .m.m.m.0-.m.<.0
30. 0Aa. Amm.AAa0 AA0.00a0 A0a.A00

mm.0a 03.0Aa a0.aaa mmmmg0-.m.m.0
0a.- mmo. A00.00a0 A0N.mma0 A00.mqa0

0A aa- 00.0ma 0A.Asa Amgmamm-Aaammgg
0N. 000. Aa0.a0a0 Ass.gqa0 ANA.0ma0

AN.0 0a.ama 00.40a Aomgoo-Aaammgg
am.- N00. Aam.m0a0 AAN.0ma0 A00.mma0

NN.A- Nm.N0a mA.00a .m.m.m.g-Aaammag
as.- NaN. AmN.Ama0 Aaa.NA0 Aa0.Nma0

aA A- Na.Nma 00.0ma mmmmgm-Aaammgg
0A. NN0. Aam.00a0 AAN.0ma0 AmN.mma0

00.0a 0a.0ma 0a.Ama .m.<.0-Aaammgg
0a.- m00. Am0.00N0 AaN.A0a0 Amm.mma0

00.0a- 00.00a 00.a0a Amgmamm-Agmaamm .3

I. -. . . mmm . . . .
A ml .mv cme .m cmoz m

 

Apmncaucoov m manna

 

 

 

100

mgu.a.m .gmmg mmaamg-osm .a00.v0 «mm
mgu.g.m .mmmg mmaamm-osg .a0.v0 mm
mgn.a.m .ammg mmaama-oza .m0.vm m

ammoaoo wmumasaasmza

 

 

mw.a 0aa. AON.AAa0 AON.mma0 AAm.ama0
am.aa mm.0sa 0N.00 Ammmamu-Aomgoo
mm.- 0A0. A30.amN0 Ama.sma0 AOA.00a0
Na.sa- N0.00a sm.moN Amemamo-.m.m.m.g
AA.- aA0. A00.0mN0 AON.aga0 Am0.Ama0
0N.mN- 0m.AAa 30.00N sommoo-.m.m.m.0
0N. maa. AmN.mAa0 A00.0sa0 A03.00a0
0m.s NA.00a mm.N0a Amgmamo-mmmmmo
0N.- me. Aaa.0Na0 AmA.A00 AmN.00a0
00.0- AN.mma m0.Ama aomgoo-mmmmgm
0m.- Nma. Amm.mma0 A00.000 A00.0Na0
ma.0- mm.mma 00.0ma .m.m.m.g-mmmmm0
I. I. A.g.mv emmz A.n.mv A.o.mv
u .a ma mun 3 ma mdoaumz m0 .323
A ml .3 new: .m new: m

 

Ammmeaggouv m magma

 

 

 

101

 

 

00.a 0am.mmm AN0.0sv Aam.am0 AmN.0m0
mm.aa AA.NHH AH.HOH .m.m.m.D
00.nmmm 000.mmm Amm.0sv A0A.000 Asa.0mv
«H.HN AN.Nm ma.am mommau
om.N« emm.««« Aom.wmv Amo.mmv Aqa.mqv
mm.aa mA.mm ow.c¢ .m.<.o
om.m«« wom.«e« Amo.mqv Amq.mqV Amq.mqv
mo.wa qm.mm Hm.qm *aawmam
Hw.N«« wmq.««« Aqm.mqv Auo.qu Aoo.mmV
wo.oa N¢.Noa qm.ow NAcame-ammo .3
mq.m««« omq.««« Aqm.qu Aqm.oqv Aqm.wmv
mm.mH om.No mm.q¢ *anam
00.- a0m.mmm Aa0.m00 Ama.mev Amm.40av
qq.l AN.Hm om.Hm manna
0a.smmm 000.mmm Aam.0m0 Amm.000 A00.0mv
NN.HN Hq.ow ma.mm pamaom
m0.smmm amm.mmm Aaa.0av Aam.Nev Aaa.000
om.qm Hm.mw om.mo *Hmwnuaom
0a.a www.mmm Am0.qma0 ANN.aaN0 A00.m0a0
qm.Am om.mmm Nm.wma .¢.m.D
mm.m««a mam.e«« Aow.mqv Amm.qu Awq.mmV
cm.wa Hm.maa mm.om coaxoz
Aw. mmo. AHA.cNHV AAm.mmv Amw.AHHV
00.ma A0.AA Aa.sm ammommmmam
Am.a wmq.««« Aqq.wmv Aqm.qu Aqm.cov
cm.qa mm.woa mm.qm measo
Im- IM. Ammomv A.Q.mv A.Qomv GOHUQZ
a a a a
saw: A.cl..cv new: .. cmoz .c
.mcmmz wmumamaaoo aom wuwmuhw mew
”mew: ummuumom nuas ummumam mo mcoaomamaaoo cowamwm ”mum: ca mmwemno ammuumom
lummumam new mmmmmz ammuumom .mmmwmz ammumam mo meoauwa>mm pampcmum can memos .o magma

 

 

102

 

 

 

m0u.a.0 .gmmg emaamg-osg .a0.vg mm
m0u.a.0 .gmma emaamg-osm .00.vm m
0A. Nma. A00.mma0 AN0.0Na0 Aa0.N00
00.Na 00.0A 00.A0 aammgg-ammsgaoa
AN. amm.mm A00.0ma0 A00.msa0 A00.000
a0.0 N0.00a am.00a mmmamm-omgoo
0N.- 0am.m Asa.000 Amm.a00 A00.N00
0N.N- Ne.ms 00.00 aaaa-maogmwgam
a a. A000 mmmz A000 A000 mmmmmmz
aa aa aa aa
Ml .M flmwz AM Gwmz m
.wcwmz vmumeaaoo How mummulw.pcm mmmsam> owmmmmz_ummuumom SuHB ammumam mo mdoaumawaaoo
comamwm “moumaaumm pamucoo owmwmmz CH mmwcmso ummuumomlummumam mam .moumefiumm uamuaoo
owmmmmz ummuumom .moumaauwm uaousoo wwmwmmz ummumam mo maoauma>mm unaccepm mam mammz .m mHQwH

00-.a.0 .gmma emaamg-oaa .a00.vm «mm
m0u.a.m .gmmg emaamg-osm .a0.v0 mm
m0n.0.0 .gmmg emaamg-osg .00.v0 «

uaoocoo pmumasaacmz *

 

 

 

a0.0mmm 0m0.mmm A00.000 AAN.000 Amm.000
0N.Nm 00.A0 00.00 Amgmamo

00.0mm 000.mmm A00.000 A00.m00 A00.000
NA.0a 00.00 0A.a0 aommoe
m. m. A.g.00 A.g.mv A.g.00 goaumz

H H H H

awe: A.ml..:v dmmz ..c cme .c

Ammmgaggomv .0 magma

103

Table 8. Pearson Correlations* of Mean Pretest Inter-concept Distances

(Sij) with Mean Posttest Inter-concept Distances (S'ij)'

 

 

 

 

Indirectly
Unmanipulated Manipulated Changed
Method of Dimensions All Distances Distances Distances
Deriving Included in Distances Only Only Only
S'ij Calculations (N=105) (N=36) (N=69) (N=66)
No Stable 1 .964 .949 .973 .972
Concepts
Rotation 1-2 .954 .933 .964 .963
1—3 .921 .918 .925 .919
1-6 .877 .880 .891 .875
1—9 .837 .845 .842 .836
1—12 .863 .887 .858 .860
1-15 .835 .862 .823 .825
Stable 1 .973 .968 .976 .975
Concepts
Rotation 1-2 .903 .945 .880 .876
1—3 .918 .955 .904 .905
1-6 .838 .922 .808 .788
1-9 .811 .912 .779 .770
1-12 .824 .901 .800 .795
1-15 .804 .929 .759 .752
Observed -— .865 .914 .835 .848
V
S ij

 

* All correlations are significant (p<.001, one—tailed test).

104

All of the correlation coefficients were positive and statistically
significant (they were, of course, highly interdependent); and the corre-
lations were, in absolute terms, quite within the range of reliability
usually considered acceptable. No computation yielded a correlation
below .75; 27 of the 60 correlations were greater than .9 and 54 were
greater than .8.

The correlations tended to decline as more dimensions were included
in the analysis, a result which indicates that measurement errors were
concentrated in the smaller, ”residual” dimensions.

The effect of rotation procedures on the results is also evident
in Table 8. For the no stable concepts rotation there was no noticable
difference between the reliabilities of unmanipulated and manipulated
distances. For the stable concepts rotation, however, the unmanipulated
distances were consistently more reliable-—an intended outcome of the
rotation procedure. Particularly important are the coefficients for
the directly observed posttest distances, for these were undistorted by
rotation of the coordinate system. Here the reliability of unmanipu-
lated distances was .914 while that of the manipulated distances was
.835. Thus the stable concepts rotation gives results more in line with
those of the actually observed distances than does the no stable con-
cepts rotation.

The third way of assessing reliability is by examination of the
stability of the coordinate system. This is done by correlating the
pretest coordinates with the posttest coordinates for each dimension.

These correlations are given in Table 9.

105

Although complete correlation matrices were computed only the
correlation of each dimension with itself over time is given in the
table. In principle all other correlations should have equalled either
unity or zero. The correlation of each coordinate with itself within a
given time period is necessarily perfect. The correlation of each co-
ordinate with each other coordinate in the same time period should be
null as a consequence of the orthogonality of the MDS solution. This
was true for the pretest coordinates. Slight correlations were observed
among the posttest coordinates and among non—corresponding pretest and
posttest coordinates, however. The correlations among the posttest
coordinates presumably resulted from rounding errors during rotation,
while those among non-corresponding pretest and posttest coordinates
presumably resulted both from rounding errors and from change in the
coordinates over time. With a few, isolated exceptions, these corre—
lations were less than .1-—too low to be of any concern.

Turning now to the correlations in Table 9, one can conclude, in
general, that all but the smallest dimensions were quite stable. The
outstanding exception was the fourth coordinate for the no stable con-
cepts rotation, whose correlation was essentially zero. The correla—
tions for the first three dimensions compare favorably with those re—
ported in previous studies (Cf. Gillham, 1972; Barnett, n.d.; Danes
and Woelfel, 1975).

Validity

Validity of measurement was assessed in two ways. The first

'method was to observe the pattern of t-tests for correlated means

computed on the raw (unaggregated) data (see Tables 5, 6 and 7).

 

1

06

 

 

 

 

 

Table 9. Pretest-Posttest Pearson Correlations
of MDS Coordinates.
No Stable Stable Concepts
Dimension Concepts Rotation Rotation
l ***.987 ***.990
2 ***.978 ***.925
3 ***.946 ***.942
4 -.O7O **.697
5 ***.944 **.619
6 ***.951 *.469
7 **.631 *.541
8 *.554 .101
9 ***.745 **.699
10 ***.790 .327
11 .406 *.445
12 -.011 .263
13 **.638 ***.786
14 **.597 *.524
15 ***.895 ***.777
* p<.05, two-tailed test, d.f. = 14
** p<.Ol, two-tailed test, d.f. = 14
*** p<.01, two-tailed test, d.f. = 14

107

Only five of the changes in the 105 inter-concept distances were
significantly different from zero. Of the five significant changes, four
Tame manipulated distances. The fact that only one change occurred among
the unmanipulated distances is consistent with the assumptions of the
experiment, but the fact that only four of the 69 manipulated distances
changed is not. The very high variances of the changes seem to preclude
statistically significant t-ratios in most cases.

There was a general tendency for the concept mass estimates to
increase from pretest to posttest——10 of the 15 underwent statistically
significant changes, all positive. 5 of the 10 significant changes were
of those among the 6 manipulated concepts. That is consistent with the
fact that information (mass) about the manipulated concepts was given
in the experiment. None of the changed masses had a pretest value
greater than 90; while only one concept with a pretest mass of less than
90 (Singapore—-a manipulated concept) failed to change. This is gener-
ally (except for the failure of Singapore to change) consistent with the
concept of inertial mass: lower masses should be more susceptable to
change by the addition of information over a short period of time. The
general increase in masses is also consistent with the idea of mass,
Which is supposed to accumulate. In the present case, however, it may
be as reasonable to attribute the changes to some undetermined feature
0f the experimental situation.

None of the three message content estimates changed significantly,
nor was there any recognizable pattern in the observed changes. This is

as expected if message content is a stable quantity.

 

108

The second way of assessing validity was to observe the pattern of
means to determine whether the aggregate measurements correspond with
what one would expect intuitively, based on general knowledge.

The inter—concept distances are most conveniently examined in the
form of plots of the multidimensional scaling results (Figures 1 through
6). Figures 1 through 3 are plots of the results of the no stable con-
cepts rotation procedure, and Figures 4 through 6 are plots of the re—
sults of the stable concepts rotation procedure. Examination of the
plots, or of the data in Table 5, confirms that the observed distances
are generally reasonable. One apparent exception is the greater close-
ness of Guyana to the African nations of Congo and Central African
Republic than to the Latin American nations of Mexico and Brazil. That
apparent misplacement, however, is consistent with what the author has
informally observed: that uninformed people frequently assume that
Guyana is in Africa because its name "sounds" African (four students
informally interviewed prior to the study all located Guyana in Africa).
Among the largest distances at both pretest and posttest measurements
were those of China-U.S.A., Congo-U.S.A., Fiji-U.S.S.R., Congo—U.S.S.R.
and Guyana—U.S.S.R. None of these would be expected to be a small dis—
tance. Among the smallest distances at both times are Mexico-Brazil,
Poland-U.S.S.R. and U.S.A.-West Germany. These, too, are reasonable.
.Another indication of the validity of the measurements of inter-concept
distances is the overall similarity of the present results to those
<flbtained by Wish, Deutsch and Biener (1972) in another study of nations.

Turning now to the inertial mass data, the question is whether

thezlneans appear to correspond in general to the prominence of the

 

 

109

nations. The four greatest masses at both points in time are those of
U.S.A., Mexico, U.S.S.R. and China; while smallest masses are those of
Fiji, Central African Republic and Guyana. The higher mass countries
are all ones about which Americans would be expected to know something
because of their physical proximity or international importance; while
the lower mass countries seem relatively unimportant or at least un-
publicized.

Finally the three message content estimates indicate, as expected,
that the message arguing that Congo and Guyana are "very different" was
thought to place those countries at greater distance than average, and
at about three times the distances at which Singapore—Fiji and Portugal—
Brazil were placed by their messages.

Procedures

 

Three checks were made of the experimental procedures. The first
was whether the manipulated concepts were, as intended, of low to
moderate mass and at moderate distances from each other within the mani—
pulated pairs.

The mean mass of all concepts at both points in time was 88.2 and
the standard deviation 39.0. The mean of the six manipulated concept
masses was 67.6. The highest mean mass among the manipulated concepts
was Brazil's 83.3. Thus the six manipulated concepts were of low to
moderate inertial mass.

The grand mean of the 105 pretest inter-concept distances was 148.9
and the standard deviation 30.8. The grand posttest mean was 149.8 and
the standard deviation 24.3. The pretest distances of the three mani—

pulated pairs were: 102.0 (Singapore-Fiji), 105.8 (Portugal—Brazil),

110

and 99.2 (Congo—Guyana). Thus the three manipulated mean distances were
all quite similar, but were all nearly two standard deviations below the
grand mean. A regression artifact would tend to increase these distances.
Two of the three experimental messages, however, argued for a decrease in
distance.

A second precedural check was whether the messages, as measured by
the message content estimates, actually advocated the intended changes
in distance. Comparing the means in Table 7 to the corresponding pretest
means in Table 5, it is evident that the messages did advocate the in-
tended changes. The first message argued (45.7) that Singapore and Fiji
(102.0) are similar. The second message argued (165.3) that Congo and
Guyana (99.2) are different. The third message argued (57.9) that Brazil
and Portugal (105.8) are similar.

The third procedural check was whether the experimental messages
had the intended direct effects-—whether, that is, the three manipulated
distances actually changed in the intended directions. All three of the
observed mean changes (as given in Table 5) were in the advocated di-
rections. The distance of Singapore from Fiji changed from 102.0 to 95.6
for a decrease of -6.39. The distance of Congo from Guyana changed from
99.2 to 140.5 for an increase of 41.3. The distance of Portugal from
Brazil changed from 105.8 to 76.2 for a decrease of 29.6. None of these
changes was statistically significant, although the latter two approached
significance (p<.08 for Portugal—Brazil; p<.07 for Congo-Guyana). At
the individual level of analysis, then, the manipulations cannot be claimed
to have succeeded. At the aggregate level it is perhaps of more importance
that the mean of the three manipulated absolute changes was 25.8 as com-

pared to a mean absolute change of 12.2 for all 105 inter—concept distances.

111

Hypothesis Tests

The main hypothesis of the study was tested by three sets of pro-
cedures. First, the mean changes were directly examined. Second, the
correlations of predicted with observed inter-concept distances were
examined. Third, the correlations of predicted with Observed coordinates
were examined.

Test One: Mean Changes

The questions to be answered by a direct examination of the mean
distances are whether the three kinds of changes (direct, indirect and
no change) occurred as predicted and whether the overall pattern of
changes (as visible in the plots of the MDS analysis) is interpretable
in a way consistent with the hypothesis.

The mean of the absolute changes of the three directly changed dis-
tances was 25.8. The mean of the absolute changes of the 66 indirectly
changed distances was 12.3. The mean of the absolute changes of the 36
-pg_change distances was 10.8. This pattern is consistent with the hypo-
thesis.

Turn now to the plots and coordinate matrices of the MDS analysis.
Examine the motions of the manipulated concepts pair by pair, considering
all views and rotations. While the BEE Change in each case was as pre-
dicted, the motion was not, as assumed by the theory, directly along the
lines connecting the pairs. The slight net convergence of Singapore and
Fiji resulted mostly from changes along dimensions not plotted. The two
countries actually diverged on the first and third dimensions (in the
latter case bypassing one another) and converged on the second dimension
only because of Singapore's greater velocity: Fiji moved in the direction

opposite to that predicted. Again, Congo and Guyana's net divergence

112

resulted from movements at large angles to the directions predicted.
Regardless of rotation procedure one of the most prominent changes was
Congo's movement, contrary to prediction, along the second dimension.
The divergence of the two nations on the third dimension was about as
expected, but their lock—step motion on the first dimension was quite
opposite to that predicted. Finally, Portugal and Brazil's net con-
vergence occurred despite Brazil's movements Opposite to predictions on
the first and third dimensions and Portugal's opposite movement on the
first and second dimensions. Net convergence on the second and third
dimensions occurred only because the country moving in the "right" di-
rection tended to overtake the other country.

There are evident in the plots other changes that are not inter-
pretable in terms of the hypothesis. Even in Rotation #2, which was
designed to minimize their change, several unmanipulated nations exhibited
apparently substantial movements. One noticeable tendency was for the
more extreme countries to move inwards in the general direction of the
origin——a pattern suggestive of the phenomonon of regression toward the
mean. The specific observed changes are not interpretable in terms of
facts known to the investigator.

Test Two: Inter-concept Distances

 

The second hypothesis test was by means of a correlation between
predicted and observed inter-concept distances. As discussed in Chapter
III, the study provided many distinct bases upon which such a correlation
may be computed. The results are presented in Tables 10 through 13.

In Table 10 are the zero order Pearson correlations between the

posttest inter-concept distances (S'ij) and those predicted by the theory,

 

113

either including concept masses in the computations (gmij) or excluding
concept masses from the computations (§ij). All of the correlations
(which, of course, were highly interdependent) were statistically highly
significant. Most were greater than .8. Several general patterns in
these correlations may be noted. First, there was a tendency for the
correlations for the "computed" posttest distances to increase in magni—
tude as less dimensions were included in the computations. This would be
expected since the larger (lower) dimensions are more stable. The cor—
relations for the actually observed posttest distances, however, fit an
opposite pattern, yielding higher correlations for predictions based on
more dimensions. This also would be expected, however, since the pre—
dictions based on only a few dimensions are not truly comparable to the
actually observed posttest distances, which are, as it were, based on
all dimensions. Second, different patterns resulted from the different
rotation procedures. The stable concepts rotation displayed a pattern,
for all but computations based on only the first dimension, of higher
correlations for unmanipulated distances than for manipulated distances.
The no stable concepts rotation produced no such pattern. The pattern
of correlations for the actually observed posttest distances was more
similar to the stable concepts than to the no stable concepts rotation
--a fact which may suggest the greater validity of the stable concepts
procedure. Finally, there was no clear pattern of differences between
correlations involving predictions taking account or not taking account
of the concept masses. Thus inertial mass, as measured in the present

study, did not clearly contribute to the theory's predictive power.

 

114

 

 

 

Table 10. Pearson Correlations* of S'ij with Smij and Sij, Broken
Down by Number of Dimensions Included in Computations, by
Method of Obtaining S'ij’ and by Subsets of Cases.
Distances S',. Comp. S',, Comp.
13 13
Included Dimensions Predictor From No From Stable Actually
in the Included in A=Smij Stable Con— Concepts Observed
Analysis Computations B=Sij cepts Rotation Rotation S'ij
All 1—15 A .836 .804 .866
(N=105) B .858 .815 .885
l-12 A .864 .825 .867
B .878 .831 .885
1-9 A .838 .812 .866
B .854 .822 .882
1-6 A .888 .838 .841
B .883 .838 .858
1-3 A .921 .917 .821
B .922 .922 .828
1-2 A .954 .903 .757
B .953 .904 .763
l A .964 .973 .619
B .964 .973 .619
Unmani— 1-15 A .862 .929 .914
pulated B .862 .929 .914
$i§auces 1—12 A . 887 . 901 .889
(N=36) B .887 .901 .889
1-9 A .845 .912 .881
B .845 .912 .881
1—6 A .878 .922 .857
B .878 .922 .857
1-3 A .918 .955 .806
B .918 .955 .806
1-2 A .933 .945 .814
B .933 .945 .814
1 A .949 .968 .594
B .949 .968 .594

 

 

 

115

Table 10. (continued)

 

 

 

Distances S'ij Comp. S'ij Comp.
Included Dimensions Predictor From No From Stable Actually
in the Included in A=Smij Stable Con- Concepts Observed
Analysis Computations B=Sij cepts Rotation Rotation S'ij
All 1-15 A .824 .759 .836
Manipu- B .862 .773 .867
gizignces 1—12 A .859 .801 .858
(N=69) B .885 .810 .887
1—9 A .843 .780 .864
B .870 .796 .890
1-6 A .891 .808 .847
B .898 .807 .872
1-3 A .925 .904 .831
B .928 .912 .843
1—2 A .964 .880 .736
B .963 .881 .746
l A .973 .976 .631
B .973 .975 .631
Indirectly 1-15 A .826 .752 .849
Changed B .837 .747 .851
p;:22?ces 1-12 A .860 .795 .870
B .861 .788 .869
1—9 A .836 .770 .874
B .844 .768 .873
1-6 A .876 .788 .855
B .877 .785 .860
1-3 A .919 .905 .856
B .919 .910 .856
1-2 A .963 .876 .765
B .960 .876 .762
l A .972 .975 .616
B .972 .975 .616

 

* A11 correlations in this table are significant, p<.OOl, one—tailed test.

 

116

In Table 11 are the first order partial correlations controlling
for the pretest interconcept distances (sij). These correlations were
substantially lower than the zero order correlations, demonstrating that
much of the accuracy of prediction displayed in Table 10 was due simply
to the stability over time of the aggregate cognitive space, a stability
rightly assumed by the theory. Three additional facts about this table
are worth noting. First, several of the partials were large enough to be
statistically significant (the meaning of this, however, is complicated
by the interdependence of the correlations). Second, the correlations
were lowest when restricted to the 66 indirect changes, although a few
(including, however, none of those for the actually observed posttest
distances) were still large enough to be significant. Third, negative
partials were observed for correlations based on the first dimension only,
and those correlations are among the largest in the table in absolute
magnitude. The negative correlations are clearly contrary to the theory.

In Tables 12 and 13 are the zero order correlations of predicted
with observed changes in distance. The use of change scores is a second
way of controlling for the pretest distances. The pattern of these cor-
relatiOns was much like that of the partial correlations: they were sub-
stantially lower than the correlations in Table 9; many of them were
large enough to be statistically significant; the correlations for the
indirect changes were substantially smaller than those for all manipu-
lated distances; and negative correlations were Observed for computations
based on the first dimension only.

Overall the correlations between predicted and observed inter-

concept distances were not strongly supportive of the theory.

117

Table 11. First Order Partial Correlations (Controlling Sij) of S'ij
with Smij and Si., Broken Down by Number of Dimensions Included

in Computations, by Method of Obtaining S'ij’ and by Subsets

 

 

 

of Cases.
Distances S',. Comp. S',, Comp.
13 1
Included Dimensions Predictor From No From Stable Actually
in the Included in A=Smij Stable Con— Concepts Observed
Analysis Computations B=Sij cepts Rotation Rotation S'ij
All l—15 A *** .346 * .209 *** .336
(N=105) B *** .358 ** .230 *** .370
1—12 A *** .317 * .212 *** .331
B *** .330 * .225 *** .360
1-9 A ** .294 ** .228 *** .315
B *** .311 ** .237 *** .341
1—6 A * .186 .057 *** .334
B * .200 .091 *** .356
1—3 A .142 ** .280 ** .275
B .137 ** .260 ** .256
1-2 A .017 .078 * .194
B .051 .120 * .180
l A —.120 ***—.346 .060
B —.144 ***-.317 .032
All l—15 A *** .444 * .224 *** .385
Manipu- B *** .455 * .244 *** .425
gigiinces 1-12 A We .41:- =2 .239 w: .412
*t* A ***
(N=69) B = .425 .249 .444
1-9 A *** .388 * .262 *** .402
B *** .405 * .264 *** .430
1—6 A * .238 .059 *** .420
B * .253 .094 *** .450
1—3 A * .207 ** .357 *** .373
B .196 ** .325 ** .347
1-2 A .006 .072 * .261
B .050 .116 * .234
1 A —.l7l ***—.436 .074
B *—.204 ***-.402 .040

 

118

Table 11. (continued)

 

 

Distances S'ij Comp. S'ij Comp.
Included Dimensions Predictor From No From Stable Actually
in the Included in A=Smij Stable Con- Concepts Observed
Analysis Computations B=Sij cepts Rotation Rotation S'ij
Indirectly 1-15 A * .242 .062 .150
Changed B * .249 .079 .183
p;:22?ces 1-12 A .171 .066 .149
B .179 .074 .173
1-9 A .204 .094 .137
B * .216 .093 .155
1—6 A .112 -.021 .165
B .126 .024 .187
1—3 A .114 * .255 .082
B .105 * .227 .052
1—2 A —.054 .026 .006
B -.004 .080 —.033
l A —.153 ***—.424 -.035
B -.l9O ***-.386 —.066

 

* p<.05, one-tailed test
** p<.Ol, one-tailed test
*** p<.001, one-tailed test

 

119

 

 

 

Table 12. Pearson Correlations of Asij with ASmij and ASij, Broken
Down by Number of Dimensions Included in Computations, by
Method of Obtaining S'ij’ and by Subsets of Cases.
Distances Dimensions Predictor A913 Computed Sij Comp. From
Included in Included in A=ASmij From No Stable Stable Con-
the Analysis Computations B=ASij Concepts Rotation cepts Rotation
All l—15 A ** .297 * .198
(N=105) B ** .301 * .213
1—12 A ** .258 * .199
B ** .260 * .206
1-9 A ** .254 * .210
B ** .262 * .212
1-6 A * .206 .095
B * .219 .125
1-3 A .112 * .224
B .126 * .225
1-2 A .017 .071
B .081 .138
l A —.099 **-.291
B -.139 **—.287
All 1-15 A ** .374 * .219
Manipu- B ** .373 * .234
fiigignces 1—12 A ** .329 A .233
7H: 9‘:
(N=69) B .323 .236
l-9 A ** .328 * .247
B ** .329 * .241
1-6 A * .257 .104
B * .270 .136
l-3 A .171 .290
B .184 ** .286
1—2 A .033 .084
B .115 .157
l A -.124 **—.357
B -.178 **—.356

 

120

 

 

Table 12. (continued)
Distances Dimensions Predictor Agij Computed ng Comp. From
Included in Included in A=ASmij From No Stable Stable Con-
the Analysis Computations B=ASij Concepts Rotation cepts Rotation
Indirectly 1-15 A * .219 .072
Changed B * .220 .086
€§:22§Ces 1-12 A .147 .071
B .144 .075
1-9 A .186 .101
B .188 .096
1—6 A .190 .064
B * .216 .115
1-3 A .138 * .251
B .162 * .259
1—2 A .042 .081
B .135 .166
l A -.090 **-.335
B —.152 **-.333

 

* p<.05, one-tailed test
** p<.01, one-tailed test

121

Table 13. Pearson Correlations of A3,. with A§m.. and A§.., As..
13 13 13 13

Computed from Actually Observed S'ij’ and §mij and gij
Computed from Fifteen Dimensions, Broken-down by Subsets

of Cases.

 

 

Distances Predictor
Included in the A= §mij
Analy51s B= g.. r
13
All (N=105) A **.267
B **.286
All Manipulated
Distances A **.314
B **.334
Indirectly
Changed A .139
Distances B .159

 

Test Three: Coordinates

 

The third hypothesis test was by means of a correlation between
predicted and observed spacial coordinates. The several versions of
this correlation as a function of predictor, rotation procedure, di-
mensions considered, concepts considered and statistical control of the
pretest coordinates are given in Tables 14 through 16.

In Table 14 are the zero order Pearson correlations between the
posttest coordinates (f'ik) and those predicted by the theory, either

including concept masses in the computations (fm ) or excluding concept

ik

masses from the computations (fi ). All of the correlations were sta-

k
tistically highly significant (recall that they are statistically inter-
dependent). The pattern of these correlations was much like that of the

inter-concept distance correlations. The magnitudes of the correlations

were greater when fewer dimensions were considered in the computations,

Table 14. Pearson Correlations* of F',

122

1k

With Fmik and Fik for Two

Rotations, Cases Broken Down by Cumulative Dimensions and
Experimental Groups.

 

Concepts
Included in
the Analysis

Dimensions
Included in

Predictor
A=Fm

. _ ik
the Ana1y31s N B-Fik

No Stable

Conc.

Stable Conc.

Rotation Rotation

 

 

A11 1-15 225 A .834 .784
B .839 .789

1—12 180 A .846 .793

B .851 .797

1-9 135 A .812 .814

B .877 .817

1—6 90 A .909 .861

B .911 .859

1—3 45 A .973 .957

B .973 .959

1-2 30 A .983 .962

B .983 .962

1 15 A .987 .990

B .987 .990

Unmanipu- 1—15 135 A .821 .960
lated B .821 .960
SEECEPtS 1-12 108 A .832 .967
y B .832 .967
1-9 81 A .861 .978

B .861 .978

1—6 54 A .893 .980

B .893 .980

1—3 27 A .975 .982

B .975 .982

1—2 18 A .982 .986

B .982 .986

 

123

Table 14. (continued)

 

 

 

Concepts Dimensions Predictor
Included in Included in A=Fm,k No Stable Stable Conc.
the Analysis the Analysis N B=FiR Conc. Rotation Rotation
Manipu— 1-15 90 A .855 .559
lated B .867 .568
3°???“ 1—12 72 A .868 .578
n y B .880 .587
1-9 54 A .889 .617
B .905 .623
1-6 36 A .943 .695
B .947 .688
1-3 18 A .973 .911
B .975 .915
1-2 12 A .977 .860
B .975 .858

 

* All correlations in this table are significant, p<.001, one—tailed test.

 

124

Table 15. First Order Partial Correlations (Controlling Fik) of F',

 

 

 

1k
with Fmik and Fik for Two Rotations, Cases Broken Down by
Cumulative Dimensions and Experimental Groups.
Concepts Dimensions Predictor

Included in Included in A=Fmik No Stable Stable Conc.

the Analysis the Analysis N B=Fik Conc. Rotation Rotation

All 1-15 225 A * .152 .113

B * .151 .135

1-12 180 A ** .168 .111

B ** .166 .135

1-9 135 A .206 .102

B .205 .124

1—6 90 A .137 -.061

B .119 -.039

1-3 45 A .166 .207

B .150 .201

1-2 30 A .066 .088

B .072 .101

1 15 A -.174 -.372

B -.l99 -.348

Manipu- 1-15 90 A *8 .273 .113

lated B ** .275 .131

gzicepts 1—12 72 A *8 .299 .111

y B - 8* .300 .130

1-9 54 A ** .368 .104

B ** .370 .119

1-6 36 A * .292 -.069

B .259 -.050

1-3 18 A .336 .234

B .320 .224

1-2 12 A .092 .001

B .103 .008

 

125

Table 16. Pearson Correlations of AFi with AFmi and AFik for Two

k k
Rotations, Cases Broken Down by Cumulative Dimensions and
Experimental Groups.

 

 

 

Concepts Dimensions Predictor

Included in Included in A=AFmik No Stable Stable Conc.

the Analysis the Analysis N B=AFik Conc. Rotation Rotation

A11 1-15 225 A ** .157 * .121

B ** .162 * .147

1-12 180 A * .172 .119

B ** .176 * .146

1-9 135 A ** .204 .109

B ** .209 .133

1-6 90 A .129 -.052

B .120 -.026

1-3 45 A .204 .237

B .191 .233

1-2 30 A .147 .152

B .157 .167

1 15 A -.070 -.218

B -.113 -.245

Manipu— 1-15 90 A ** .284 .134

lated B ** .291 .158

goicepts 1-12 72 A 88 .308 .130

n Y B 88 .314 .155

1-9 54 A ** .371 .121

B ** .378 .140

1-6 36 A * .289 -.053

B .264 -.027

1-3 18 A .370 .283

B .357 .278

1-2 12 A .277 .179

B .300 .198

 

* p<.05, one—tailed test
** p<.01, one~tailed test

126

reflecting again the greater stability of the larger dimensions. Again,
the stable concepts rotation produced higher correlations for the unmani—
pulated concepts' coordinates than for those of the manipulated concepts;
while the no stable concepts rotation produced no such difference. And
again, there was no clear difference between predictions including or ex—
cluding the concept masses from the computations. If anything the pre-

dictor excluding concept masses produced slightly better predictions.

Table 15 gives the first order partial correlations controlling the

pretest coordinates (fi ). The partials were substantially lower than the

k

zero order correlations, demonstrating again that the theory's accuracy of
prediction rested mainly upon the stability of the coordinate system. Once

again several of the partials for the manipulated concepts were large
enough to be statistically significant, but only for the no stable concepts
rotation. Unlike the inter—concept distances, the coordinates cannot be
partitioned into direct and indirect changes. Consequently the effect
noted for the inter-concept distances—-lower partials for the indirect
changes—-cannot be observed here. No consistent differences emerged be—
tween predictions including or excluding concept masses in the computations.
Finally, there were small, observed negative partials for the first and the
first six coordinates. Thus the theoretical predictions were in the wrong
direction for some dimensions.

Table 16 presents the zero order correlations between predicted and
observed changes in coordinates. The pattern of these correlations was very

similar to that of the partials, except that these correlations were slightly
higher.
Overall, then, one may conclude that the correlations between predicted

and observed coordinates , like those between predicted and observed inter-

concept distances,1«uxanot strongly supportive of the hypothesis.

CHAPTER V
DISCUSSION
This chapter discusses the findings of the study in relation to the
theory of linear motion and to the adequacy of the study as a test of that
theory, and draws implications for further research. The chapter begins
by evaluating the measurement and procedures of the study, then evaluates
the overall degree of support which the study gives to the theory of
linear motion, and then closely examines several alternative explanations
of the results. The chapter closes with a summary and conclusion of the
dissertation.

Evaluation of Measurement and Procedures

 

Measurement reliability in this study was at least adequate at the
aggregate level of analysis, but was poor at the individual level of
analysis. Since the hypothesis tests were conducted with aggregated
data, the adequate degree of reliability achieved at the aggregate level
is of primary importance. Measured reliability of the aggregated data
was somewhat higher than the best results achieved by Barnett in his
study of the reliability of metric MDS techniques. Since the size and
homogeneity of the subject sample and the number and homogeneity of the
concepts scaled in this study were similar to Barnett's studies, the
higher measured reliabilities in this study may be attributed to its
shorter (one week) interval between measurements. Thus the reliabilities
reported by Barnett may still be regarded as typical for the conditions.

Questions of measurement validity and the success of experimental

procedures are less straightforwardly answerable than is the question of

127

128

reliability. Our data were tested against severa1_a priori criteria.
Again, the criteria were quite well satisfied whenever the test involved
aggregated data, but were not so well satisfied when the tests involved
individual-level data. One can view this finding in several ways. The
finding is perfectly reasonable given the findings concerning reliability,
and given the theoretical principle that reliability is a necessary con-
dition for validity. And again, since the hypothesis tests were conducted
with aggregated data, the positive results for the aggregated data may

be of prime importance. On the other hand, the criteria for the aggre-
gated data were generally less formal, more intuitive. One cannot, in
these circumstances, rule out the possibility that wishful thinking by
the experimenter might influence his interpretations. Furthermore, the
assessment of validity of measurement and procedures becomes involved in
a delicate balance between theory and data. If one strongly believes
one's theory, then the failure of theory-testing studies may, in the
absence of external criteria of construct validity, be attributed to in-
valid measurement and procedures. After repeated use over a period of
time, of course, such an argument must begin to wear thin. In any case,
there seems no strong and self-evident reason to reject this study on

the ground of invalidity alone.

As an aside to the discussion of measurement we should mention the
interesting tendency for the inertial mass estimates to increase between
pretest and posttest. The explanation that the subjects' information
about the experimental concepts actually increased during the study seems
too facile; yet no other explanation comes readily to mind. The further

fact that measured inertial mass did not relate to cognitive change in

129

the theoretically expected manner suggests that we must search further
for a valid explanation of its behavior.

Evaluation of Results

 

The results of this study do not appear to support the hypothesis.
The first test, the inspection of mean changes in distance, disclosed
several anomalies. The second and third tests, the correlations of pre-
dicted with observed inter-concept distances and coordinates, showed that
the theory predicts very well, but only because it predicts the general
stability of the cognitive structure. When the change component is iso—
lated by statistically controlling the pretest scores or by correlating
predicted with observed changes, the predictive power of the theory is
quite poor in absolute terms: seldom does it account for as much as five
percent of the variance in the dependent variable. Isolated correlations
might appear promising, but the overall pattern does not.

Certain results are strongly negative in their implications. Were
the theory correct, one would expect better results for the stable con-
cepts rotation than for the no stable concepts rotation, since the former
assumes the success of the experiment. The reliability tests found that
the stable concepts rotation gave results which were more like those for
the actually observed distances than did the no stable concepts rotation.
Yet the no stable concepts rotation, in the hypothesis tests, gave results
which were, if anything, slightly more supportive of the hypothesis than
did the presumably more valid stable concepts rotation. This suggests
that whatever apparent success the theory may have had in some instances
was accidental. Even more disturbing are the negative results on the

first dimension. Some of the strongest partial correlations are negative

130

correlations for computations based on the first dimension only. These
correlations are contrary to the theory. It is clear from inspection of
the plots hgw_this result occurred, but it is not at all clear why it
occurred.

Perhaps the most rigorous single test of the hypothesis is in the
correlations at the bottom of Table 13, the correlations for indirect
changes in the inter—concept distances based on the actually observed
posttest distances. These correlations are unaffected by the uncertain
meanings of rotation procedures and computed "observations." The corre-
lations are .139 for the predictor including inertial mass and .159 for
the predictor excluding mass. Neither of these correlations is statis—
tically significant. Some indication of the insubstantial nature of
these correlations is given by comparing them to those immediately above
them, which differ only in including the three direct changes. The
correlations including the three direct changes are almost .2 higher than
those not including the direct changes. The addition of only three cases
(which are trivially consistent with the theory) doubles the magnitude of
the correlations. One cannot consider the correlations as indications of
a reliable trend in the data.

Alternative Explanations

 

If the results of this study are not explicable by the hypothesis,
then how may they be explained? This chapter suggests and evaluates
seven possible responses to that question. In considering each of seven
alternative explanations of the results we will both present whatever
facts in the present study might fall under the explanation, and discuss
features that might be incorporated in future studies to test the explafi.

nations.

131

The first three alternative explanations all have in common the
implication that this study failed to support the theory only because it
failed adequately to control the information to which the subjects were
exposed.

The first alternative hypothesis is that the experiment failed, not
because the theory is false, but because of a failure of the experimental
manipulations to work. This hypothesis holds that the experimental mes-
sages simply had no systematic effect on the aggregate cognitive structure.
If the messages had been "stronger"—-if more, or more credible information
had been provided, or if more powerful techniques of persuasion had been
employed-—then the resulting cognitive change might have conformed to the
theory of linear motion. This hypothesis cannot strictly be ruled out,
because none of the direct changes in distance supposedly induced by the
messages were statistically significant; although we have argued that the
overall pattern of mean changes suggests that the manipulations did work.
A future study designed to rule out the hypothesis would have to have
three features. First, the messages would be strengthened, perhaps by
adding information or by adding redundancy, as in a multi-media presen-
tation. Second, the messages would be more thoroughly pretested to ensure
their effectiveness prior to the main study. Third, a separate control
group of subjects would be used so that treatment—control comparisons
could be made of the same inter-concept distances (rather than only be—
tween manipulated and unmanipulated distances as in the present study).

A second alternative explanation is that the messages were powerful
enough to bring about cognitive change, but the contents of the messages

were not those which the experimenter intended. The messages, in other

132

words, were noisy; they contained "unintended" information, and so moved
the concepts in unintended directions.

Here we confront a serious dilemma which no future experiment of
this sort can ignore. A realistic and credible message concerning a
particular pair of concepts must, it would seem, make references to many
"third" concepts by way of introducing points of comparison or contrast
between the experimental concepts. In comparing Fiji and Singapore, for
example, we said that both were small, tropical, former British colonies,
recently independent, and parliamentary democracies. Perhaps the weakest
aspect of this study, in retrospect, was its assumption that the infor-
mation incorporated in the messages would exert force only along the line
directly connecting the pairs of manipulated concepts. In retrospect it
would havelmxuljust as reasonable, and perhaps more reasonable to assume,
for example, that saying that Singapore and Fiji are both parliamentary
democracies not only would move Singapore and Fiji toward each other but
also would move bg£h_8ingapore and Fiji toward the concept of "parlia-
mentary democracies." This, then, is the dilemma: on the one hand, we
want realistic, credible messages; on the other hand, we can only include
a limited number of concepts in the multidimensional scaling analysis.
It seems that we must choose either ineffective or invalid manipulations.

The dilemma might be avoided if we had a truly adequate spacial
model of message content. More immediately, the dilemma might be avoided
by thorough pretesting of the messages in several pilot studies which
would incorporate, in overlapping parts, all of the concepts referred to
in the messages. The meaning of the message would then not be measured,

as it was in this study, by a single item referring to the single pair

133

of experimental concepts. Rather the meaning would be measured by a set
of items referring to a set of reference concepts common to all of the
pretest studies and the main study. And the movement of the manipulated
concepts would not be predicted to occur along the lines connecting the
pairs; nor would the force of the message be assumed divided equally be-
tween the two experimental concepts. Rather, the movement of each con-
cept would be predicted as a linear function of its predicted movements
with respect to the whole set of reference concepts. The theoretical
prediction of "indirect" changes would then be based on a set of concepts
included in the main study but not in any of the pilot studies.

By comparison to this ideal set of procedures the messages used in
this study were little better than shots in the dark. Can the apparently
chaotic movements apparently induced by the experimental messages be ex-
plained by assuming that the messages were noisy? The answer, in general,
is trivially ”yes." Less trivially and more concretely, certain unpre—
dicted changes do seem directly attributable to certain unintended mes-
sage contents. The example of Singapore and Fiji is a case in point.
Both countries, which were said to be parliamentary democracies having
capitalist economies, moved toward the "conservative" end of the second
dimension, which seemed to represent political ideology. Another case
concerns Congo. It was mentioned earlier that Congo's movement toward
the "radical" end of the second dimension was one of the most prominent
changes in the study. This movement, which was not at all predicted, is
not at all surprising in view of the assertions, in the message about
Congo and Guyana, that Congo has a socialist economy and a one-party

government, and is a self-proclaimed "communist" state. Perhaps we could

134

even explain Brazil's movement toward the African cluster as a consequence
of the reference in the message to Brazil as a former colony. Perhaps we
could explain Guyana's movement in a general "European" direction as a
result of references to it as a parliamentary democracy or as a member of
the British Commonwealth of Nations.

These post hog explanations must be viewed with appropriate skepti—
cism. They do, however, support the general contention that the noisiness
of the experimental messages cannot be ruled out as an alternative ex—
planation which preserves the basic character of the theory of linear
motion.

A third alternative hypothesis is that the observed movements of
concepts were affected by messages other than the experimental messages,
such as news reported in the mass media during the interval between pre—
test and posttest measurements. This hypothesis, like the previous two,
holds that the theory is correct but that the experiment failed to con-
trol adequately the information inputs to the subjects. Information such
as mass media news was treated as environmental noise in the design of
this study-~uncontrolled and assumed to be randomly distributed among
the 105 inter—concept distances. If a separate control group of subjects
had been included in this study, then the environmental noise might have
been controlled statistically. Wisely or not, the experimenter decided
not to allocate scarce subjects in that fashion. A future study might
do so and might achieve superior results. On the other hand, an unsys-
tematic review of mass media references to the fifteen nations during
the week of the study failed to identify any apparent relationships with

the movements of concepts.

135

The fourth and fifth alternative explanations both raise the issue
of control of time. Both explanations could more easily be ruled out by
a study which took measurements at three or more points in time.

The fourth explanation holds that the theory may be correct but
not enough time was allowed for equilibrium to be establishedin cogni-
tive space following the messages. This explanation might have been
ruled out had a second posttest been administered. If the results failed
to improve from first to second posttest, then the hypothesis would be
false. Even the presently available data, however, rule out this hypo-

thesis as a sufficient explanation. The hypothesis seems to require,

 

even in the short run, that all changes would be in the predicted dif

rection; but that clearly was not the case in this study.

The fifth explanation is Woelfel's proposed cognitive Law of Motion,

or something like it: the idea that concepts have resistance not to

 

velocity but to acceleration in cognitive space, and that, consequently,
one cannot predict the effect of a message without knowing the velocity
of the affected concepts prior to the message. The posttest distances
would be a result of the prior velocities and the message inputs. Under
this hypothesis, failure to take account of prior velocities could lead
to just the sort of apparently chaotic results found in this study.
Statistical control of velocities prior to the messages would require
that a second pretest be administered. Prior velocity would be measured
by change occurring between the two pretests.

A thorough consideration of the fourth and fifth alternative ex-
planations, in short, would require that observations be made at at least

four points in time, including two pretests and two posttests.

136

The last two alternative explanations raise even more complex
issues than did the first five, for they raise the specter of a hetero—
geneous cognitive space.

The sixth explanation is that not all concepts or sets of concepts
in cognitive space behave lawfully, and that the concepts in this study
failed to behave lawfully because there were too many of them, or be-
cause they, or some of them, were not meaningful. Two factors are in-
volved in this explanation. First is the notion of information proces-
sing capacity. People can handle only a limited amount of information
in a given period of time. If the environment presents information
beyond this limit, then excess information is simply not processed sys-
tematically. By rough analogy with experiments on short term memory we
might suppose that in an experiment such as ours the maximum number of
concepts that would behave lawfully would be about seven (Miller, 1960).
The second possible factor is meaningfulness. Perhaps we cannot expect
a concept to behave lawfully just because it is included in an MDS in—
strument; perhaps we must know, in addition, whether the concept meant
anything to the subjects prior to administration of the instrument. How
many subjects in our study had ever heard of Guyana or Fiji? Can we
claim to have measured the meaning of these concepts, or must we admit
to having merely created an apparent meaning by including them along with
the rest of the concepts? And can we expect such pseudo-cognitions, if
they exist in the study, to behave lawfully?

' a set of con*

These two factors point to the concept of "domain,'
cepts that behave together as a unit, or are, in Scott's (1969) terms,

"functionally equivalent." Under this explanation the laws of motion do

137

not apply to just any set of concepts; the concepts must compose a domain.
There may be an upper limit to the size of domains. Spaces including more
than that number of concepts would not behave lawfully. If the limit is
around seven, then this study, with fifteen concepts, exceeds the limit.
Or again, there may be some "critical mass" that a concept must attain
before it can function as part of a domain. The theory of linear motion
has assumed that mass is important only as resistance to motion: the
more mass the more resistance. Now we must wonder whether nearly mass—
less concepts are at all capable of lawful motion.

The data of this study were examined from several standpoints in
an effort to test this alternative hypothesis. Particular attention was
focused on subsets of about seven concepts that might, for one or another
reason, constitute a domain. Predictions of distances involving the
seven highest mass concepts, and predictions of the smallest third of the
inter-concept distances, were examined and found to be no better than
predictions for the whole set of distances. Thus the present study offers
no direct support for the contention that concepts can belong to a domain
only if they have a certain critical mass or if they are close to each
other in cognitive Space.

A third subset of distances, however, was found to conform more
closely to the theory than did the data as a whole. These were the dis—
tances among the six manipulated concepts: fifteen distances, or if the
three directly changed distances are excluded, twelve distances. Table
17 displays the partial correlations (controlling pretest distances) of
predicted with observed posttest distances for the twelve indirectly

changed distances among the six manipulated concepts. These partials

138

are, on the whole, substantially higher in absolute magnitude than the
corresponding partials in Table 11. Few of them are statistically sig—
nificant, but then it must be considered that they have only nine degrees
of freedom. Had these partials appeared in Table 11 they would have been
touted as strong support for the theory, this despite some anomolies
among them, most notably the (now even stronger) negative correlations
for the first dimension. Three factors seem to favor the theory. The
first is the large magnitude of the partials. The second is that the
best results are achieved with the stable concepts rotation, which assumes
the success of the experiment. The third favorable factor is that the
correlations "peak" around the middle of the range of cumulative dimen-
sions (2 through 6 dimensions), which presumably include the greatest
proportion of reliable information.

One must, of course, view_pg§tnhgg_analyses with some skepticism.
Still we can ask whether this particular subset of the concepts falls
under the alternative explanation. Do they compose a ”domain" in a
sense that the whole set of concepts does not? One interpretation is
that the six manipulated concepts constitute a domain just in consequence
of being manipulated, which entails both being mentioned in connection
with each other and being infused with information in the form of experi-
mental messages that might create the needed "critical”mass." This in—
terpretation is interesting, but it should not be taken too seriously
until the finding has been replicated. The sixth alternative explanation
might be ruled out by a future study which experimentally varied the

number of concepts scaled.

 

139

Table 17. First Order Partial Correlations (Controlling Sij) of
S',, with Sm,, and 8,, for Indirectly Changed Distances
1] 13 13

Among Manipulated Concepts Only.

 

Dimensions Predictor S'ij Computed S'ij Computed Actually
Included in A=Smij From No Stable From Stable Observed
Computations B=Sij Concepts Rotation Concepts Rotation S'ij
1-15 A .436 .359 .359
B .449 .402 .402
1-12 A .384 .392 .403
B .397 .424 .444
1-9 A .322 .416 .352
B .357 .436 .414
1—6 A .336 * .532 .511
B .321 * .528 * .523
1—3 A .335 .466 .165
B .362 .437 .163
1-2 A .333 ** .775 -.213
B .474 ** .793 —.138
l A —.490 -.512 .004
B *—.553 -.484 -.027

 

* p<.05, one-tailed test, d.f. =
** p<.01, one-tailed test, d.f. =

KOO

140

The seventh and final alternative explanation to be considered here
is that the results of this study seem unsystematic because a radically
inappropriate model has been applied; the mind is not at all space-like
but is instead a network.

A network model views the mind as a set of concepts which are or
are not connected by various sorts of links. The mathematical model is
a set of nodes or points connected by lines which may or may not be di—
rectional (asymmetrical) and labeled (Harary, e£_al., 1965). For example,
"A likes B” might be represented as A_;:Q.B, or more abstractly as A ___B.
The former expression is directed and signed, while the latter expression
says only that there is some connection between A and B. A network model
focuses attention on the kinds of links and on higher—level phenomena
that emerge when links are composed into larger networks. Network models
may be fairly simple. Balance theory (Heider, 1958), for example, con-
siders only two kinds of links--unit relations and sentiment relations,
each of which may only be positive or negative. Network models may,
however, be astonishingly complex, as a recent paper by Frederiksen (1975)
well shows.

Network and spacial models make radically differently assumptions
about how the mind is organized. The heart of the matter is that under
the strong spacial assumptions of theorists like Osgood and Woelfel
(and Craig) all cognitive objects are comparable, for all are scalable
in cognitive space. If we regard psychological distance as a kind of
relation or connection, then a "network" defined on that relation has
highly determined structural properties. First, the network necessarily

is completely interconnected, in that any scaled object necessarily is

 

141

some distance from every other scaled object. Second, the relation

 

necessarily is symmetrical, in that Sij’ the distance from i to j, is
necessarily identical to Sji’ the distance from j to i. Third, the re-

lation necessarily is intransitive, in that sij and s, puts only a loose

jk

 

restriction on Sik (assuming a real, multidimensional space-—in imaginary
space there is no restriction at all). In short, the key structural
variables of network models, such as continuity, direction, symmetry and
transitivity of relations, and connectedness, integration and structural

differentiation of networks, are all invariants, and thus essentially

 

meaningless, in spacial models.

Spacial models assume that cognitive space exists as a kind of
"medium” in which objects are located, regardless of whether or not the
subject is aware of the medium as such. Network models, in contrast,
focus upon the question of explicit cognitive connections between things,
and thus do not assume that such connections exist. In a network model
cognitive elements may not be connected. Concepts may be "similar" yet
unrelated; or concepts may be quite different or distant, and yet be
highly related by an asymmetric relation. Thus the crucial structural
assumption of "distance" in the spacial model is meaningless or para-
doxical from the standpoint of a network model; unrelated concepts have
no distance, and the various kinds of connections seem to have no clear
translation into distance. Robert Abelson (1968) has distinguished be-
tween "maximalist" and "minimalist" positions on cognitive structure.
The spacial model, with its highly restrictive assumptions, necessarily

takes a maximalist position; it assumes a great deal of structure.

“M
’V \,

 

141

some distance from every other scaled object. Second, the relation
necessarily is symmetrical, in that Sij’ the distance from i to j, is
necessarily identical to Sji’ the distance from j to i. Third, the re-
lation necessarily is intransitive, in that sij and sjk puts only a loose
restriction on Sik (assuming a real, multidimensional space——in imaginary
space there is no restriction at all). In short, the key structural
variables of network models, such as continuity, direction, symmetry and
transitivity of relations, and connectedness, integration and structural
differentiation of networks, are all invariants, and thus essentially
meaningless, in spacial models.

Spacial models assume that cognitive space exists as a kind of
"medium” in which objects are located, regardless of whether or not the
subject is aware of the medium as such. Network models, in contrast,
focus upon the question of explicit cognitive connections between things,
and thus do not assume that such connections exist. In a network model
cognitive elements may not be connected. Concepts may be "similar" yet
unrelated; or concepts may be quite different or distant, and yet be
highly related by an asymmetric relation. Thus the crucial structural
assumption of ”distance” in the spacial model is meaningless or para—
doxical from the standpoint of a network model; unrelated concepts have
no distance, and the various kinds of connections seem to have no clear
translation into distance. Robert Abelson (1968) has distinguished be—
tween "maximalist" and "minimalist" positions on cognitive structure.
The spacial model, with its highly restrictive assumptions, necessarily

takes a maximalist position; it assumes a great deal of structure.

 

 

v’v\

 

142

Under the assumption that the mind is "really" structured like a
network rather than like a space, some apparently unsystematic features
of our results become plausible. In a network model change in a single
relation is not generally expected to change the relations between the
two elements involved and all other elements in the network, if only
because it is not generally expected that all such possible relations
exist. Nor does a network model require that change in a single rela—
tion wouldleaveunchanged relations at more than one step remove from
the changed relation. Rather, such implicational change is a function
of whatever higher—order structural principles (such as balance) are
operative. The spacial model, in contrast, requires both that a change
in distance between two concepts changes the distances between each of
those concepts and all other concepts scaled and that the distances
among the unmanipulated concepts are unaffected. This reasoning would
suggest that the present study supports a network model of cognitive
structure, since neither of the mentioned requirements of the spacial
model is strongly evident in the data. Such reasoning, however, would
be spurious, because the "evidence" for the network model is entirely
negative; the network hypothesis becomes, in effect, the null hypothesis.

Can any feature of our data be used to test the network hypothesis
more forthrightly? No direct test can be designed because we have no
very good basis for assuming what kinds of connections, if any, are
present among the concepts. Two indirect tests, however, were tried.

The first test requires that the cognitive network is ruled by
the higher—order principle of cognitive balance. Phillips (1967) has

shown that a cognitive network can be represented as a matrix of

W\

 

143

relations, and that the matrix can be factored. Thus it is mathemati—
cally possible to represent a network as a multidimensional space, as-
suming that the network is completely connected and is composed of con—
tinuous (i.e. numerical) relations. Phillips has also shown that a
perfectly balanced cognitive network would be unidimensional (i.e. one
factor would perfectly account for the relational matrix). Thus a ten—
dency toward cognitive balance might appear in our data as a tendency
for the cognitive "space" to become unidimensional. A glance at the
tables in Appendix C will confirm that no such tendency was present in
the data. The dimensions, if anything, become more equal in importance
over time as indicated by the relative sizes of their eigenvalues.

The second indirect test of the network hypothesis requires that
we assume that the spacial concept of psychological distance is identi—
cal to the network concept of "relatedness." Then we must further assume
that a "balance" tendency operates such that when we change a concept's
relation to some other concept (as by transmitting an experimental mes—
sage), then concepts highly related to the changed concept will tend to
"change along" with it, while unrelated concepts will not be affected
by its motion. One might imagine the more tightly connected concepts
being "dragged along by their connections” when we "move” a concept. It
follows from this that the closer (more related) a concept is to a ”moved"
concept the less the change in relatedness of that concept should be to
the moved concept. In other words, for distances involving a manipulated
concept there should be a strong positive correlation between magnitude

of distance and absolute change of distance, while for distances involving

 

 

144

an unmanipulated concept, any change in which is assumed to be random,
the correlation would not necessarily be strongly positive.

Table 18 displays the correlations between distance and absolute
Change in distance computed separately for each of the fifteen concepts.
Manipulated and unmanipulated concepts are listed in separate columns to
facilitate comparison. If the above reasoning is correct, then the net—
Work model is false, since the pattern of correlations, if there is a
pattern, is just the opposite of that expected.

The author has imagined several interpretations of these corre—
lations, only one of which is credible enough to mention here. The in—
terpretation is that the negative correlations for the manipulated con—
cepts indicate that the experimental manipulations had systematic effect
only in the regions nearby the manipulated concepts. Thus large absolute
changes occurred between the manipulated concepts and nearby concepts
but not between the manipulated concepts and far away concepts. This
suggests a "domain" interpretation of the study, with domains comprising
local regions of cognitive space. Unfortunately, as was noted several
paragraphs above, there was no detectable tendency for the theory of
linear motion to make more accurate predictions of small distances than
of large distances. If, in other words, our interpretation of the corre-
lations in Table 18 is correct, we still have not saved the theory of
linear motion. We imply instead that some other "law of motion" governs
the movement of concepts within regional cognitive domains.

The two indirect tests attempted do not, in any case, support a
network interpretation of the present study. The author has not devised

a means by which a future study might rule out the hypothesis of network

145

Table 18. Pearson Correlations of Distance From Each
Concept with Absolute Change of Distance
From that Concept.

 

 

 

MANIPULATED CONCEPTS UNMANIPULATED CONCEPTS
Concept Concept

No. r No. r

2 -.417 l —.347

5 —.256 3 —.203

8 .332 4 * .581

10 *-.582 6 —.072

14 *—.576 7 —.l36

15 **—.618 9 * .489

11 ***-.750

12 * .596

13 .173

 

 

* p<.05, one—tailed test, d.f. = 12
** p<.01, one—tailed test, d.f. = 12
*** p<.001, one—tailed test, d.f. = 12

 

146

structure. Continued failure of spacial models, however, would suggest
that we move toward the network model as an alternative.
Summary and Conclusion

The working assumption of this study was that models of cognitive
structure may fruitfully be elaborated into general models of informa-
tion which describe the structure of messages and constrain theories of
the cognitive effects of communication. Because of its intuitive appeal
and mathematical convenience, and because of its prominence in several
disciplines, the spacial model of cognitive structure was selected for
study. A model of message structure and a theory of linear motion were
elaborated from the general spacial model by strict deduction from ex-
plicit definitions and assumptions. Previous research bearing on several
aspects of the theory of linear motion was discussed. It was concluded
that the theory of linear motion was plausible (though not at all proven),
and that research on such a theory would be a reasonable next step from
several points of view.

An empirical study was conducted in an attempt to test the theory
of linear motion. The study employed a pretest—manipulation-posttest,
within-subjects experimental design. Subjects were presented with in—
formation designed to change directly three of the 105 pairwise distances
among fifteen concepts. The hypothesis was that the messages would bring
about cognitive change as predicted by the theory of linear motion.

The results were basically negative; the theory was not supported,
except insofar as it correctly assumed the general stability over time
Of cognitive space. The observed changes in location of concepts gener—

ally were inexplicable from the standpoint of the theory.

147

Several alternative explanations of the results were considered.
Several of these "save" the theory by indicting the experiment. Others
suggest alternative theories. One general indictment of the experiment

is that it may have failed to control adequately the information to which

 

subjects were exposed (used ”weak" messages; included extraneous (or
merely unaccounted for) information in the messages; failed to control
for information from the environment beyond the experiment). The experi—
ment may also have failed to control adequately the variable 0f.E£EE
(failed to allow sufficient time for the theoretical effects to occur;
failed to take measurements at enough points in time to allow observa—
tion of accelerations). The theory may have failed to take adequate
account of the concept of cognitive domain——a set of functionally equi-
valent concepts. Thus the experiment may have included a number of con-
cepts which exceeded the information processing capacities of the subjects,
or it may have included meaningless concepts that could not be expected
to behave lawfully. Some evidence suggests that the theory might have
been successful had predictions been restricted to a domain comprising
the manipulated concepts. Finally, the theory may be false because it
makes a radically false assumption about cognitive structure. If, for
example, the mind is ”really" a network rather than a space, a study
such as ours would be expected to produce apparently unsystematic re—
sults. No specific evidence was found in these data to support a network
interpretation, however. Future research should be directed toward re-
solving the issues raised by these alternative explanations.

As we pointed out in Chapter I, a test of a particular theory is

not equivalent to a test of the general spacial model. If this study

148

has not been entirely decisive regarding the theory of linear motion,
much less has it been decisive concerning the general spacial model.
If the theory of linear motion is false, some other cognitive "law of

motion,”

perhaps more complex, may ultimately be found true.

The results of this study, all considered, do not vindicate the
working assumption; but neither is the failure of a single experiment
sufficient to warrant rejecting a general strategy of inquiry. Our

investigation must be considered as only a step along the way to an—

swering the broad questions which stimulated it.

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APPENDICES

 

APPENDIX A

PRETEST QUESTIONNAIRE AND POSTTEST COVER LETTER

Dear Participant,

This is a study of human information processing. We hope to
learn more about how people understand and structure information. A
second part of the experiment will be administered in a few days.
At that time we will more fully explain the purpose of the study.

Please follow the instructions carefully. Answer_§ll questions.
Leaving blanks unfilled may make your questionnaire unusable. Always
put down an answer, even if you have to guess. Complete each page
before going on to the next.

If for any reason you do not wish to participate in this study,
just do not fill out the questionnaire.

Thank you very much for your cooperation.

Sincerely yours,

Robert T. Craig

 

 

What is your date_p£ birth? .___ PLEASE DO NOT
Month Day Year WRITE IN THIS
SPACE
What is your ESE? Male (Card 1)
0
No. _________
Female 1 2 3
l
Gp.__ Wv__1_
4 5 6
Card Jl__l_
7 8
Yr, Sx_________
9 l 1

156

157

The following set of questions asks you to guess how much infor—
formation you have-—how much you know-—about each of fifteen countries.
Consider all that you know about each country, from whatever source.

If zero (0) represents the complete absence pf knowledge, and 100

each country?

Remember, if you feel that you have less than an average amount
of information about a country, write a number less than 100. If you
have more than average information about a country, write a number
larger than 100. You may write any number you want.

 

 

 

COUNTRY AMOUNT OF INFORMATION
China (12—15) (Card 01)
Singapore (16—19)

Mexico (20—23)

U.S.A. (24~27)
Portugal ______1 (28-31)

Poland (32-35)

India (36—39)

Fiji (40-43)

West Germany (44-47)

Brazil (48-51)
Central African Republic (52—55)

Greece (56—59)
U.S.S.R. (60-63)

Congo (64—67)

Guyana (68—71)

 

158

The following set of questions asks you Egg different (or in
other words "far apart") you perceive the countries to be. Differences
in concepts are measured in units, so that the mppg different two con—
cepts are, the more units apart they are from each other. To help you
know how big a unit is, assume that Italy 229 England g£g_lgg_pplp§
apart.

If you think that two countries are mppg different from each
other than Italy and England, write a number larger than 100. If you
think that two countries are lpgg different from each other than Italy
and England, write a number lggg than 100. If you think that two
countries are exactly phg.§§mg, that you see no difference at all be-
tween them, write a zero (0). Remember, the mppg different the coun—
tries are from each other, the higher the number you should write.

You may write any number you want.

Please answer all questions. Even if you feel unsure of your
answer, 5235.3 guess.

Work as quickly as you comfortably can. Once you "get going"

each answer will take only a few seconds.

How far apart are each of the following?
COUNTRIES UNITS APART

(Card 01) 72-80 0102 China
(Card 02) 9—17 0103 China
Dup 1-6 18-26 0104 China U.S.A. . . . . .
02 7—8 27-35 0105 China Portugal . . . .

& Singapore . . . . .
&
&
& . . . . .
36-44 0106 China & Poland . . . . . . . . . .
&
&
&
&

Mexico . . . . . . . . . . .

45—53 0107 China India . . . . . .

54-62 0108 China Fiji . . . . . . . . . .
63-71 0109 China West Germany . . . .
72-80 0110 China Brazil . . . . . . . . .

 

159

How far apart are each of the following?

(Card 03)
Dup 1-6
03 7-8

(Card 04)
Dup 1-6
04 7-8

(Card 05)
Dup 1—6
05 7-8

(Card 06)
Dup 1—6
06 7—8

9-17
18—26
27—35
36-44
45-53
54-62
63—71
72—80

9—17
18—26
27—35
36-44
45—53
54-62
63—71
72-80

9-17
18—26
27—35
36-44
45-53
54-62
63-71
72—80

9-17
18—26
27—35
36—44
45-53
54-62
63-71
72-80

0111
0112
0113
0114
0115
0203
0204
0205

0206
0207
0208
0209
0210
0211
0212
0213

0214
0215
0304
0305
0306
0307
0308
0309

0310
0311
0312
0313
0314
0315
0405
0406

COUNTRIES

China & C
China & G
China & U
China & C
China & G
Singapore
Singapore
Singapore

Singapore
Singapore
Singapore
Singapore
Singapore
Singapore
Singapore
Singapore

Singapore
Singapore
Mexico &
Mexico &
Mexico &
Mexico &
Mexico &
Mexico &

Mexico &
Mexico &
Mexico &
Mexico &
Mexico &
Mexico &
U.S.A. &
U.S.A. &

UNITS APART

entral African Republic
reece
.S.S.R.
ongo .
uyana
& Mexico
& U.S.A.
& Portugal

Poland

India . .
Fiji....

West German

Brazil . . . . . . . .
Central African Republic
Greece . . .

U.S.S.R.

Q‘QQ‘QQQ’QWQ"

& Congo .

& Guyana
U.S.A.
Portugal .
Poland .

India
Fiji . . . . .
West Germany .

Brazil . . . . . . . . . .
Central African Republic .
Greece .

U.S.S.R.

Congo

Guyana .

Portugal .

Poland .

160

Remember: ITALY and ENGLAND are 100 UNITS apart

How far apart are each of the following?

COUNTRIES UNITS APART

(Card 07) 9—17 0407 U.S.A. & India
Dup 1—6 18-26 0408 U.S.A. & Fiji . . . . .
07 7-8 27—35 0409 U.S.A. & West Germany .

36—44 0410 U.S.A. & Brazil . . . . . . . .

45-53 0411 U.S.A. & Central African Republic .

54—62 0412 U.S.A. & Greece .

63-71 0413 U.S.A. & U.S.S.R.

72—80 0414 U.S.A. & Congo

(Card 08) 9-17 0415 U.S.A. & Guyana .

Dup 1-6 18-26 0506 Portugal & Poland .

08 7—8 27—35 0507 Portugal & India
36-44 0508 Portugal & Fiji . . .
45-53 0509 Portugal & West Germany .
54—62 0510 Portugal & Brazil . . . . . . .
63—71 0511 Portugal & Central African Republic .
72—80 0512 Portugal & Greece .

(Card 09) 9—17 0513 Portugal & U.S.S.R.
Dup 1—6 18—26 0514 Portugal & Congo
09 7-8 27—35 0515 Portugal & Guyana .
36-44 0607 Poland & India
45—53 0608 Poland & Fiji .
54-62 0609 Poland & West Germany .
63—71 0610 Poland & Brazil . . . . . . .
72—80 0611 Poland & Central African Republic .

(Card 10) 9-17 0612 Poland & Greece .
Dup 1—6 18—26 0613 Poland & U.S.S.R.
10 7-8 27-35 0614 Poland & Congo
36—44 0615 Poland & Guyana .
45-53 0708 India & Fiji . .
54-62 0709 India & West Germany
63-71 0710 India & Brazil . . . . . . . .
72—80 0711 India & Central African Republic

(Card 11)
Dup 1—6
11 7—8

(Card 12)
Dup 1-6
12 7—8

(Card 13)
Dup 1—6
13 7-8

(Card 14)
Dup 1-6
14 7—8

161

far apart are each of the following?

9-17
18—26
27-35
36—44
45—53
54-62
63-71
72-80

9~17
18-26
27-35
36-44
45—53
54—62
63-71
72-80

9-17
18-26
27-35
36—44
45-53
54-62
63-71
72—80

9-17
18-26
27—35
36-44
45-53
54—62
63—71
72—80

0712
0713
0714
0715
0809
0810
0811
0812

0813
0814
0815
0910
0911
0912
0913
0914

0915
1011
1012
1013
1014
1015
1112
1113

1114
1115
1213
1214
1215
1314
1315
1415

COUNTRIES UNITS APART
India & Greece . . . . . .

India & U.S.S.R. . .

India & Congo . . . . . . . . .
India & Guyana . . . . . .

Fiji & West Germany . . . .

Fiji & Brazil . . . . .
Fiji & Central African Republic .
Fiji & Greece . . . . . . . . .
Fiji & U.S.S.R. . . . . . . . . . .
Fiji & Congo . . . . . . .

Fiji & Guyana . . . . . . . .

West Germany & Brazil . . .

W. Germany & Central African Republic
West Germany & Greece . . . . . .
West Germany & U.S.S.R. . . . . . .
West Germany & Congo . . . . . . .

West Germany & Guyana . .
Brazil & Central African Republic .
Brazil & Greece . . . . . .
Brazil & U.S.S.R.

Brazil & Congo . . . . . . . . .
Brazil & Guyana . . . . . . . . .
Central African Republic & Greece .
Central African Republic & U.S.S.R.

Central African Republic & Congo .
Central African Republic & Guyana .
Greece & U.S.S.R.

Greece & Congo

Greece & Guyana . . . . . . . .
U.S.S.R. & Congo . . . . . . .
U.S.S.R. & Guyana . . . . . . .
Congo & Guyana . . . . . . .

162

Please read carefully the short messages on the following
three pages. Each message is about a pair of countries and consists
of a set of facts taken from the Encyclopedia Britannica. After you
have read each message, you will be asked to estimate ppy different
the two countries are according lp_ppg_message.

Differences between concepts are measured in units, so that the
mppg different two concepts are, the more units apart they are from
each other. To help you know how big a unit is, assume that Italy £29
England 332.199 units gpgpp.

If you think that according £p_ppg message two countries are mppg
different from each other than Italy and England, write a number larger
than 100. If you think that according £p_ppg message two countries are
_lg§§ different from each other than Italy and England, write a number
lgpg than 100. If you think that according £p_ppg message the countries
are exactly EES.§§EE’ write a zero (0). Remember, the mpg; different
the message says two countries are from each other, the higher the number

you should write. You may write any number you want.

163

FACTS ABOUT SINGAPORE AND FIJI

 

Fiji and Singapore are remarkably similar countries.

Both Singapore and Fiji are small, tropical island countries in
the Eastern Hemisphere (Singapore at the tip of the Malay Peninsula,
and Fiji in the South Pacific north of New Zealand). Both countries
have tropical climates——hot, humid and quite uniform in temperature.

Fiji and Singapore are both former British colonies which have
attained independence within the past decade. Both countries are
relatively stable parliamentary democracies, with multiple political
parties and legal systems rooted in the British tradition. Fiji and
Singapore are both members of the British Commonwealth of Nations.

In each of the two countries the majority of citizens are non—
European, but are not racially native to the country. This is due to
migration during the colonial period. The majority of Singapore is
Chinese, although the native population of the islands is Malay. In
Fiji the descendants of emmigrants from India outnumber the native
Fijians. So both countries have non—native majorities.

Another unusual feature is that both Singapore and Fiji can
claim an achievement that is the envy of many other developing coun—
tries: successful family planning programs have substantially reduced
birth rate in both countries. That should facilitate improved standards
of living in the future.

(Card 15) Remember: ITALY and ENGLAND are 100 UNITS apart.
Dup 1—6
15 7—8

How far apart are Singapore and Fiji according pp
the message?

9-12 UNITS APART

164

FACTS ABOUT CONGO AND GUYANA

 

Guyana and Congo are two very different countries.

Congo is a former French colony located in Central Africa.
France continues to control much of the economy of Congo, and French
is the official language of the country.

The governments of Congo since 1960 have become increasingly
militaristic and authoritarian. The country is ruled by a single
political party, and there is no national assembly or parliament.
Congo, in addition, is a self—proclaimed Communist state which intends
to develop a socialist economy.

The citizens of Congo are predominantly the same black peoples
who inhabited the region before the arrival of the French. Immigration
from abroad during the colonial period was relatively low.

Guyana, located in Northeastern South America, is a former
British colony, and is a member of the British Commonwealth of Nations.
The economy and culture of Guyana are still strongly influenced by the
British. English is the official language of the country.

Guyana is a parliamentary democracy, with several political
parties and a British—based legal system. Guyana has a private enter—
prise economy, such that there is only minimal government participation
and control.

The largest racial group in Guyana is East Indian. The native
American Indians are a small minority of the population.

(Card 15) Remember: ITALY and ENGLAND are 100 UNITS apart.
How far apart are Congo and Guyana according pp the

message?

13-16 UNITS APART

165

FACTS ABOUT PORTUGAL AND BRAZIL

 

Portugal and Brazil are closely related nations.

Brazil is made up of the former Portuguese colonies in South
America. Alone among the nations of South America, Brazil has adopted
Portuguese as the official language. Along with the Portuguese language,
Brazil has imported much of the culture of Portuga1-—for example, the
tradition of a patriarchal family structure. Both countries are over-
whelmingly Roman Catholic. Over the years, the bulk of immigrants to
Brazil have been from Portugal.

During the colonial period the ties between Portugal and Brazil
were remarkably strong. In fact, Brazil became the seat of the Por—
tuguese monarchy and government for a period of fourteen years during
and shortly after the Napoleonic wars.

Soon after, Brazil became independent, but the two countries
have retained close ties and many similar traits. The two countries
have become urbanized and industrialized in roughly parallel fashion;
while agriculture in both countries has remained highly traditional
and inefficient.

At the present moment, as has rather frequently been true in

their modern histories, both Brazil and Portugal are ruled by military—
dominated governments.

(Card 15) Remember: ITALY and ENGLAND are 100 UNITS apart.
How far apart are Brazil and Portugal according pp

the message?

17-20 UNITS APART

166

Dear Participant,

This is the second part of a study of human information processing.
The purpose of the study will be explained more fully after the question-
naires have been collected.

Please follow the instructions carefully. Answer all qpestions.

 

Leaving blanks unfilled may make your questionnaire unusable. Always
put down an answer, even if you have to guess. Complete each page
before going on to the next.

If for any reason you do not wish to participate in this study,
just do not fill out the questionnaire.

Thank you very much for your cooperation.

Sincerely,

Robert T. Craig

 

What is your date of birth? PLEASE DO NOT
Month Day Year WRITE IN THIS
SPACE
What is your sex? Male (Card 1)
0
No._________
Female 1 2 3
1
Gp. ______ WV LL
4 5 6
Card Jl_ll_
7 8
Yr, Sx

 

APPENDIX B

PROGRAM TESTLAW

 

 

167

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27¢ CONTINUE

APPENDIX C

COORDINATE MATRICES FROM GALILEO

173

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ha ~« 5 . a Na
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sakes! NmNo: monoonl unnon40 msmomoc
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m t n N a

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