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RESPONSE HIERARCH-IES IN PRODUCTIVE THINKING

Thesis for the Degree of Ph. D.
MICHIGAN STATE UNIVERSITY
RICHARD PAUL STRATTON-
1970

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Response Hierarchies
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Productive Thinking

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Richard Paul Stratton

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ABSTRACT

RESPONSE HIERACHIES IN PRODUCTIVE THINKING
By

Richard Paul Stratton

In an effort to investigate processes involved
in productive thinking, this experiment tested the
response hierarchy theory of problem solving with a
problem requiring subjects to write a series of
sentences. This theory predicts that under free
responding instructions, as more solutions are
produced, the solutions will be less like initial
solutions and will be Judged to be of higher quality,
i.e. more clever, etc. The quality dimension will be
based on criteria which reflect prior learning. Since
the sentence problem requires subjects to write many
sentences which include four given words, there
could be associative hierarchies involving pairs of
the given words and word meanings. The theory would
predict that strong adjective-noun associations and
popular word meanings would appear early in a series

of solutions. Remote associations and unusual meanings

Richard Paul Stratton

would appear later and should be correlated with high
quality. Under instructions which restrict responding
by specifying criteria for high quality solutions,
early solutions should be the same as later solutions
in all respects, i.e. there should be no response
hierarchy.

The present experiment used two naive Judges to
evaluate quality on a scale from one (low) to seven
(high). Interjudge reliability was .86. With criteria-
cued instructions and non-criteria-cued instructions
regression analyses indicated that quality could be
predicted by the number of word pairs (negatively
correlated), unusual meanings, and sentence length.
Quality increased over the response sequence for
noncriteria-cued instructions when subjects wrote five
or ten solutions, but not with criteria-cued instructions
and ten solutions. Average quality was not significantly
affected by quantity or criteria-cued instructions.

The eXperimental treatments involved subjects
learning six sentences prior to producing solutions.
These sentences included word pairs, unusual meanings,
relevant words without pairs or unusual meanings, or
irrelevant words. Results for subjects learning irrelevant
sentences or none at all were identical. Learning word
pairs increased the associative strength between the

learned adjective-noun pairs such that (a) more word pairs

Richard Paul Stratton

were used, (b) learned pairs shifted upwards in the
associative hierarchy such that they were given more
frequently and earlier in the response sequence,

(c) sentence length decreased, and (d) mean solution
quality was lower. Learning sentences with relevant,
but unpaired, words increased the use of word pairs,
but relative position of pairs within the associative
hierarchy did not change from that shown by control
conditions. Also both conditions increased the
associative strength between the words and their most
common meanings, so that less unusual meanings were
used. In both conditions quality increased as more
remote associations were used.

Learning sentences with unusual meanings also
increased the number of word pairs used, but the nouns
acquired more new and unusual meanings. As more
solutions were produced, unusual meanings became more
unique, hence quality increased over the response
sequence. Mean quality for this condition was higher
than for other conditions, because unusual meanings were
more highly weighed in judging quality than other
-variab1es.

These data were interpreted to be consistent with
the response hierarchy theory and the general view that
creativity involves a process of breaking up old

associations and forming new ones, i.e. a divergent

Richard Paul Stratton

process. To the extent that externally or internally
produced instructions provide cues to high quality
solutions, the response hierarchy may be by-passed or
may remain covert. Then no low quality solutions
will be recorded, and no response hierarchy will be

apparent in the solutions.

RESPONSE HIERARCHIES IN PRODUCTIVE THINKING

By

Richard Paul Stratton

A THESIS

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

DOCTOR OF PHILOSOPHY

Department of Psychology

1970

,_ A I { ‘J
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To Karin and Jason

11

ACKNOWLEDGMENTS

The good parts of this paper reflect the assistance
of many people. To my wife, Karin, I owe a debt of
gratitude for her consistent support and encouragement.
Dr. Donald M. Johnson helped in many ways, so much so
I am sure that he will never be aware of all that he has
done. Drs. Gordon Wood, John Paul McKinney, and Charles
Hanley gave much of that invaluable practical advice
which is evident in every section of this paper. As a
student I was privileged to be acquainted with many
teachers who became models of what good teachers and
researchers were like. I hope I may do the same for my
students. As a son I was privileged to have parents who
have helped in so many ways for so long. I hope that I

can do that much for my son.

iii

TABLE OF CONTENTS

Page
DEDICATION . . . . . . . . . . . . . . ii
ACKNOWLEDGMENTS . . . . . . . . . . . . iii
LIST OF TABLES. . . . . . . . . . . . . vi

LIST OF FIGURES . . . . . . . . . . . . viii

LIST OF APPENDICES . . . . . . . . . . . ix
Chapter
I. INTRODUCTION . . . . . . . . . . l
Maltzman' 3 Approach. . . . . . . 3
Response Hierarchies in Recall Problems . 5
Response Hierarchies in Creativity

Problems. . . . . . . . lO
Theories of Creativity . . . . 13

Response Hierarchies in the Sentence
Problem . . .- . . . . . . . 16
A Pilot Study . . . . . . . . . 20
Summary . . . . . . . . . . 21
The Present Study . . . . . . . . 22
II. METHOD. . . . . . . . . . . . . 27
Subjects . . . . . . . . . . . 27
Materials . . . . . . . . . . . 27
Procedure . . . . . . . . . . . 29
III. RESULTS . . . . . . . . . . . . 31
Solution Scoring. . . . . . . . . 31
Standard Instructions . . . . . . . 33
Quality and Position. . . . . . . 3A,
Predicting Quality . . . . . . . 36
Response Measures and Position . . . 39
Effects of Quantity Instructions. . . Al
Criteria-cued Instructions . . . . . AA
Quality and Position. . . . . . . AA
Predicting Quality . . . . . . "6
Response Measures and Position . . . 48
Effects of Quantity Instructions. . . A9

iv

Chapter Page

Quality and Quantity Instructions . . 52

Effects of Learning Old Pairs . . . . 52

Use of Word Pairs . . . . . . . 5A

Other Response Measures . . . . . 62

Solution Quality . . . . . . . 65

Predicting Quality . . . . . . . 66

Word Pairs in Group NClO . . . 68

Effects of Learning Unusual Meanings. . 69

Use of Unusual Meanings . . . . . 70

Solution Quality. . . . . . . . 70

Other Response Measures . . . . 76

Analyses of Group TUM Solutions. . . 76

Intersentence Associations . . . . . 8“

IV DISCUSSION . . . . . . . . . . . 9O
Divergent Processes Under Normal

Conditions. . . . . . . . . . 91

Old Pairs. . . . . . . . . . . 95

Unusual Meanings . . . . . . . . 105

Instructional Effects. . . . . . . 111

V SUMMARY . . . . . . . . . . . . 115

BIBLIOGRAPHY . . . . . . . . . . . . . 118

APPENDICES . . . . . . . . . . . . . 123

'Pable

10.

ll.

12.

13.

LIST OF TABLES

Rating Guide for Sentence Problem .

Intercorrelation Matrices for Response
Measures of Solutions from Group N010
and NC5 o o o o o o o 0

Means and S.D.'s for Response Measures
of Solutions in Groups N010 and NCS.

ANOVA Summary for Response Measures of the

First Five Solutions of Groups N010 and
NCS . . . . . . . . . . . .

Intercorrelation Matrices for Response
Measures of Solutions in Group CClO and
C05 0 O O O O O O O O 0

Means and S.D.'s for Response Measures of
Solutions in Groups CClO and CCS

ANOVA Summary for Response Measures of
First Five Solutions in Groups CClO and
cos c o o o o o o o o o 0

Means and S.D.'s for Quality of Solutions
in Groups NClO, NCS and CClO, CCS . .

ANOVA Summary for Old Pairs in Solutions
in Groups NClO, TOP, TR and TIR

Means and S.D.'s for Response Measures of

Solutions in Groups NClO, TOP, TR and TIR.

ANOVA Summary for Response Measures of
Solutions in Groups NClO, TOP, TR, TIR.

Frequency of Use and Position for Each
Word Pair in Solutions for Groups NClO,
TOP and TR . . . . . . . . .

Intercorrelation Matrix for Group TOP.

vi

Page

19

38

A2

‘43

M7

50

51

53

56

58

59

61
67

Table

1A.

15.

16.

17.
18.

19.

20.

21.

Al.

A2.

A3.

A4.

Page

ANOVA Summary for Unusual Meanings in
Solutions in Groups NClO, TUM, TR and
TIR o o o o o o o o o o o o 72

Means and S. D. 's for Response Measures
of Solutions in Groups NClO, TUM, TR

and TIR . . . . . . . . . . . 7A
ANOVA Summary for Response Measures of

Solutions in Groups NClO, TUM, TR and TIR. 75
Intercorrelation Matrix for Group TUM . . 78
Use of Unusual Meanings in Group TUM

Solutions . . . . . . . . . . . 79
Mean Position of Unusual Meanings as a

Function of Frequency of Occurrence. . . 80
Mean Number of Associations per Subject . . 86

Correlations between Solution Quality .
and Associations . . . . . . . . . 87

Intercorrelation Matrix for Quality and
Descriptive Variables . . . . . . . 128

Factor Matrix for Varimax Rotations with
Intact Sample . . . . . . . . . . 129

Factor Matrices for Varimax Rotations with
Split Sample . . . . . . . . . . 131

Factor Matrix for Oblique Rotation with
Intact Sample . . . . . . . . . . 132

vii

LIST OF FIGURES

Figure Page

1. Group NClO, ten solutions (solid line)
and Group N05, five solutions (broken
line). Means for response measures as
a function of position . . . . . . . 35

2. Group CClO, ten solutions and criteria-
cues (solid line) and Group CC5, five
solutions and criteria-cues (broken line).
Means for response measures as a function
of position. . . . . . . . . . . A5

3. Groups NClO, TOP, TR and TIR. Mean number
of old pairs as a function of position. . 55

4. Groups NClO, TOP, TR and TIR. Mean quality
as a function of position . . . . . . 63

5. Groups NClO, TUM, TR and TIR. Mean number
of unusual meanings as a function of
position. . . . . . . . . . . . 71

6. Groups NClO, TUM, TR and TIR. Mean quality
as a function of position . . . . . . 73

7. Group TUM. Cumulative percentage of unusual
meanings as a function of position . . . 82

viii

LIST OF APPENDICES

Appendix Page

A. A Quantitative Description of Responses
to the Sentence Problem . . . . . . 12a

B. Memory Tasks for Groups TOP, TUM, TR

and TIR . . . . 136

ix

CHAPTER I

INTRODUCTION

A "problem" exists as a problem, because the
required response is initially not preeminent in the
,‘problem solver's response repertoire. Although this
definition may be acceptable to most researchers in
the field, the reason why the required response is
not preeminent is a source of considerable
disagreement.

Beyond this initial distinction problems may be
classified as to the number of possible solutions.
Many common problems, like Maier's two—string problem
or an arithmetic problem, require a single solution
which is either correct or incorrect by some obvious
criterion. Other problems, like what title to use
for a table of data, have several possible solutions,
but only a few desirable solutions. Lastly, there are
the problems which have an almost infinite number of
possible solutions and a large number of desirable
solutions. Writing a clever sentence which includes
four specific words is an example of this type of
problem. Furthermore, solutions to the latter may be
easier to produce, but are certainly more difficult to

SCOPE.

Guilford (1967) uses these differences between
problems to separate convergent thinking (toward one
solution) from divergent thinking (toward several
solutions). Divergent problem solving has also been
designated as productive thinking, orginality, or
creative thinking by various researchers. The present
study will investigate problem solving processes
involved in solving divergent problems.

Problem solving may be viewed as being similar to
learning. A pigeon in a Skinner box for the first
time has many responses available to him. Learning is
said to have occurred when the pecking response becomes
dominant over grooming, fear and other irrelevant
responses. When a problem is encountered by a human,
the first solution omitted cannot be the best solution,
or it would not be a problem. Other ineffective
responses must be eliminated before the solution
response can become preeminent. Perhaps it is this
striking similarity between learning and problem solving
that prompted Maltzman, Cofer and others to analyze
problem solving processes in terms of learning theory.
This introductory discussion will deal specifically with
Maltzman's approach, and supportive evidence will be
given first for recall problems, then for the more

complex creativity problems.

Maltzman's Approach

Maltzman (1955) analyzed problem solving processes
in terms of Hull's principles of learning. This
extension focused upon Hull's concept of a spatial habit
family hierarchy. In this type of hierarchy, groups
(or families) of similar responses are arranged in
hierarchical order in terms of the probability of
occurrence, which is determined by habit strength,
drive, etc. A spatial habit family hierarchy represents
the hierarchical ordering of motor responses, and
habit strength of motor responses varies as a function
of spatial location relative to the goal.

In human problem solving, however, responses to
changing spatial relations to a goal are rarely
elicited. More commonly responses are verbal, and
response changes are related to temporal proximity to
the solution. Maltzman represented human thought as
a compound temporal habit family hierarchy and assumed
that principles operating in the spatial habit family
hierarchy would also operate in temporally-based
hierarchies as well.

As in simple trial—and-error learning, a problem
stimulus is capable of eliciting a hierarchy of responses,
and the correct response is initially low in the hierarchy
superseded by incorrect responses of greater habit

strength. According to Maltzman, the order of dominance

in the response hierarchy may be changed as a result of
three processes. (a) Dominant responses may be
elicited, and the effective reaction potential of these
may be reduced as the result of extinction. (b) The
probability of occurrence of a habit family containing
correct responses could increase due to reinforcement
of individual members of that habit family. (c) The
arousal of an anticipatory goal response would produce
an increment in effective reaction potential for
related responses. The antecedent condition for the
anticipatory goal response would be commerce with the
goal or a goal substitute, such as instructions which
describe the goal.

The application of a response hierarchy
interpretation to convergent problems with one correct
solution is straightforward. Divergent problems would
be expected to follow similar processes with "good"
solutions behaving as correct solutions would in
convergent problems. The unusual uses problem will
serve as an example. In this problem §s are required
to write many uses of a common object, such as a brick.
The most desirable solutions are usually defined by
the experimentor as solutions which are infrequent in
a large sample of solutions obtained from many §$'

For the uses of a brick an uncommon use would be to

crush it and use it as a filter for a moonshine still.

A common use would be to use a brick for building a house.
According to Maltzman common uses of an object are omitted
and reinforced more frequently in everyday life, and
subsequently common uses are more likely to be given for
similar laboratory problems. .Thus, it may be said that
the many uses of an object form a response hierarchy based
on frequency of occurrence and concomitant reinforcement.
Such a response hierarchy would be evidenced when an
individual produces a series of solutions and the common
uses precede the uncommon ones. I

Maltzman has been very careful to distinguish
between orginality, where his theory was meant to apply,
and creativity. The latter was said to conjure up the
unfavorable connotations of individual differences, social
influences, and the social value of solutions which cannot
be controlled in the laboratory setting. Mednick (1962),
on the other hand, assumes associative hierarchies, as
does Maltzman, but uses them to account for individual
differences in creativity. Although the present approach
emphasizes solution processes and solution characteristics,

it clearly does not deemphasize individual differences.

Response Hierarchies in Recall Problems
For the purposes of organization, divergent problems
will be classified as to the degree to which problem

solution depends upon simple recall. Verbal association

problems may be seen as one end of the continuum where
responses are stored in memory,and problem solution
depends upon memory scanning. Initial solutions to the
unusual uses problem are simply recalled, but, after
these common solutions are exhausted, uncommon solutions
must be constructed from what the problem solver knows
about the object, its uses, etc. At the extreme are
problems like the sentences problem where §s are only
given four words and must construct sentences which
include all four. In this case every solution must be
constructed from scratch, since the problem solver has
never previously encountered the problem or its solutions.
In accordance with other researchers, recall problems
in this discussion will include verbal association,
anagram and unusual uses problems. Creativity problems
will include plot title, sentences and similar problems.
Initial evidence which may be cited in favor of
Maltzman's approach was presented by Christensen,
Guilford and Wilson (1957). In this study subjects were
required to produce several solutions to a variety of
problems. Unusual uses of a button and pencil were
requested, and the number association problem consisted
of writing down things commonly associated with the
given numbers. An example of the latter would be

"four-square." The frequency of occurrence of each

solution was tallied, and each solution was given a

value for uncommonness based on this frequency. It

was found that, as Ss proceeded through the response
sequence, the solutions became more uncommon.

Duncan has published several studies which present
evidence for verbal response hierarchies based on
association strength and frequency of occurrence in the
language. Duncan (1966a) presented §s with a stimulus
word and a list of five associates to the stimulus.

The task was to guess which associate was "correct."

The order of their guesses proceeded from the strongest
to the weakest associates. When §S were told to guess

a word with a particular association level to the
stimulus, §S were very accurate on the first guess and
got more accurate with subsequent guesses (Duncan, 1967).
In the unusual uses problem Manske and Davis (1968) and
Turner (1967) note that responses were omitted in
associative clusters (e.g., uses of a tire were "use as
a wheel for a car, bike, boat trailer, etc."). They
suggested that the order of association went from
strongest to weakest.

Frequency of occurrence of a word in the language
is also a powerful variable in other verbal problems.
In Duncan's (1966b) study Ss were presented with the

first and last letter of a five-letter word, and the

task was to guess what word was intended. The several
solutions for each problem varied in frequency, and
the number of solutions omitted was greater for words
of higher frequency. When the number of possible solu—
tions was restricted to one high and one low frequency
word, first guesses contained more high frequency
solutions. In another experiment the task involved
finding a word of a given length, beginning with a
given letter and being in a given class, for example
"trees." With only two possible solutions, when the
high frequency solution was given as an example, more
low frequency solutions were given. When the low fre-
quency word was given as an example, there was no
increase in the number of high frequency solutions.

In anagram problems frequency is one of the most
powerful variables determining success and solution time
(Johnson, 1966). Anagram solution time is inversely
related to the frequency of the solution word when there
is only one possible (Mayzner and Tresseit, 1958;
Dominowski, 1965 and 1967). With more than one possible
solution the order of emission of solutions will
correspond to the frequency of the solution word (Johnson
and Van Mondfrans, 1965). When the solutions vary in
frequency and Se are required to find both solutions, the

high frequency solution is given first (Mayzner and

Tresseit, 1966). In these studies past experience in
the form of frequency of usage determined the position
of the responses in the verbal hierarchy.

The response hierarchy concept has been used by
Geriach, Shutz, Bakerand Mazer (1964) to explain the
results of some brainstorming research. They used the
unusual uses problem and hypothesized that a response
hierarchy would exist with these problems such that §s
would give the most common response first and subse-
quently work down the hierarchy to less common responses.
Their results showed that more "good" responses (based
on judged uniqueness and value) were produced in the last
two-thirds of the production sequence. Importantly, when
S3 were informed of the criteria by which their solutions
were to be evaluated (criteria-cued instructions), such
a production order did not exist. Using the same type of
problems Parnes (1961) and Manske and Davis (1968) have
also found that quality was related to position in the
response sequence without criteria-cued instructions, and
with criteria-cued instructions that relationship was
weaker if it existed at all.

The preceeding studies using the unusual uses
problem and criteria-cued instructions found that these
special instructions increased mean quality and disrupted

the response hierarchy such that quality was unrelated to

10

position within the response sequence. These results
would be explained within the Maltzman (1955, 1962)
framework as being due to instruction-induced
anticipatory goal responses. The brick uses problem
will serve as an example. When a long series of uses

is elicited, the uses usually are recorded in associative
clusters (Manske and Davis, 1968, Turner, 1967).

Members of a cluster would have some property in common,
such as a "weight use." Now let us say that the task
instructions in addition to presenting the problem do
not explicitly state, but implies, the desirability of
weight uses. These instructions would be the external
stimulus, and the internal representation (or the
derived implication of "weight use") would be the
anticipatory goal response which in turn would key off

a series of weight use responses. Maltzman specifically
discusses instructions as one source of the anticipatory
goal response. In essence, the anticipatory goal
response resembles a description of the desired solution
and may be derived from task instructions or self-
instruction. The result is that only a specific type

of response is recorded, and the usual progression

from common to uncommon responses is eliminated.

Response Hierarchies in Creativity Problems
The results of several experiments suggest that

creativity problems may have response hierarchies

11

associated with them. Christensen, 33 al. used the
consequences problem and the plot title problem in
addition to the ones already mentioned. The consequences
problem asks such questions as "what would be the
consequences if everyone in the world suddenly went
blind?" Solutions were scored by judges on a three—
point scale for the remoteness of the consequence from
the initial situation. For example, "there would be a
lot of stumbling" is less remote than "the congenitally
blind would become world leaders." Solutions in the
second half of the production sequence were significantly
more remote than those in the first half. They also
used the plot title problem. The plot titles were
rated by judges for cleverness and appropriateness, but
no improvement was found over the production sequence.
Importantly Plot Title instructions asked for "clever"
or "apprOpriate" solutions. With criteria-cued instruc-
tions the response hierarchy would be disrupted to the
extent that one would not expect the normal ordering of
responses. Instead SS were just as likely to produce
good solutions in the first half of the production
sequence as in the last half.

Johnson, Parrott and Stratton (1968) worked with
the plot titles problem and four similar problems. The
solutions were judged for "quality" based on criteria

which varied with the problem. (a) They found that

12

solutions above the 90th percentile in quality were more
likely to occur in the last half of the production
sequence for the plot title, sentence and cartoon

caption problems. The ordering was found, however, only
if instructions did not contain reference to evaluation
(i.e. were not criteria-cued instructions). (b) An
individual problem solver produced six to seven solutions,
on the average, but the solutions varied widely in quality
(the median range of quality was seven points out of 13).
Thus it would have been possible for each individual

to have produced some poor solutions before producing
some good ones. (c) Finally, §S writing one solution
had a higher mean quality than SS writing several
solutions. Since all §S had the same time to write
solutions, single-solutions SS could have covertly
produced and rejected several inferior solutions while
multiple-solution §S recorded every solution. By
producing and rejecting some solutions, single—solution
gs could have advanced further down the response
hierarchy to better solutions. They would also have had
more time to produce solutions, since they did not write
down unacceptable solutions. These results, although
based on judged quality, are similar to those obtained
with statistical frequency (unusual uses problem) or

judged remoteness (consequenCes problem).

13

Johnson (1968) reports a study, designed by
Stratton, using four different problems where production
time was limited. There was a significant increase in
quality for Ss writing one solution in two or four
minutes over SS writing one solution in a half-minute
or one minute. With criteria—cued instructions a half
of a minute was as good as four minutes in producing
one solution. Response hierarchies may be invoked as
one explanation for these data. Without criteria-cued
instruction one way to produce good solutions would be
to advance down the response hierarchy by producing and
rejecting several solutions. Limiting time then would
limit the consideration of alternative solutions.
Criteria-cued instructions would have made more time
unnecessary for the construction of good solutions by

providing cues to the nature of the desired solution.

Theories of Creativity

 

Mednick and Guilford present theories about
creativity which stress individual differences, but
which make assumptions about solution processes in
creativity problems. Most theories of creativity
assume the solution process to be a divergent one, so
the ones discussed here will be more exemplary than
exhaustive. The divergent nature of the creative

process is quite similar to the notions of British

1L:

associationists from Locke (1690) to Bain (1855).
Psychologists whose work reflects the speculations of
the associationists also argue for divergent processes
in creativity. Freud (1938), Hollingworth (1928) and
Binet (1899) will serve as examples. Golann (1963)
presents an excellent summary of theories of creativity,
and he concludes that divergent mechanisms are included
in most theories.

Mednick (1962) stresses the associative nature of
creativity as a basis for a theory about individual
differences. He defines creative thinking as "the
forming of associative elements into new combinations
which either meet specified requirements or are in some
way useful. The more mutually remote the elements of
the new combination, the more creative the process of
solution (p. 220)." Based on this assumption Mednick
proposes to separate the creative from the noncreative
person. When a creative person free associates to a
stimulus word or produces a series of solutions to a
problem, the associative strength between the stimulus
and each successive response would be approximately
equal. The associative strengths for a noncreative
person would be very high for the first few responses
and very low for the remainder of the responses. As
a result the noncreative person does not produce as

many uncommon solutions. Were one to plot associative

15

strength as a function of position in the response
sequence, a creative person would show a flat associative
hierarchy, a noncreative person would show a steep
associative hierarchy.

Mednick's definition is a reapplication of the old
maxim that great discoveries are just old ideas combined
in new ways. Relating it to the unusual uses problem
one can see its possible validity. Let us assume that
our intuitive notion of the associative strength
between the word "tire" and its uses will suffice for
empirical data. The use of a tire as "to put on the
wheel of an automobile" may be said to have high
associative strength. The use of a tire as "to burn
for keeping fruit trees warm during the spring frosts"
has a low associative strength. Thus, a creative
person would be able to produce many solutions of all
associative strengths, or perhaps to produce all
solutions of low associative strengths. The noncreative
person, on the other hand, would produce common uses
with high associative strengths and few uncommon ones.
Furthermore, Mednick assumes that an individual's
organization of associations will influence the
probability and speed of attainment of a creative solution.
Creative people, then, are assumed to store experiences

differently from noncreative people.

16

Guilford's (1967) approach is based on his familiar
structure-of-intellect model. The plot title, remote
associates, consequences, and unusual uses problems are
included in the cell called "Divergent Semantic Trans-
formations" (DMT). Previous researchers had called this
the orginality factor. The assumptions underlying this
factor are illustrated by the fact that tests loading on
this factor emphasize either (a) ability to produce
responses that are statistically rare in the population,
(b) ability to produce remotely related responses, or
(c) ability to produce clever responses. Verbal fluency,
foresight, reasoning and other problem solving abilities
are included in other factors. In the DMT factor the
emphasis is on production of semantic units which
differ from the original problem by being uncommon,
remotely associated or clever responses (i.e. are
transformations of stored information). His model for
problem solving and creative production emphasizes the
recall and transformation of information to create new
informational products.

Response Hierarchies in the
Sentence Problem

 

 

The above results and theories suggest that
creativity problems may also have response hierarchies

associated with them. To examine this question further

17

it would be necessary to establish two things: (a) that
responses are ordered along some dimension when there

are no criteria—cued instructions, and (b) that this
dimension is responsive to learning. Christensen, gt _1.
found a progression of solutions to the consequences
problem which went from less to more remote between halves
of the response sequence. Johnson, et a1. obtained the
same results with Plot Titles, Sentences, and Cartoon
Captions.

In the problems used by Johnson, 33 al. the dimension
upon which the resposes were ordered was "quality," as
defined by two judges. Unlike the "commonness" of Unusual
Uses solutions, "quality" is more difficult to define,
especially since the criteria on which quality is rated
varies between problems. In the Johnson, 33 a1. study
the judges rated the quality of about a thousand solutions
to a problem, then they constructed a Rating Guide, which
expressed the characteristics of the solutions at each
quality level. If learning does determine the order of
solution production, it may be illustrated by the
characteristics on which quality was evaluated.

The sentence problem will serve as an example. The
task for this problem is to write many sentences, each

of which includes the words happy, expensive, horse, and

 

lake. The basic criteria for evaluation were that

sentences include all four words and be grammatically

18

well—constructed, and that the words appear unobtrusive
in the sentence. The solutions were rated by each
judge on a scale from one (bad) to seven (best).

Table 1 summarizes the criteria by which solutions
to the sentence problem were evaluated. There are
several criteria which may reflect learning. (a)
Grammatical structure is learned prior to the experiment.
On the other hand, the length and complexity of sentences
could be increased if Ss learned from one sentence to
another, i.e., built each sentence upon elements of
preceeding sentences. From the Rating Guide it is
apparent that better sentences are those which are
longer, more complex and grammatically well-constructed.

(b) The adjectives and nouns have varying degrees
of associability which may be attributed to usage
prior to the experiment. When two of the given words
appear together, they are called an "old pair." For

example, the old pair happy horse appears more frequently

 

and makes more sense than happy lake. Solutions which

 

break up these pairs are given better quality ratings.
Maier (1967) introduced this concept to measure the
reorganization of experience in creative problem solving.

(c) The meanings of the given words are well
established prior to the experiment. Each word normally
has several meanings, but some are more common than

others. A horse is initially "a four-legged mammal with

19

TABLE 1.--Rating Guide for Sentence Problem

 

The sentence must have these

 

For a rating of characteristics
1 does not use all four words.
2 lists the words.
3-5 a clumsy, mediocre sentence.
A—7 well—constructed sentence

with words having novel
meaning or usage (e.g.,
Horse Lake).

6-7 well-constructed sentences
which are clever or humorous.

Additional considerations: any rating may be increased
one point

(a) if the sentence is complex, and

(b) if happy and expensive modify nouns other than
horse or lake.

N. B. "A" is an average rating.

 

20

solid hoofs and a flowing mane and tail," but it is also
”slang for heroine, a sawhorse, gymnastics vaulting

' or the verb "to horse around." These unusual

horse,’
meanings receive consistently higher ratings. Osgood
(1953) proposed that meanings form associative hierarchies
with their words such that some meanings are more highly
associated with a word and would tend to be the first
meaning recalled and used to solve a problem.

(d) Finally, good sentences incorporated the
given words into their context so well that the judge
had to look twice to make sure all four words were used.
The obtrusiveness of the given words is reflected in
the subject and direct object of the sentence, and
better solutions use words other than the given ones
for the subject and direct object clauses. This reflects
learning in that, the more familiar a word, the easier
it is to have it function in any part of the sentence,
and SS become more familiar with a word as they use it
in more sentences. This variable is called "topic

freedom." Yngve (1960) described a similar measure to

relate word depth to syntactic structure.

A Pilot Study

 

To illustrate the potency of these variables a
pilot study will be briefly discussed (see also Appendix

A). Before the Rating Guide for the sentence problem

21

was constructed about a thousand solutions had been
evaluated by two judges with interjudge correlations
above. 80. The 215 complete solutions produced under
standard instructions were analyzed in terms of 16
variables including the above. A multiple regression
analysis showed that 50% of the variance in the judges'
ratings could be accounted for by sentence length,
sentence complexity, number of word pairs, unusual
meanings, and topic freedom. These variables correlated
with quality between .39 and .A6 (word pairs correlate
with quality -.38). The judges could see these features
of the sentences when rating the sentence. If a response
hierarchy in the sentence is based on quality and if

it is to be controlled by learning, it would be good

to look at the fate of these influential variables

over the production sequence.

Summary
The foregoing discussion suggests that better

solutions to creativity problems are uncommon in the
sense that they contain word uses, meanings and
associations which do not occur frequently in the normal
sample of solutions. In other words, better solutions
appear to diverge from the usual meanings, etc. normally

associated with the words in this problem. If quality

22

is related to these aspects of the solution, and if
quality is to increase over the response sequence,
initial solutions should be ones which most closely
correspond to the normal properties associated with

the problem elements. In the sentence problem the
elements are the words. Later solutions should use

less common meanings, etc. of the words and consequently
receive higher quality ratings. The same progression

of meanings and associations are assumed to occur if

§S were to simply produce all possible meanings and
associations. The first meanings produced, then,

would also be the first to be used in solving a problem.
The progression of solution quality would represent a
response hierarchy in that there would be an orderly
progression of solution quality which is determined by
learning prior to the experiment or during an experimental

treatment.

The Present Study

 

The major purpose of this study was to investigate
the existence of response hierarchies in creativity
problems. Two questions were investigated: (a) Does
quality increase over the response sequence? (b) What
conditions in the instructions and in the nature of the
words affect this increase?

The sentence problem was used with the words pgppy,

expensive, horse, and lake. Using a variety of words

 

23

would increase the generality of the results, but it
would be difficult to equate the quality ratings for
sentences using different sets of words. Thus, two
treatments were introduced to change the meaning and
associative characteristics of the nouns pppgg and lgkg.
These treatments also reflect the importance of learning
in establishing response hierarchies in this type of
problem.

The dependent variables were quality, sentence
length and complexity, number of old pairs (or word
pairs), number of unusual meanings, and topic freedom.
These variables were defined in the previous discussion.
The critical feature of the analyses was the variation
of these solution characteristics over the response
sequence.

Two groups of Ss were used to observe changes in
the above variables under "normal," or unrestricted,
production conditions. Group NClO wrote ten solutions
to the sentence problem and Group N05 wrote five
solutions. It was expected that quality would increase
over the response sequence, and that changes in other
highly correlated variables would indicate why the
change in quality occurred.

Two other groups were used to investigate the
effects of criteria-cued instructions. Group 0010

wrote ten solutions to the sentence problem, and Group

2A

CC5 wrote five. The additional instructions should
provide cues about desired solutions such that mean
quality would be higher and there should be no
increase in quality over the response sequence. This
would agree with previous research. Other dependent
variables would also show the solution characteristics
which accounted for the increase in quality.

There were two treatments designed to illustrate
the effects of the nature of the words on the observed
changes in quality and thus to show the importance of
learning in determining the order of solution production.
The first treatment was designed to increase the

associative strength between the words happy horse and

 

egpensive lake. The treatment for Group TOP consiSted

 

of learning six sentences which included both of these
old pairs prior to reading the problem and writing
ten solutions.

It was expected that the total number of old
pairs used in solutions would be greater in this group
than other groups. Furthermore, more old pairs should
be used initially than later in production. Because
quality is reduced by the use of old pairs, later
solutions should increase in quality.

The second treatment was designed to alter the
hierarchy of meanings associated with horse and lpkg_by

increasing the associative strength of unusual meanings.

25

Group TUM Ss learned six sentences which included novel
meanings before reading the problem and writing ten
solutions. It was expected that the total number of
unusual meanings used in solutions would be greater in
this group than in comparison groups. Because unusual
meanings are highly weighted in quality ratings, mean
quality should also be greater in this group. Further-
more, it was eXpected that other §s would have to
discover unusual meanings after the use of common meanings,
but Group TUM SS would start out using the same unusual
meanings. Thus, Group TUM §s should show no increase in
unusual meanings over the production sequence and
consequently no increase in quality.

There were three comparison conditions for the two
learning treatments. The standard comparison was
Group NClO where ten solutions were produced with standard
instructions. There were two controls for the learning
treatment. To control for learning sentences which used
the same words as the problem, Group TR §S learned
sentences which included the four given words but no
old pairs or unusual meanings. Group TIR was a control
for learning any sentences, and these §S learned
sentences with four other words. It was expeced that
the comparison groups would not differ from one another.

To summarize, this research may be conceptualized

as occurring in three phases: (a) A comparison of

26

instructional conditions of five or ten solutions
produced with or without criteria-cued instructions.
(b) An attempt to change solution quality by increasing
the associability of specific adjective-noun pairs.

(c) An attempt to change solution quality by increasing
the associative strength of uncommon meanings of the
nouns to be used.

The major hypotheses were: (a) Under instructions
with no criteria—cues, sentences will increase in quality
over the response sequence whether five or ten solutions
are requested. There should be no such increase with
criteria-cued instructions. (b) Learning old pairs will
increase the use of old pairs in solutions, and the use
of old pairs will decrease over the response sequence
with a concomitant increase in quality. (0) Learning
unusual meanings for nouns will increase the use of the
unusual meanings in solutions to the sentence problem,
but the use of unusual meanings will not increase over

the response sequence.

CHAPTER II

METHOD

Subjects

 

In each of the eight conditions there were
30 volunteer Ss. Males and females were roughly
equated across conditions. There were 31 additional
gs who did not complete the task or were randomly

discarded to equate the groups.

Materials

 

The sentence problem included the words happy,

expensive, horse, and lake. Ss were required to

 

produce five or ten sentences, each of which included
all four words.

The standard instructions read: "Your task in
this experiment will be to write ten (or five) sentences.

Each sentence must include the words happy, expensive,

 

pppgg and lpkg. You will have as much time as you need."
The criteria-cued instructions read: "Your task

in this experiment will be to write ten (or five) good

sentences. Each sentence must include the words pappy,

eXpensive, horse, and lake. Furthermore, a good

 

sentence is grammatically well-constructed and reads

smoothly. The four given words fit smoothly into the

27

28

sentence structure of a good sentence. You will have
as much time as you need to write ten (or five) good
sentences.”

The sentences used in the memory tasks were
selected from previous experiments and were equivalent
in judged quality and length between groups. The
mean quality of each set of sentences was about average.
The irrelevant sentences contained the words pig, glppg,
ppipg and mppgy, while relevant sentences included the
words to be used later in the sentence problem. Three
types of relevant sentences were used; without old
pairs or unusual meanings, with old pairs, and with
unusual meanings. Verbal instructions for memory task
Ss posed the situation as consisting of two short
unrelated experiments with the first being a memory
eXperiment. In addition to the standard instructions
for the sentence problems, Ss with memory tasks were
instructed "Do not simply copy the sentences you have
just learned. Think of your own." Memory task instruc-
tions and sentences for each group are included in
Appendix B.

The memory task and the problem were assembled in
booklet form. A cover sheet required S to record his
name, student number, etc. The memory task followed

if applicable. The heft page was for recording the

29

memorized sentences. The following page contained the
problem and sufficient space for recording the

required number of solutions.

Procedure

 

Three experimenters randomly assigned §S to
-treatments such that each treatment was represented
in almost every session. After.filling out the cover
sheets all groups were timed in subsequent activities.
The memory task took ten minutes, and Ss were given
15 minutes to record ten solutions or ten minutes to
record five solutions. SS were informed of the time
at various stages of production.

Group NClO wrote ten solutions to the sentence
problem and were given no criteria-cued instructions.

Group CClO was the same as Group NClO but had
criteria—cued instructions.

Group TOP memorized six relevant solutions which

included the pairs happy horse and expensive lake.

 

 

Then, they read the problem and wrote ten solutions
under Group NClO instructions.

Group TUM memorized six relevant sentences which
included several unusual meanings for pppgg and lgkg.
Then, they wrote ten sentences under Group NClO
instructions.

Groups TR and TIR were control groups. Group

TR §S memorized relevant sentences which did not have

30

any old pairs or unusual meanings. Group TIR Se memorized
irrelevant sentences. These groups controlled for famili—
arity with the problem or solutions. Both groups then
read the problem and produced ten sentences under Group
NClO instructions.

Group N05 was comparable to Group NClO, except that
§S were requested to write only five solutions.

Group C05 wrote only five solutions and had criteria-

cued instructions. This group is comparable to Group CClO.

CHAPTER III
RESULTS

Solution Scoringl

 

The obtained sentences were typed on IBM cards
and coded on the reverse side. Coding included the
group and subject numbers and the solution position,
After shuffling the solutions, two judges who were
naive as to the purpose of the experiment rated
solution quality from 1 (bad) to 7 (good). The data
for this experiment are the sum of these ratings. A
Rating Guide established in previous experiments assisted
in the rating (see Table l). Spurious agreement was
prevented by the first judge recording his rating on
the back of the card, and the second judge recording his
rating first on the front of the card, then on the back.
The correlation between the two judges' ratings for the
2100 solutions in this experiment was .86, which is
acceptable.

Prior to rating solutions for the present

experiment the judges trained on a judgment training

 

1The assistance of John Jerome, Bill Gould,
Jerald Wilbur and Karin Stratton in this stage of
the analysis is gratefully acknowledged.

31

32

program, which was developed and validated in another
experiment (Johnson, 22 al., 1968). The training
essentially presented the Rating Guide and practice in
discriminating good and poor solutions with examples
and feedback. It was designed to enable judges to
rate solutions on the same judgment scale as the
judges who developed the Rating Guide and on whose
judgment styles this experiment is based. After
training, the judges practiced with the seven-point
scale until they established a high interjudge
agreement.

After all solutions were scored for quality, each
solution was scored on the following variables by
different judges who were also naive: (a) Length--the

total number of words in the sentence. (b) Complexity--

 

a three-point rating based on the grammatical complexity

of the sentence. (c) Old Pairs——the number of times

 

happy horse and expensive lake occur in the sentence.

 

Total pairs or word pairs refers to all combinations of

 

the given words. (d) Unusual Meanings--meanings or

 

uses of the given words which differ from the ordinary,
e.g. "Happy Lake Dude Ranch" or "to horse around."

(e) Tgpic Freedom—-the number of times the given nouns

 

are used as other than the subject or direct object of

the sentence.

33

The identification codes and scores were then
punched onto IBM cards for computer processing.

With respect to the assumptions underlying the
analysis of variance tests to be used, it should be
noted that nowhere have the assumptions been violated
to the extent that the conclusions should be suspect
(Boneau, 1960). With 30 Ss per group, n = 300 for
comparisons between groups with ten solutions per S,
and n = 150 for comparisons between groups with five
solutions per S. Variances for these comparisons were
inspected and there were no differences as large as
3:1. The distributions are without marked skewness,
except for complexity and unusual meanings. Complexity
has a skewness of about -2.0 (zero for a normal
distribution) in each group. This results from a
ceiling effect of the three—point scale. Unusual meanings
are generally positively skewed at a value of about 2.0.
This is due to the fact that most solutions have no
unusual meanings in all but Group TUM. Boneau states
that with large samples and equivalent variances such
deviations from normality should have little effect
on obtained probability values, even when a J-shaped

distribution is tested against a rectangular distribution.

Standard Instructions

 

This section is concerned with two questions;

"Does quality increase over the response sequence under

3A

standard instructions?" and "How are changes in
quality mediated by response variables which reflect
learning?” This section will also present data on
the effects of quantity instructions on the

solution process.

Quality and Position

Figure 1 presents the mean quality for each
position in the response sequence for Group NClO with
ten solutions per S and Group NC5 with five solutions
per S. Both groups show a general increase in quality,
but it is more pronounced for Group NC5. Single-factor
analyses of variance for repeated measures across
positions tested the statistical significance of
changes in quality. Quality increases over the response
sequence in Group NClO (F = 2.76; df9, 26l:p<.01) and
in Group NC5 (F = 3.15; de, ll6:p<.05). Newman-Keuls
comparisons for repeated measures across positions show
for Group NClO that only position 5 solutions are of
higher quality than solutions in positions 1 or 3
(p<.05). For Group NC5 the same comparisons show that
the solutions in position A and 5 are better than those
in the first position (p<.05).

The question posed initially may be better answered
by analyzing the variance between positions for a
linear trend component. The curve of best fit should be

linear and have a positive slope. A trend analysis for

Mean

Mean

Mean

9.0

 

35

QUALITY 18'

 

 

 

 

 

1

8.5 7
16

8.0
15
705 14
7.0 13
2'9 COMPLEXITY 1'1
2.7 .9
2.5 .7
2.34;- --A-- .5
'7 UNUSUAL "3

MEANINGS

.5
1.1

.3
.9

 

 

 

 

. a

V

 

LENGTH

 

 

 

 

I TOPIC

FREEDOM

 

 

1 5 3.11 5 £3 i i3 9 10
Position

.1 - - A .__11. .4 - - - A
‘1 2 :5 A 55 6 '7 8 £9 10
Position
Fig. 1. Group NCIO, ten solutions (solid line) and

Group N05 (broken line). Means for response measures
as a function of position.

36

repeated measures indicates for Group NClO that 22.6%
of the variance between positions may be predicted by
a linear regression. Nonlinear trends are nonsignificant.
The linear equation giving the best fit for quality in
Group NClO is: Y = .095X + 7.A7, where Y is quality and
X is position. The slope is small but positive, and
the linear correlation between position and quality is
.128. Since this correlation takes into account the
within-position variance (n = 300), this correlation is
statistically significant at the .05 level, but it
accounts for only a meager portion of the total variance
(1.6%).

For Group NC5 the linear regression accounts for
79.8% of the variance between position with no
significant nonlinear trends. The curve of best fit is:
Y = .3A3X + 7.12. The linear correlation (n = 150)
between position and quality is .232 which is significant
beyond the .01 level and accounts for roughly 5.A% cf

the total variance.

Predicting Quality

 

In both groups there is a linear increase in
quality over the response sequence.' The next question
is, "How can learning variables account for this change?"
This section will probide a partial answer by looking at
multiple linear regression analyses and analyses of

variance.

37

The present experiment emphasizes the importance
of quality—related response measures such as unusual
meanings and old pairs, because in judging solutions
from previous experiments these variables were found
to be influential in determining solution quality
(see Appendix A). Table 2 gives the correlations
between response measures for Groups NClO and NC5.
Correlations between single solutions are confounded by
the covariance due to each S writing several
solutions. To prevent this, response measures were
summed to give a total score for each S on each measure.
Thus, the high negative correlation between total pairs
and sentence length in Group NClO indicates that Ss
writing short sentences also used many pairings of the
given words. Subsequent regression analyses of
necessity must predict performance for Ss rather than
for individual solutions.

Correlations (n s 30) above .3A9 and .AA9 are
significant beyond the .05 and .01 levels respectively.
Both groups show significant correlations between
quality and unusual meanings and topic freedom. For
Group NC5 length and total pairs are also correlated
with quality. Note also that total pairs and length
are correlated in Group NClO but not in Group NC5.

Multiple linear regression analysis gave partial

correlations between quality and each response measure.

38

 

 

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nsopm Eosm mCOHpSHom no mopsmmmz mmcoammm pom movapums cofiumampsoosmch11.m mqm<e

39

Darlington (1968) states that such an analysis

cannot give an accurate estimate of the relative
importance of predictor variables when the predictor
variables themselves are intercorrelated. Thus, the
results cannot be interpreted to indicate the amount

of the independent contribution to variance in quality.
It only indicates which variables are useful in
predicting solution quality, although relative
usefulness still cannot be inferred from the data.

The present results were obtained after a stepwise
deletion of nonsignificant variables. For Group NClO
the only variables which predicted quality were sentence
length (partial correlation = .A3) and unusual meanings
(.71) accounting for 53% of the variance in quality. For
Group NC5 total pairs (-.7A) and unusual meanings (.77)
were the only useful variables and accounted for 68%

of the variance.

Response Measures and Position

 

Unusual meanings and total pairs were hypothesized
to reflect learning and do accurately predict quality.
That is to say, those Ss who write few total pairs and
many unusual meanings will write higher quality solutions.
The next step, then, is to see which measures change
over the response sequence as does quality. Figure 1
presents this information. (a) The quality of solutions

in Group NClO appears to increase for the first five

A0

solutions for length, complexity, unusual meanings

and topic freedom. Total pairs appears to decrease
for these solutions. (b) Quality drops off from
solutions five to eight, and decreases are also found
in unusual meanings and topic freedom. Total pairs
appears to increase from solutions four to eight. (c)
Quality also seems to increase for solutions nine and
ten. Length, unusual meanings and topic freedom
increase, and total pairs decreases for these solutions.

Sincle—factor analyses of variance (df9, 261)
test the statistical significance of these changes
over the response sequence. For Group NClO quality
(F = 2.76, paGl), and length (F = 3.23, p<.Ol) show
the only significant increases. Unusual meanings with
an F-value of 1.66 (df9,26l) comes the closest of the
other variables to being statistically significant
(p<.l).

Figure 1 shows that in Group NC5 solutions there
is an increase in quality for all five solutions with
the greatest increase between the first two solutions.
Length, complexity, and unusual meanings show similar
increases. Total pairs shows a decrease over the
response sequence. Single—factor analyses of variance
(de,ll6) show that the increases in quality (F = 3.15,
p<.05) and length (F = 77.A3, p<.Ol) are statistically

significant.

Al

Effects of Quantity Instructions

 

Groups NClO and NC5 differ only in that one wrote
ten solutions and the other wrote five solutions. In
terms of the increase in quality over the response
sequence Figure 1 shows that Ss writing five solutions
write better solutions earlier in the response sequence i
than those Ss writing ten solutions. But, as Table 3 F'
shows, the means for all solutions in each group do not 7;
differ for quality or any other response measure.

Figure 1 indicates that each group produces solutions
of about equivalent quality over the first five solutions
apparently decrease in quality.

Comparing the first five solutions of Groups N010
and NC5 by pppp ppp analyses will illustrate changes in
the solution process as a result of differing quantity
instructions. The two-factor analyses of variance with
repeated measures on position (Table A) show that the
first five solutions of Groups NClO and NC5 do not differ
on any response measure. There are increases over posi—
tion for quality (p<.01), length (p<.01), complexity
(p<.05) and unusual meanings (p<.05). The absence of
significant interactions reinforces the decision that the
first five solutions are the same whether produced as the
entire assignment or as only half of the assigned task.

Furthermore, a linear regression analysis of the

first five solutions in Group NClO produces a curve of

A2

TABLE 3.--Means and SD's for Response Measures of Solutions
in Groups NClO and NC5.

 

 

Response.Measures GrOUp NClO Group NCS
Quality I 7.99 8.15
SD 2.1A 2.10
Length K 15.6A 15.93
SD A.08 A.35
Complexity I 2.57 2.65.
SD .7A .59
Total Pairs Y .81 .77
SD .9A .9A
Unusual Meanings K .36 .37
SD .72 .80
Topic Freedom 7 1.08 1.10
SD .60 .56

N 300 150

 

_._....__.......
. _-p
..
. ' .1“ . .

“3

TABLE A.--ANOVA Summary for Response Measures of the First

Five Solutions of Groups NC10 and NC5.

 

 

 

 

 

 

 

 

 

Source df MS F MS F MS F
i
Quality Length Complexity r_
Treatment 1 9.36 1.53 6A.A0 1.82 .65 1.80 i
by
Error 29 6.12 35.38 .36
Position A 23.2A 6.29** 92.18 6.66** .99 2.A5*
T x P A 3.16 .85 25.30 1.83 .33 .82
Error 261 3.69 13.83 .Al
Unusual Topic
Total Pairs Meanings Freedom
Treatment 1 .21 .1A .00 .00 .05 .12
Error 29 1.57 1.05 .A3
Position A .92 1.09 l.A0 2.A5* .AO 1.2A
T x P A 1.09 1.28 .A5 .80 .IA .A5
Error 261 .85 .57 .32
*p<.05 **p<.Ol

AA

best fit which is: Y = .360X + 6.72. Nonlinear trends
are nonsignificant. This is very comparable to the
same curve for Group NC5 which is: Y = .3A3X + 7.12.
Groups N05 and the first five solutions of Group NC10

appear to be very similiar in terms of the rate of

‘1

quality increase and in the fact that for both conditions

‘7

quality and length increase over the response sequence.
Furthermore, quantity instructions do not significantly 1
[gm

influence production in terms of quality or any other

response measure.

Criteria-cued Instructions

 

This section addresses itself to the effects of
criteria-cued instructions on the increase in quality
and the change in response measures over the response
sequence. The interaction of criteria—cued instructions

and quantity instructions will also be presented.

Qualipy and Position

 

Figure 2 presents the mean quality for each position
for Group CClO with ten solutions per S and for Group CC5
with five solutions per S. It is apparent that quality
increases in Group CC5 and not in Group CClO. Single-
factor analyses of variance for repeated measures on
position show that there is no increase in quality over
the response sequence for Group C010 (F<l). For Group

CC5 the increase in quality is statistically significant

Mean

Mean

45

 

 

   

 

 

 

 

   

 

 

QUALITY 18 LENGTH
9 .
8 .
7 l
i”
1.2 F 0 g,
3.0 COMPLEXITY . TOTAL PAIRS 11-“
1
1.0 . ‘
2.8 b
2.6 b 08 I-
2.4 L .6 '
202 " A . - . i . . . .4 . i . L 1 A
UNUSUAL 0 TOPIC
Q. MEANINGS ‘ FREEDOM
.5 1- ’ \ I
1.3 1
1.2 P
03 "
101 "
1 -- 1.0 .
"12355678910 12335375910
Position Position

Pig. 2. Group CClO, ten solutions and criteria-cues

(solid line) and Group CC5, five solutions and crit-

eria-cues (broken line). Means for response measures
as a function of position.

(F<l). For Group CC5 the increase in quality is
statistically significant (F = 6.12; df A, 116; p<Ol).
For the latter group Newman-Keuls comparisons, adjusted
for repeated measures, indicate that solutions in the
first position are significantly lower in quality than
those in other positions (p<.Ol).

The linear trend in the increase in the quality
of Group CC5 solutions accounts for 81.27% of the variance
between positions. Nonlinear trends are nonsignificant.
The regression line is: Y = .3A6X + 7.25. The linear
correlation between position and quality (n = 150) is

.335 which accounts for about 11.2% of the total variance.

Predicting Quality

 

The correlations between solution quality and
response measures are given in Table 5. The correlations
are based on the sum for each S across all solutions
(n = 30). Values above .3A9 and .AA9 are significant
beyond the .05 and .01 levels respectively. In Group
CClO quality is correlated with sentence length, unusual
meanings, and topic freedom. For Group CC5 quality is
correlated with sentence length and complexity. Notice
that sentence length and total pairs show high negative
correlations in both groups.

Multiple linear regression analysis using a step-
wise deletion procedure was used to determine which

variables were useful in predicting quality. For Group

 

A7

 

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A8

CClO sentence length (partial correlation = .59),
unusual meanings (.57) and topic freedom (.A8) account
for 68% of the variance in solution quality. For Group
CC5 sentence length (.57), unusual meanings (.A0) and

complexity (.5A) account for 67% of the variance.

Response Measures and Position

 

According to the original predictions, criteria-
cues should eliminate any increase in quality over the
response sequence. This is true for Group CClO but not
for Group CC5, which differed only in the number of
solutions written. Changes in influential response
measures should also reflect this difference between
groups. Single-factor analyses of variance with repeated
measures over position show that for Group CClO only
sentence length changes over position (F = 2.2A; df9,
26l:p<.05). Newman-Keul's comparisons show only solution
10 to be longer than solution 1 (p<.05). For Group CC5
position differences (df A, 116) are significant for
length (F = A.33, p<.01), total pairs (F = 3.02, p<.05),
and unusual meanings (F = 2.73, p<.05). For length,
individual comparisons show the first solutions to be
shorter than the rest (p<.05). Solutions in the fourth
position have fewer word pairs than the first solution
(p<.01), and the fourth solution also has more unusual
meanings than the first two solutions (p<.05). Appar-

ently the increase in quality in Group CC5 is also

A9

accompanied by increases in the use of unusual meanings
and a decrease in the number of word pairs. On the

other hand, Group CClO which does not increase in quality
does not show changes in the use of unusual meanings or

word pairs.

Effects of Quantity Instructions

Previously comparisons between solutions produced
under different quantity instructions proved to be
valuable. Figure 2 indicates that such a pppp p93 analysis
would also point out some meaningful differences between
Groups CClO and CC5. Table 6 gives the means and standard
deviations based on all solutions in each group. Two-
tailed t—tests show that solution quality for Group CC5 is
slightly higher than Group CClO (p<.05; deA8). Other
differences are not statistically significant.

Table 7 presents the results for two-factor analyses
of variance with repeated measures across the first five
solutions of each group. There are no significant differ-
ences between the means of the groups for the first five
solutions. Only the treatment—by-position interaction for
quality approaches significance (p<.06). From Figure 2
the quality of Group CC5 solutions appears to increase
faster than the quality of Group CClO solutions. Increases
across position are significant for quality and length

(p<.01). Total pairs significantly decreases over the

50

TABLE 6.--Means and SD's for Response Measures of Solutions
in Groups 0010 and CC5.

 

._—.-—M. _
no
.50
. L

 

Response Measures Group CClO Group CC5 t

Quality T 7.85 8.29 1.99*
so 2.29 2.09

Length T 15.98 16.u9 1.1M
so u.55 4.38

Complexity I 2.59 2.67 1.1u
so .76 .62

Total Pairs I .83 .79 .A8
so .91 .83

Unusual Meanings K .38 .33 .79
SD .67 .66

Topic Freedom I 1.07 1.1A 1.30
so .58 .SA

N 300 150

*p<.05

 

51

TABLE 7.--ANOVA Summary for Response Measures of the First

Five Solutions in Groups CClO and CC5.

 

 

 

 

 

 

 

 

 

Source df MS F MS F MS F

Quality Length Complexity
Treatment 1 19.76 3.71 82.16 2.7A .A8 .57
Error 29 5.32 29.96 .85
Position A 16.20 3.88** 82.5A A.89** .10 .23
T x P A 9.57 2.29 5.52 .33 .15 .33
Error 261 A.l7 16.87 .AA

Unusual Topic
Total Pairs Meanings Freedom

Treatment 1 .33 .36 .00 .00 .21 .AA
Error 29 .93 .A9 .A9
Position A 2.A8 3.68** .71 1.70 .3A 1.17
T x P A .39 .58 .AA 1.06 .Al 1.38
Error 261 .67 .A2 .29

 

**p<.01

response sequence (p<.01). Figure 2 shows that other
than for quality the first five solutions for each

group are very similar for all response measures.

Quality and Quantity Instructions

 

Up to now solutions produced with criteria-cued
instructions have not been compared to solutions
produced with standard instructions. Table 8 compares
the means for all solutions produced under each condi-
tion of quality and quantity instructions. A 2 x 2
factorial analysis of variance compares these means
which are based on a mean quality per S. The results
show that there is no significant difference due to
criteria cued instructions (F<l) and no significant
difference due to quantity instructions (F = 2.56; df l,
116). The interaction was also nonsignificant.
Apparently when each S is specifically assigned a number
of solutions to produce, mean quality does not depend
on how many solutions he is required to write or what

type of instructions he is given.

Effects of Learning Old Pairs

 

In Group TOP Ss learned sentences with the old

pairs happy horse and expensive lake. Group TR S learned

 

 

sentences with the same words, but they were unpaired.
Group TIR Ss learned sentences with four other words. and

Group NC10 Ss had no learning experience during the

53

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.m Hon mpHHmsv some so pmmmmm

 

 

mo.H so.H mo.H am
so.w so.m Ho.m m Hoooe
so. so.H gm. om
mo.e mm.» mm.» m meoHooHom OH ocoHpoospmcH
Ho.H so. HH.H om soHocooo
mm.m om.m mH.m m meoHoaHom m
mono mono
Hoooe 1oHpooHLo 1oHpopHeo oz

 

mCOHpospumcH zuHHmsa

 

$.moo 6cm CHOU .moz .oaoz masopo Ca wCOHpSHom mo mpHsta pom m.Qm 6cm mamm211.m mqm¢e

5A

experiment. The hypothesis is that learning old pairs
will make Group TOP Ss use more old pairs in sentences 1
but that such use will decrease as more solutions are
produced. As a result of the reduction in the use of

old pairs, one would also expect quality to increase

 

over the response sequence in Group TOP. I
i

Use of Word Pairs E.
Figure 3 presents the mean number of old pairs in Ll

each position for each group.2 (Group means are given

in Table 9). The results of a two-factor analysis of
variance with repeated measures on position are given

in Table 16. Group TOP Ss used more old pairs than

other Ss (p<.01) and Ss in Group TR used more old pairs
than Ss in Groups NC10 or TIR (p<.05) by Newman-Kuels
tests. Position has a significant effect (p<.05) with
solutions in position 1 having more old pairs than those
in position 6 (p<.05) by Newman-Keuls tests. The signif—
icant interaction between treatment and position (p<.01),
which can be seen in Figure 3, can be analyzed by single-
factor analyses of variance for each group separately
with position being the repeated measure. Only Group TOP

shows a significant decrease in the use of old pairs

 

2Learning sentences with old pairs lowered the
variance of total pairs in the first solution from .87
for Group 1 total pairs to .A6 for Group 3. For quality
the variance in the first solution was 3.70 for Group 1
and 2.96 for Group 3.

Mean Frequency Old Pairs

1.3

.9

.5

.1

 

55

Group NC10 o—o TR 0- -0
Top 0"" TIR o--o

 

 

 

Position

Fig. 3. Groups NC10, TOP, TR and TIR. Mean
number of old pairs as a function of position.

 

56

TABLE 9.--ANOVA Summary for Old Pairs in Solutions of
Groups NC10, TOP, TR and TIR.

 

 

 

Source df SS MS F
Treatment 3 9A.1A 31.38 25.72*
Error 116 1Al.26 1.22

Position 9 5.72 .6A 1.89*
T x P 27 17.07 .63 l.88**
Error lOAA 351.71 .3A

 

*p<.05 **p<.01

57

(F = 2.92; df 9, 261; p<.01). Newman-Keuls comparisons
indicate that in Group TOP solutions 6 and 9 have signif-
cantly less old pairs than solutions 1 and 3 (p<.05).

Old pairs are happy horse and expensive lake, and

 

 

total word pairs are all combinations of these four words.
The effect of learning sentences with the four words to

be used later can also be seen in the frequency of use of
total word paris. Table 10 shows that Groups TOP and TR
used more word pairs than other groups. Table 11 gives
the results of a two-factor analysis of variance with
repeated measures on position. The difference between
treatments (p<.01) is attributable to Group TOP using

more word pairs than all other groups (p<.01), and Group
TR using more than Groups 1 and 6 (p<.05), which do not
differ. The use of word pairs decreases over the response
sequence (p<.01). Individual comparisons indicate the
first two solutions have more word pairs than other solu—
tions (p<.01), and all solutions have more word pairs than
the last solution (p<.01).

Single-factor analyses of variance with repeated
measures (df 9, 261) shows that the use of word pairs
decreases over the response sequence for Group TOP
(F = 2.28; p<.05) and Group TR (F = 2.55; p<.01), but not
for Groups NC10 (F = .91) or TIR (F = 1.78). Apparently
learning sentences with the four words to be used later

in solving provlems has the effect of increasing the use

‘

”7

58

TABLE 10.--Means and SD's for Response Measures of Solutions
in Groups NC10, TOP, TR, and TIR.

 

 

Response Measures Group Group Group Group
TOP TR NC10 TIR
Quality T 6.89 7.56 7.99 8.08
so 2.02 1.96 2.1A 2.12
Length T 12.79 1A.26 15.6A 15.53
so 3.72 3.66 A.08 A.7u
Complexity T 2.u7 2.63 2.57 2.63
so .65 .55 .7A .62
Old Pairs T .96 .52 .31 .2A
SD .8A .67 .55 .A8
Total Pairs T 1.51 1.10 .81 .80
so .9u 1.00 .9A .89
Unusual Meanings Y .13 .ll .36 .29
so .AA .A2 .71 .63
Topic Freedom T .86 .97 1.08. 1.0A
SD .5A .56 .60 .58

 

TABLE ll.--ANOVA Summary for Response Measures of Solutions
in Groups NC10, TOP, TR and TIR.

 

 

 

 

 

 

Source df MS F MS F MS F
1
Quality Length Complexity e1
Treatment 3 89.20 7.1A** 533.66 8.36 1.86 3.3A*
I
Error 116 l2.A9 63.80 .56 '
Position 9 19.89 6.17** 199.85 20.08** 1.13 2.89**
T x P 27 3.15 .98 7.56 .76 .A2 1.10
1 Error lOAA 3.23 9.95 .39
Unusual Topic
Total Pairs Meanings Freedom

 

 

 

Treatment 3 32.75 16.52** A.A9 5.29** 2.89 5.81**

Error 116 1.98 .85 .50
Position 9 2.92 3.87** .Al 1.21 .A7 1.50
T x P lOAA .75 .3A .31

 

*p<.05 **p<.01

60

of pairs of these words in problem solutions. Learning

sentences with specific pairs increases the use of those
specific pairs, but in both cases the use of word pairs

decreases over the response sequence.

It is important to ask about individual word pairs,
because it provides information about how the treatments
change the associative hierarchy. The solutions were
reread and frequency of use was tallied for each word
pair. The obtained totals may be slightly different,
because the present judge may have used a stricter
criterion for a word pair than used by the original judge.

Table 12 gives for each word pair in Groups NCIO,
TOP and TR the frequency of occurrence and average posi-
tions of occurrence. In every group the average position
of occurrence of a word pair is inversely related to the
frequency of occurrence. That is, the more popular word
pairs occur earlier in the response sequence than less
popular pairs. Expensive horse is the most popular word
pair in the groups which did not learn old pairs. Group
TOP learned the pairs happy horse and expensive lake, and
they are the most popular word pairs in this group.
Apparently the most common word pairs are used before less
<sommon ones. Learning specific word pairs makes them more
common and makes them occur earlier than in other groups.

iflqen relevant sentences without word pairs are learned, the

61

TABLE l2.-—Frequency of Use and Position for Each Word Pair
in Solutions for Groups NC10, TOP and TR.

 

 

 

 

 

Mean Median
Position Position Frequency

Group NC10
l. Expensive Horse 5.01 A.50 106
2. Happy Horse 5.83 5.75 53
3. Expensive Lake 7.10 7.A0 21
A. Horse Lake 8.18 8.78 11
5. Happy Lake 7.86 8.50 7
Total 6.80 6.99 198

Group TOP
1 Happy Horse A.92 3.80 136
2. Expensive Lake 5.03 A.00 106
3. Expensive Horse 5.60 5.10 91
A. Happy Lake 6.16 5.75 19
5. Horse Lake 6.75 7.00 A
Total 5.69 5.13 356

Group TR
1 Expensive Horse A.5A A.00 11A
2. Happy Horse A.90 A.00 82
3. Expensive Lake 6.57 6.80 A2
A Happy Lake 7.67 7.00 6
5. Horse Lake 7.00 7.00
Total 6.00 5.76 2A7

 

62

word pairs are used more frequently but in the same

a3sociative hierarchy as in the group with no learning.

Other Response Measures

 

Treatment conditions also produce significant
differences on other response measures as well. Table 11
also gives the results of these analyses of variance.
Individual comparisons show that Group TOP solutions are
shorter in length (p<.05), have less topic freedom (p<.05),
and use more word pairs (p<.01) than all other solutions.
They are as complex as Group TR and TIR solutions (p<.05).
They have as few unusual meanings as Group TR solutions,
but both have less/than solutions in Groups NC10 and TIR
(p<.05). Group TR solutions differ from those in Groups
NC10 and TIR only in having more word pairs (p<.05) and
less unusual meanings (p<.05). Group NC10 and TIR
solutions do not differ on any response measure. Learning
sentences with old pairs not only decreases mean quality,
but also increases the use of word pairs and produces
shorter and less complex solutions which have fewer
unusual meanings and less topic freedom than most other
groups. Learning sentences which use the words to be later
incorporated in solutions seems to increase the use of word
pairs and decrease the use of unusual meanings.

Solutions in Group TOP use word pairs less often as
more solutions are produced, and solution quality increases.

Figure A shows this increase in quality. A single-factor

Mean Quality

63

 

 

Position

Fig. 4. Groups NC10, TOP, TR and TIR.
quality as a function of position.

 

Mean

6A

repeated-measures (position) analysis of variance of
quality yielded an.F-value of 3.17 for position

(df 9, 261; p<.01). A linear trend accounts for 80.36%
of the variance between positions with no significant
nonlinear trends. The curve of best fit is: Y = .16AX

+ 5.99. The linear correlation between position and
quality is .23A (n = 300) which is statistically signif-
icant at the .01 level. With the decrease in the use of
old pairs Group TOP also shows a linear increase in
solution quality over the response sequence.

The same analysis of variance for other response
measures (df = 9, 261) for Group TOP shows that other
response measures do change over the response sequence.
Length (F = 8.A3; p<.01) and complexity (F = 2.12; p<.05)
increase over the response sequence. The use of all word
pairs, of course, decreases over the response sequence
(F = 2.28; p<.05). The frequency of use of unusual meanings
and topic freedom do not change. For Group TOP the increase
in solution quality over the reSponse sequence is accOm-
panied by a decrease in the use of all word pairs and
increases in solution length and complexity.

The same analysis (df 9, 261) can be applied to Group
TR, since these solutions so closely resemble those produced
tut Group TOP. Quality increases slightly over the whole
.response sequence (F = 1.8A; p = .06) and significantly over

true first five solutions (F = 5.03; df A,ll6; p<.01).

65

Sentence length (F = 5.62; p<.01) increases and use of

all word pairs decreases (F = 2.55; p<.01). There are

no significant changes in sentence complexity, unusual
meanings or topic freedom. For Group TR a slight increase
in quality is also accompanied by large increases in

sentence length and decreases in the use of word pairs.

Solution Quality

 

Learning sentences with old pairs affects the
subsequent use of old pairs, but it also affects solution
quality and other response measures. Table 10 presents
the means and standard deviations for quality in each

group. Table 11 presents the results of two-factor

analyses of variance with one repeated measure for quality.

The main questions under investigation are whether quality
increases over the response sequence and under what
conditions is this the case.

As Figure A and Table 11 indicate, quality does vary
between treatments (p<.01) and between positions (p<.01).
Newman-Keuls comparisons show that Group TOP solutions are
of inferior quality to other groups (p<.01), which do not
differ from one another. Totaling across all groups shows
that quality does increase over the response sequence with
the lowest quality solutions occurring in the first three
positions (p<.05). Solutions in positions 2, 3, A, and 8
do not differ from one another but are of lower quality

than those in positions 5, 6, 7, 9, and 10 (p<.05).

'rl'ilii

66

Single-factor analyses of variance with position as
a repeated measure (df 9, 261) show the change in quality
over position for individual treatments. Quality increases
in Group NC10 (F = 2.76; p<.01), Group TOP (F = 3.17; p<.Ol)
.06).

and Group TR approaches significance (F = 1.8A; p
The quality of the first five solutions in Group TR does
increase significantly (F = 5.03; df A, 116; p<.01). It is
apparent that learning sentences with old pairs increases

the use of old pairs and reduces solution quality beyond the
effects of control conditions. Learning sentences with the
four words to be later used in Solutions increases the use

of word pairs, but not as much as learning specific pairs.
Solution quality for the latter condition is not significantly
reduced. For most conditions solution quality increases over

the response sequence.

Predicting Quality

Group TOP shows a large increase in quality over the
response sequence and concomitant increases in length and
decreases in the use of total pairs. The next question is
whether the decrease in word pairs has any effect on quality.
'The results for Group NC10 indicated that total word pairs
did not have significant influence on the judges' rating of
:solution quality. Table 13 presents the intercorrelation
Tnatrix for relevant response measures in Group TOP solutions.
(The correlations are based on total scores per S (n H 30).

TMlus, correlations above .3A9 and .AA9 are significant beyond

67

 

 

 

am. H=.1 No.1 om. om. Eopmopm oHooe .m

1 mm.1 mm. am. Hp. mwchmcz Hmsmsca .m

1 m:.1 H».1 mm.1 mpfimm Hmpoe .:

1 mm. om. HponHasoo .m

1 on. cameos .m

1 szHmsa .H

.m .m .z .m .m .H opsmmoz omconmom
.aoe asopo Lou prpoz coHpoHoLLoopoocH11.MH mHmae

68

the .05 and .01 levels respectively. Note that quality is
highly correlated with length, complexity, total pairs and
unusual meanings. Note also that total pairs and length

are highly negatively correlated. A stepwise deletion
procedure was used for the multiple linear regression
analysis to predict solution quality from the other response
measures. Partial correlations with quality were -.65 for
total pairs, .51 for length and .5A for unusual meanings.-
Together these variables account for 85% of the variance in
solution quality. It cannot be concluded, however, that the
decrease in the use of word pairs is the only reason for the

increase in quality over the response sequence in Group TOP.

Word Pairs in Group NC10

 

The validity of learning sentences with old pairs could
be questioned as representing a condition which would not
happen in an unselected sample. That is, in Group NC10 Ss
who wrote solutions with different numbers of old pairs
would not differ in quality, even if the number of unusual
meanings were equated. This would imply that the low corre-
lation between quality and old pairs in Group NC10 was true
and not due to the cancelling effect of unusual meanings
which included word pairs. To test this the 30 Se in Group
NC10 were separated into the third with the highest and the
third with the lowest number of word pairs. Five Ss in
each sample could be matched exactly for the number of

unusual meanings used. The high Ss used an average of 1.38

69

word pairs per solution (compared to 1.51 for Group 3), and
the low Ss used an an average of .38. The mean quality for
the high Ss was 7.22 (SD = .68) and for the low Ss 8.2A

(SD = .63). The Eevalue is 2.A6 (df = 8) which is signifi-
cant at the .05 level for a two-tailed test. Thus, quality
is determined, at least in part, by the use of word pairs

for Se under normal conditions.

Effects of Learning Unusual Meaningp

Previous analyses have shown unusual meanings to be
one of the most, if not the most, influential variable in
determining solution quality. Group TUM Ss learned sentences
which used the four words in unusual ways, sometimes giving
them novel meanings and sometimes giving them a different
grammatical function. Using a noun as a modifier would be
an example of the latter use. The comparison groups are the
same as for the previous treatment. Group NC10 Ss had no
learning, Group TIR Ss learned irrelevant sentences, and
Group TR Ss learned relevant sentences with no unusual
meanings and word pairs. The hypotheses are that Ss learning
unusual meanings will use more of them in solutions to the
:sentence problem, and that the use of unusual meanings will
llot increase over the response sequence. Based on the use
(of unusual meanings alone, one would not expect quality to

irnsrease over the response sequence in Group A.

70

Use of Unusual Meanings

Figure 5 presents the mean frequency of unusual
meanings for each position in each group. Table 1A
presents the results of a two-factor analysis of variance
with position as the repeated measure. Treatment groups
differ in the frequency of use of unusual meanings (p<.01).
There is no significant change in the use of unusual
meanings over position, nor is there a significant inter-
action. More unusual meanings are used by Group TUM than
by other groups (p<.01). But Group TR uses significantly
less than Group NC10 (p<.05). Groups NC10 and TIR do not
differ by Newman-Keuls tests. Apparently learning sentences
with unusual meanings does increase the subsequent use of
unusual meanings in solutions to the sentence problem. But
learning sentences with the words to be used later, decreases

the use of unusual meanings.

Solution Quality

Regression analyses have shown unusual meanings to be
about the most important variable in determining solution
quality. And Group TUM seems to have solutions of better
quality as shown by Figure 6 and Table 15. The results of
two-factor analyses of variance with position as the
repeated measure are given in Table 16. They show that
groups differ also on quality, total pairs and topic freedom.
iFor quality, individual comparisons indicate that the best

solutions are in Group TUM (p<.01), and other groups do not

Mean Unusual Meanings

1.2

71

'Group NC10 o——o TR o--o
TUM o——o TIR o--o

 
   

 

 

 

 

9’ ‘ l l - 0-"l -
1 § 3 *4 5 6 7 8 ~9 10
Position

Fig. 5. Groups NC10, TUM, TR and TIR. Mean
number of unusual meanings as a function of
position.

72

TABLE lu.--ANOVA Summary for Unusual Meanings in Solutions
of Groups NC10, TUM, TR and TIR-

 

 

Source df SS MS F
Treatment 3 113.89 37.96 2U.02**
Error 116 l83.u6 1.58

Position 9 5.81 .65 1.51
'P x P 27 8.91 .33 .77
Error 104“ 450.88 .u3

 

**p<.01

73

 

 

 

 

9.5. [I
L

>5
.9
28.5.
m
3
c:
C
CU
0
2
705}
6.5 4!, . - r - L A .

1 2 3 4 5 '6' 7 5 910

Position

Fig. 6. Groups NC10, TUM, TR and TIR. Mean
quality as a function of position.

74

TABLE 15.--Means and SD's for Response Measures of Solutions
in Groups NC10, TUM, TR and TIR.

 

 

Response Measures Group Group Group Group
TUM TR NClO TIR
Quality Y 8.94 7.56 7.99 8.08
so 2.09 1.96 2.1a 2.12
Length Y 1u.u6 14.26 15.6u 15.53
SD u.19 3.66 H.08 n.7u
Complexity Y 2.60 2.63 2.57 2.63
so .57 .55 .7A .62
'rotal Pairs Y 1.0a 1.10 .81 .80
so .99 1.00 .9u .89
Unusual Meanings f .93 .ll .36 .29
so 1.0M .M2 .71 .63
Topic Freedom Y 1.19 .97 1.08 1.08
SD .59 .56 .60 .58

 

75

TABLE 16.--ANOVA Summary for Response Measures of Solutions

in Groups NC10, TUM, TR and TIR.

 

 

 

 

 

 

 

 

Source df MS F MS F MS F
Quality Length Complexity
Treatment 3 100.68 8.36** 153.04 2.25 .29 .48
Error 116 12.05 68.10 .59
Position 9 19.74 5.86** 190.43 l7.81** .92 2.55**
T x P 27 2.99 .89 6.45 .60 .34 .93
Error 1044 3.37 10.69 .36
Topic

Total Pairs Freedom
Treatment 3 6.86 3.64* 2.45 5.08**
hError 116 1.89 .u8
Position 9 3.29 4.19** .37 1.17
T x P 27 .88 1.1] .38 1.20
Error 1044 .78 .32
*p<.05 **p<.01

m-L—NH _

76

differ. Furthermore, quality increases over the response
sequence (p<.01) with the worst solutions occurring in

the first position (p<.01). Second position solutions are
significantly inferior to all subsequent solutions (p<.05),
except those in positions 3 and 4. Solutions in positions

3 to 10 do not differ by Newman-Keuls individual compari- i

7“"

sons. Learning unusual meanings, then, increases solution

quality above solutions produced under control conditions.

nun-u”; :
It .

Other Response Measures

Groups also differ on the total number of word pairs
used (p<.05) and the amount of topic freedom in solutions
(p<.01). Newman-Keuls comparisons indicate that Group TUM
and TR solutions use more word pairs than Groups N010 and
TIR (p<.05), which do not differ. There is also more topic
freedom in Group TUM solutions than in other solutions
(p<.05). Solutions produced after learning unusual meanings
are of a higher quality and have more unusual meanings, more
word pairs and more topic freedom than solutions produced
under most other conditions. Learning sentences with the
words to be used later has the affect of decreasing the
number of unusual meanings and increasing the number of

word pairs used in subsequent solutions.

Analyses of Group TUM Solutions
A single-factor repeated measures (position) analysis

of variance for Group TUM indicates that quality changes

77

over position (F = 2.46; df 9, 261; p<.01). Figure 6 shows
only a linear trend is significant, and this accounts for
60.37% of the variance between positions. The curve of
best fit is: Y = .137X + 8.19. lThe linear correlation
between position and quality is .188 which is statistically
significant at the .01 level (n = 300).

Since solution quality in Group TUM increases over
the response sequence, the next question is whether the use
of unusual meanings also increases over position. A single-
factor analysis of variance with position as the repeated
measure shows that there is no significant increase in the
use of unusual meanings (F = .72; df 9, 261). From Table 17,
however, it is apparent that Judges did use unusual meanings
to determine solution quality. A multiple linear regression
analysis using a stepwise deletion procedure indicates that
unusual meanings (partial correlation = .91) and sentence
length (.61) are useful in predicting solution quality and
account for 81% of the variance in quality.

If Judges were aware of the use of unusual meanings,
they must have been aware that some meanings were used more
frequently than others. Thus, the frequent use of flgggg
‘L§53_would reduce its effectiveness in a sentence. The
solutions of Group TUM were reread by another naive Judge
for pg§£,Qgg comparisons. Since the Judges were different
between the g priori and the pgst Egg comparisons, the

Obtained values may differ slightly. Table 18 presents the

78

TABLE 17.--Intercorrelation Matrix for Group TUM.

 

 

Response Measures 1. 2. 3. 4. 5.
1. Quality -

2. Length .21 -

3. Complexity .04 .33 -

4. Total Pairs -.19 -.74 .04 -

5. Unusual Meanings .70 -.44 .16 .40 -
6. Topic Freedom .58 -.07 .22 -.04 .59

 

‘u—n—

79

TABLE l8.--Use of Unusual Meanings in Group TUM Solutions

 

.__.__—_. -... -._____..__-

__

 

 

 

 

Lakeside cottage

Horse farm

Horse ranch

Horse barn

Horse trailer

Herse lovers

Horse hide purse

Horse skin bathing suit

Lake-View Stables

Lake-View

Lake Club

Lake Estates

Races

Lake Dude Ranch
Lakeshore town
Lake Expensive
Lakeville

Freq. Freq.
Learned Meanings
Names of Animate Objects Names of Inanimate Objects
Happy 30 Happy Horse Dude Ranch 1
Horse _3 Happy Hours Resort 0
Total 33 Lake Park ‘_9
Total 1
Unusual Word Meaning Unusual Word Function
Horsing around 10 Lake front 10
Horseback riding 6 Lake snore 2
Horse (heroin) _g Horse laugh _3
Total 21 Total 14
Total learned meanings used by
Created Heanings
Names of Animate OLjects Homes of Inanimate Objects
Happy Horse 2 Horse Lake 22
Mr. Horse 1 Horse & Lake Liquor 1
Expensive 1 Horse barn Road 1
Expensive Horse 1 Happy Horse Lake 4
Mr. Lake 3 Happy Horse Resort 2
Happy Lake 3 Happy Horse Stables 2
Joe Lake 1 Happy Horse Riding Stables 2
Lake . . . _3 Happy Horse 2
To... 11 em 1...... Pant 1
nappy Horse Lake Hotel 1
Unusual Word Meaning Fany Lake p l“
. . nappy Lake Haven 1
Horseshoe 1 “app: La“e ranch 1
Horse face 1 p;;*{ La4e Retgrt 1
Ate like a horse 1 Hiypf Ltf g 7d.°r P st 1
Lake of tears 1 Nappy 888 :Tdhlni 0”
Lake of beer 1 nappy Ldfe Horse harms l
—— Happy Lake Horse Ranch 1
Total 5 Happy Lake Farms 1
Happy Haven for Horses 1
Unusual Word Function Happy Club 1
Lake cottage Lake Happy 5
Lake resort Lake Farms 3
Lake ranch Lake Stables 2
Lake lots Lake Resort 2
Lake water Lake of Horses 1
Lake home Lake Horse 1 '
Lake supervisor Lake Happy Horse 1
1
1
1
1
1
1
I
1
_1

Horse show
Total

Total created meanings used 13

IHi—‘i—Ji-Ji—‘i—‘i—‘RJHHHrOI‘JT\)Jr\n

h)
I: \1

Expensive Lake

Total

CI)
CI)

. Dbal-h-I-..‘

In

80

frequency of use of each unusual meaning for Group TUM
solutions. Notice that ngpy as a person's name and 52333
£252 were used 52 times in the 300 solutions of Group TUM
(39% of the obtained unusual meanings). These particular
meanings were also used in about 8% of the solutions in
other groups (about 30% of the obtained unusual meanings).
These meanings, then, may be called "common-unusual
meanings." The question is whether the frequency of use of
an unusual meaning would affect solution quality. The mean
quality of Group TUM solutions with these common-unusual
meanings is 9.44 (SD = .98), and for those with uncommon-
unusual meanings the mean quality is 10.37 (SD = 1.02).
The difference between these means is significant (t = 4.51;
df 164) beyond the .01 level. Apparently those solutions
with common-unusual meanings do have a lower quality than
those with common meanings.

The position within the response sequence in which the
unusual meanings occur is also a function of the frequency

of occurrence of that meaning. Table 19 presents the mean

TABLE 19.-—Mean Position of Unusual Meanings as a Function

 

Frequency of Occurrence

.ill C. n“...-._
l

 

1-2 3-4 5-6 10-14 22-30

 

Mean Position 6.38 6.20 5.48 6.06 5.06

 

81

position of unusual meanings as a function of frequency of
occurrence (grouped in pairs to remove some irregularities).
It is apparent that the unique meanings occur later than the
more popular ones. The common-unusual meanings (22-30) occur
much earlier in the response sequence than any other unusual
meaning.

Figure 7 gives the cummulative percentages for the two
types of unusual meanings. Note that over 50% of the common
meanings are produced before the fourth solution. Whereas,
for uncommon meanings the median position is 6.0. A
Kolmogorov-Smirnov two-sample test for large, unequal n's
shows that the two distributions are in fact different
beyond the .01 level of confidence. Chi Square tests
(df 9) confirm this analysis with a value of 25.26for
uncommon meanings (p<.01) and a value of 30.70 for common
meanings (p<.01). This indicates that the majority of
common meanings do come in the first portion of the response
sequence and that the majority of uncommon meanings come in
the last portion. Furthermore, the correlation between
quality and unusual meanings (.635) is increased to .688 by
not counting those solutions with common-unusual meanings.

These analyses justify separating the common-from the
uncommon-unusual meanings. When common-unusual meanings
are counted as not being unusual meanings, a single-factor
analysis of variance for repeated measures on position gives

an F of 5.50 (df 9, 261) which is significant beyond the .01

’100

Cumulative Percentage

82

' Frequency of Occurrence
1-14 o-—o

22-30 one

 

 

 

Position

Fig. 7. Group TUM. Cumulative percentage of
unusual meanings as a function of position.

83

level. Individual comparisons show that more unusual
meanings are found in solutions 6, 7, and 8 than in solutions
1, 2, and 3 (p<.05). Other solutions do not differ. Thus,
for Group TUM it may be concluded that the increase in

quality over position is also accompanied by an increase in

the use of unusual meanings. ’
Single-factor analyses of variance (df 9, 261) for k

3

repeated measures on position show changes in other response 1
a

measures in Group TUM. Length generally increases (F = 4.90;
p<.01), and topic freedom increases (F = 1.96; p<.05) as more
solutions are produced. The use of word pairs decreases

(F = 2.20; p<.05). Increases in solution quality for Group
TUM, then, are accompanied by increases in the use of unusual
meanings and in topic freedom and sentence length, and by
decreases in the use of word pairs.

Table 18 presents the frequency of use of each unusual
meaning. The unusual meanings which were included in the
sentences §s learned are under the heading "learned meanings."
Those meanings which differed from the learned meanings are
under the heading "created meanings." It is apparent that
created meanings are used more frequently in solutions than
learned ones (134 vs. 69). There are more different created
meanings than learned ones (66 vs. 12). Also learned meanings
are used earlier in the response sequence than created

meanings (mean position 5.50 vs. 6.07).

84

Although SS did not repeat the meanings which were
learned, the meanings which were used did closely resemble
the learned'ones. Table 18 presents two striking similar-
ities. (a) Frequency of usage in sentences corresponds to
frequency of exposure during learning. (b) Created
meanings often contain only simple changes of the learned
meanings, e.g. from the learned Happy Horse Dude Ranch to
Happy Horse Stables.

In summary, learning sentences with unusual meanings
enables Ss to use more unusual meanings in sentences. Such
a use increases the judged quality, and novel meanings,
which occur later in the production sequence, increase
quality even further. These combined effects produce a
higher average quality and an increase in quality over the

production sequence.

Intersentence Associations

This section will report an attempt to measure the
strength of association between each S's solutions. After
several attempts, a naive judge was able to classify the
ways sentences could be similiar into five categories. If
a theme was developed from sentence to sentence and more
information was added, it was called a "develop" association.
An example would be where a story is developed from when a
person is thinking about going to camp, to what he does at
camp, and finally to what he is thinking about as he comes

frame.“ This is a sort of thematic continuity. The second

85

major type of association is "rework." Here the basic sen-
tence remains the same, and the new sentence is only

slightly reworded; no new information is added. For example,
"the happy horse drank from the expensive lake" could be
followed by "the happy horse jumped into the expensive lake."
The remainder of the associations are based on the repetition
of only part of the sentence. An association would be a "run
on" if the last word or phrase of one sentence were the first
word or phrase of the next sentence. "Repeat" is the simple
repetition of a particular word or phrase, and "position" is
a "repeat" in the same position.

The solutions in Groups NC10, TOP and TUM were reread,
and the associations between an S's solutions were tallied.
The first solution and incomplete solutions were not counted
in any of the calculations. Table 20 gives the mean number
of associations per S. Notice the large number of "rework"
associations as opposed to "develop" associations. From
this information it can be concluded that there is some
degree of association between some solutions, but not
between all solutions. The only difference between groups
is that Group TOP solutions had more "rework" associations.

The next question is whether an association between
sentences helps the quality of the second sentence. Table
221 gives the correlations between associations and quality
for solutions in each group. "Rework number" and "develop

runnber" are the number of sentences to which the present

86

TABLE 20.--Mean Number of Associations per Subject.

 

 

Association Group NC10 Group TOP Group TUM
Rework 2.92 4.27 2.59
Develop .66 .84 1.15
Run on 2.25 1.79 1.95
Repeat 8.00 7.48 6.90
Position 9.14 8.74 8.39

Total 22.79 23.50 21.12

 

87

TABLE 21.-—Correlations between Solution Quality and
Associations.

 

 

Association Group N010 Group TOP Group TUM
Rework -.21 -.30 —.17
Rework number —.16 -.22 -.16
Develop -.03 .10 .02
Develop number -.02 .13 .08
Run on -.04 -.10 -.04
Repeat 4.16 -.30 .05
Position -.18 -.25 -.24

Total -.30 —.38 -.16

 

88

sentence relates. For example, if a sentence is the fifth
in a series of sentences which all relate to the same
theme, the "develop number" value will be "5." If quality
is correlated to associations, one would also want to know
if quality is also a function of the length of the associa-
tive chain. With n = 300 a correlation of .113 is signifi-
cant at the .05 level.. Because solutions are the object of
this analysis, covariance due to subject abilities cannot
be removed, nor would it be desirable to do so. For Groups
NC10, TOP and TUM the correlations are generally low and
negative. Apparently the more associations a sentence has
with the preceeding one, the lower the quality will be.
This will be especially true if the sentence has been '
changed only slightly, i.e. is a "rework" association.

One could also ask if these correlations would be
changed were only sentences with at least one association
counted. The results are changed in two ways. For "rework"
and "develop" associations the correlations are increased.
'Phus, when a sentence has been reworked from previous sen-
tences, more related sentences will give lower quality
(median r = -.l9). When a sentence has been developed along‘
a theme, more related sentences will increase quality (median
4 = .18).

Other results have suggested that length increases as
more solutions are produced because of the same sort of

response chaining; i.e., building from one solution to another.

89

Correlations between intersentence associations and solution
length are generally low and negative for Group NC10 (range “~10
to -.01). Group TOP correlations are somewhat higher and
negative (range -.46 to .08). Correlations are highest for
rework, (—.26), repeat (-.37) and position (-.3l). Group TUM
correlations reflect the same conclusions (range -.16 to .04)
with the only significant correlation being for repeat (-.16).
For the type of intersentence associations that were
measured, if there is a relationship to solution quality
or length at all, it is a negative one. In terms of
solution quality there appears to be no advantage in
reworking a sentence or in building a theme from one sentence

to another.

CHAPTER IV

DISCUSSION

The rationale for the present study may be summarized
in the following way. There is a need to understand the

processes which enable a person to produce good solutions‘

E‘””“‘" -. m!-

to a problem. Good solutions may be produced as a result of
instructions or training, but such devices have not success-
fully focused on problem solving processes. A person may
also produce good solutions after several less successful
tries. The literature indicates that the process involved

in producing poor-then-good solutions may be based on
breaking up the elements of the problem and rearranging

them into new forms. The sentence problem is a complex
productive thinking problem, the solutions of which can be
analyzed into severalresponse measures which could reflect
this process. The divergent process, of course, is assumed
to operate in different types of problems as well. The

first level of analysis focuses upon the correlation of
solution quality and the response measures. The second level
of analysis is experimental and involves changing the charac-
teristics of the words used in the sentence problem and
noting changes in the response measures. In this way solu-
tion processes may be illustrated for the sentence problem

with four specific words and with slightly different words.

90

91

The results of the present experiment generally point
to a divergent problem solving process; i.e., good solutions
depend upon being different from what one would expect and,
the more solutions one produces, the more different are the
solutions from the usual first response. Correlational
analyses show that divergent response measures are highly

correlated with quality. The four original words were

la“ A.

selected only for being two adjectives and two nouns.

finang -—T_‘

Casual observation will show that the adjectives and nouns
are only moderately associated and the nouns have few
unusual meanings. Making the word pairs more highly asso-
ciated tends to make responses more stereotyped, hence
solutions are of poorer quality.. As more solutions are
produced, however, solutions become better as a result of
breaking up the word pairs. Giving the words unusual
meanings tends to make responses less stereotyped by
allowing subjects to use unusual meanings, hence solutions
are of higher quality. As more solutions are produced,
however, even more unusual meanings are created and
solution quality increases even more. The following discus-

sion will present detailed explanations of each finding.

Divergent Processes Under Normal Conditions
The production of solutions in Groups NC10 and N05 may
be considered "normal" in two ways. First, the instructions
were standard instructions giving no cues to desired perform-

ance other than the number of solutions desired. Second, the

92

words used were not selected for any special reason. As
a result two adjectives and two nouns may as well have
been randomly selected from a dictionary. The two
measures of importance for this study seem to have moder-

ate values for these words. The associability of the

 

or expensive lake certainly are not as strongly associated

 

word pairs does not appear to be very strong. Happy horse ,
r
l

as red barn or yellow canary. Thus, there would be no

 

strong need to use the given words together in a sentence.
Furthermore, neither hgggg or lakg have many unusual
meanings. Because of their contemporary usage, words such
as pgll or gap would have more unusual, and clever, meanings
which would be used to better solution quality.

The principal questions under investigation are (a)
does quality increase over the response sequence, and (b)
how do variables which reflect learning change as more
responses are produced.

When producing five or ten solutions, solution quality
increases as more solutions are produced, and the increase
is linear. These results are in agreement with those
obtained with less complex problems. Research with the
unusual uses problem (e.g., Christensen, gp_al., Gerlach,
gp_§l. and Turner) show that rated creativity of uses
increases over the response sequence, later uses are statis-
tically more novel, and more novel categories of uses occur

in later solutions. These results have been interpreted to

93

indicate a divergent process which includes breaking up
old associations between object and uses and the construc-
tion of new ones. The question is whether the same
analysis can be applied to the sentence problem.

Response measures, other than length and complexity
represent measures of the degree to which part of a sen-
tence corresponds to (or is associated with) the strongest
or most dominant response. For example, unusual meanings
reflect a breaking away from the conventional meanings.
Quality is correlated to unusual meanings, word pairs
(negatively), topic freedom and length and complexity.
Regression analyses show that quality may be most accu-
rately predicted from unusual meanings, word pairs and
length. Thus, the importance of two divergence measures
is verified.

The analyses of variance over position represent
another form of correlational analysis. In this case the
hypothesized relationships take the form of a multiple
correlation. If quality is correlated to position, is a
variable which is correlated with quality also related to
position? And, like the correlational analyses, this
analysis is more suggestive than convincing. Graphically
fluctuations in solution quality appear to be matched by
changes in unusual meanings, topic freedom, length and
complexity. The use of word pairs appears to be inversely

related to quality in Group NC5. Statistical analyses,

94

however, weigh heavily the subject variance and show that
only solution quality and length change over position.
The use of unusual meanings increases slightly.

To explain the increase in quality several expla-
nations may be invoked. (a) Warm-up is evident in most
extended exercises. Perhaps it takes a few solutions to
find out enough about the problem and its solutions to
produce a good solution. (b) The first few solutions
could be hurried efforts which are later revised and made,
for example, more grammatically correct. 3(c) Initial
solutions could be more similar to one another, hence are
more common and of lower quality. 'Later solutions are
less alike and different from the initial solutions, hence
are less stereotyped and of higher quality. Or (d) initial
solutions represent the response which is most strongly
associated to the problem. Later solutions have a lower
associative strength, because they are further down the
associative hierarchy.

It is apparent that additional data will be needed to
discriminate between these possible explanations. The fol-
lowing considerations led to the treatment conditions repre-
sented by Groups TOP and TUM. Solution quality is determined
by several variables. The exact relationship of any one
variable to quality is obscured by the fact that there are
many variables correlated to quality and that most of them

are intercorrelated. For example, unusual meanings frequently

95

use old pairs, such as Horse Lake. This obscures the rela-

 

tionship between word pairs and quality by making the corre-
lation more positive. Furthermore, the relationship between
position and quality is so small that it would be difficult
to show that a quality—related variable had the same rela-
tionship to position as quality. The treatment conditions
represent an effort to resolve this problem by increasing
the importance of a variable in determining quality so that
changes in quality would be accompanied by changes in this
variable. The influence of a variable would be increased if
the frequency of its occurrence were increased and the use
of confounding variables decreased.

Since the words happy, expensive, horse and lake essen-

 

tially represent moderate associability and meaningfulness
values, it is reasonable to ask what would happen if they
had more extreme values. By increasing the frequency of
occurrence of word pairs and unusual meanings the extreme
values are better approximated.

Lastly, Ss differ greatly in the frequency of use of
word pairs and unusual meanings. It was felt that the
observed relationships would be more evident if Ss were at
about the same level to begin with and were free to become

different as more solutions were produced.

Old Pairs

 

Learning sentences with old pairs alleviated some of

the problems with the normal case. First, the variance

96

(

between is for total word pairs used and for quality was
reduced below that of Group NClO for the first solutions.
Thus, Ss began at about the same point. Second, the
associative strengths for word pairs were increased such
that word pairs were used more frequently and hierarchy
positions were adjusted in line with the learning
conditions. Third, by the increase in the use of word
pairs and the decrease in the use of unusual meanings,
the correlation between word pairs and quality was
increased greatly.

It was hypothesized that learning sentences with
old pairs would (a) increase the mean frequency of old
pairs in solutions, (b) increase the initial use of old
pairs, but that use would decrease over position, and (c)
allow for_more of an increase in quality over position.
These hypotheses were confirmed and will be discussed in
order.

When associative hierarchies are assessed by the
method of continued association, associative strength is
inferred from the average position in the response
sequence and the frequency of occurrence of a particular
response. Taking Group NC10 as an example, the relative
associative strengths of word pairs may be inferred by
the average position of occurrence in the response
sequence, and frequency of occurrence agrees almost

perfectly. The associative hierarchy for five word pairs

97

may be said to go from strongest to weakest: expensive

 

horse, expensive lake, happy lake and horse lake.

 

 

Why should such an associative hierarchy exist at
all for the normal case? Or why should §S use word pairs
in sentences? Without adequate associative norms one can
only speculate as to the cause or the strength of associ-
ative links. -First, the motivation to use word pairs
could come from the fact that it makes the problem easier
by using two words in one thought or language unit.
Secondly, conceptually it makes sense to write about an

expensive horse, more so than a happy lake. Furthermore,

 

one has encountered more expensive horses than happy lakes.

 

 

Thus, one could attribute the motivation to initially use
word pairs to §S, and account for the order of their use by
established language habits.

After learning sentences with old pairs, SS in Group
TOP used vastly more old pairs and other word pairs than
Se in any other group. And the learned old pairs shifted
to the top of the associative hierarchy. It is not sur-
prising that §s learned old pairs or that they used them in
solutions, but it is somewhat surprising that they were
used earlier in the response sequence that other word pairs
in their own solutions and earlier than word pairs in other
groups. Voss (1968) assessed individual Ss' associative
hierarchies for eight words, then changed the hierarchies

‘with paired-associate learning of the stimulus word and low

98

level response words. A second free association session
verified the hierarchy shifts. Such a shift persists up

to 48 hours, although slight attenuation does occur (Bruder,
1968). These studies used associative hierarchies as
assessed for individual Ss. McConkie (1969) obtained similar
results using the Minnesota and Connecticut free association
norms. By learning sentences with old pairs, then, the
specific word pairs accumulate a higher associative strength
between the member words. As a result, when the words are
recalled for a solution, the pairs with stronger associative
links are emitted first. Apparently the learning was suffi-
cient to override normal language habits so that more word
pairs were used and old pairs were used prior to "natural"
pairs in the solutions of Group TOP and prior to "natural"
pairs in other groups.

A more difficult finding to explain is the word pairs
in Group TR. This group used word pairs more frequently
than Group NC10 SS, but Group TR SS learned relevant sen—
tences without word pairs. A second result of importance
is that the associative hierarchy is the same as the normal
case, except for the reversal of the weakest members.

Several investigators have found paired-associate
learning to be facilitated by pre-exposure to contextual
phrases (Epstein, Rock and Zuckerman, 1960), by pre-exposure
to meaningful syntactically structured verbal strings

(Rohwer, 1966) or by instructions to form sentences on the

99

first study trial (Jensen and Rohwer, 1965). These
investigators used response learning and verbal mediation
to explain the facilitation, and they point out several
characteristics of the material which influence the amount
of facilitation.

In general, the sentences as used in the present
experiment would provide the situation for the greatest
facilitation in subsequent learning. To some degree
response learning must be involved, especially since Ss
also learned and subsequently used only conventional
meanings for the given words. Secondly one would expect
some sort of special effort on Ss' part to learn the only
words common to all sentences. If this were the case, it
would not be surprising if the words were memorized
according to pre-existing language habits; i.e., word pairs
that were familiar or were meaningful were memorized first.
Also, in the first two sentences the phrase "the horse was

happy" was included, and in several sentences expensive and

 

lake were connected by prepositions or things around a lake
were labeled expensive. Rohwer (1966) found verb connectors
facilitated learning the most and prepositions were almost
as effective. In this way, the given words would be salient
and would be stored according to existing language habits to
be recalled later in solving the problem.

It would be interesting to see if syntactic facilita—

tion in the Jensen and Rohwer paradigm would be influenced

100

by the associative strength of pairs prior to learning
sentences. In other words, if a noun was learned in a
sentence with one highly associated adjective and one
lowly associated adjective, would the increment in asso-
ciative strength be only in the highly associated pair?
The present results indicate that naturally occurring
(or strong) associations would be strengthened first.

The data show that the majority of word pairs are
in solutions of Groups TOP and TR. In each of these groups
the number of word pairs decreases over the response
sequence? A simple explanation would suggest that Ss simply
forgot the word pairs. This is doubtful in 15 minutes.
Another explanation would suggest extinction or nonrein—
forcement as a reason for suppression of the response, even
though the pairs may still be available. This is possible
since sentences using word pairs are commonly very poor and
unexciting. As these data show SS then use the next
strongest associated pair, then the next, until they use
different pairs entirely. Furthermore, as in free asso-
ciation trials, §S do not repeat solutions, so they are
forced to move to different word combinations. Usually one
can also note thematic shifts between sentences, just as if
§S were instructed not to repeat the same idea.

It is one thing to describe associative hierarchies
and shifts in them, but it is another thing entirely to use

associative hierarchies to explain changes in solution

101

quality. In Group NC10 quality increased over the response
sequence in a linear fashion. But the use of word pairs
did not change significantly, and the correlation between
word pairs and quality was very low. One could argue that
the associative strengths between members of those word
pairs were not high enough to demonstrate a decrease over
ten solutions. This would be true especially if one con-
sidered all the possible adjectives which could be used

in pairs, such as brown horse or smelly horse. Surely

 

 

some would be stronger associates than expensive horse.

 

Furthermore, the lack of a correlation between solution
quality and word pairs could be due to the confounding
effect of unusual meanings which were frequently word pairs.
Whereas the use of word pairs alone will reduce the quality
ratings, unusual meanings, even with word pairs, will in-
crease quality. Thus, a correlation would include these
canceling effects.

On the other hand, solutions in Groups TOP and TR
contain more word pairs and far less unusual meanings than
solutions in other groups. As a result there is a strong
negative correlation between the use of word pairs and
solution quality. Group TOP represents an almost ideal case.
With the increased use of word pairs the mean solution
quality is lower than the quality in any other group.
Furthermore, as the use of word pairs decreases over the

response sequence, the solution quality increases. The

102

correlation between quality and number of word pairs was
-.87. Learning sentences with old pairs increases the
associative strength between the words such that more
word pairs are used in solutions. After using the pairs
with the highest associative strength, §s move down the
associative hierarchy to other word pairs. Sentence
length and complexity and word pairs are the only vari-
ables which significantly change over the response
sequence. The additive influence of increased length,
complexity and decreased use of word pairs may be said to
cause the increase in solution quality in Group TOP.

It is possible to speculate now on the relationship
between the associative structure of thought and the length
and structure of sentences. What I would like to propose
is that the length and complexity of sentences can be,
although does not necessarily have to be, determined by the
associative nature of the ideas comprising the completed
sentence. In the case of two weakly associated ideas (or
words), it would take a long, complex sentence to link the
two. Often the sentence would even specify the relation—
ship between the ideas. For example, one may wish to say,
"The horse was sticky." Since "sticky" and "horse" are
weakly associated ideas, one may wish to add a qualifying
Ifllrase to the statement such as, "the horse which_had just
tween doused with glue was sticky." The latter sentence is

lxnnger and grammatically more complex. On the other hand,

103

highly associated ideas could be used sensibly in shorter,
less complex sentences. Without a doubt the associability
of ideas does not account for a large proportion of the
variance in length and structure. But it may be the case
that in the present experiment increasing associability
also reduces the need to make long sentences.

Solutions in Group TR present somewhat of a challenge
to this interpretation. In this group the decrease in the
use of word pairs and the increase in sentence length over
the response sequence is as great as in Group TOP. But the
increase in quality is not as great. It only approaches
significance (P = .06). Perhaps this may be adequately
explained as a ceiling effect. By not using as many word
pairs as Group TOP (about 30% less), solutions rapidly
increased in quality until they could get no better without
an added boost which unusual meanings could give. But
Group TR §s used less unusual meanings than Groups NC10 and
TIR. The data show that the use of word pairs decreases
most in the first four solutions of Group TR, after which
as many word pairs are used as in Groups N010 and TIR.
Solution quality increases significantly for the first five
solutions, then levels off. It is possible, based on the
correlations with quality, that quality could get no higher
ivithout the use of unusual meanings. With the last five
scolutions being of equal quality, analysis of variance

vuould show no significant differences because of the

104

disproportionate accumulation of within-position variance
relative to the between-position variance.

As an experimental treatment learning sentences with
old pairs has some disadvantages. Group TOP solutions, on
the average, were different from those in any other group by
being of lower quality and using more word pairs. They were
also shorter and had less topic freedom. Apparently these
differences were unique to SS who learned sentences with old
pairs, even though the only differences between the learned
sentences was the word pairs, not length. Had §S not
learned sentences, perhaps these confounding results would
have been eliminated. One way to do this would be to have
.Ss learn paired-associate lists. The experimental words
could be included with several control items. Voss (1968)
and others have used this method effectively. Actually
the real question is whether highly associated pairs are
used more frequently and earlier than pairs with lower
associative strength. This being the case one could simply
compare high and low associates such as geg'ppgp and glppe
110188. Because of the lack of adequate association norms,
«one could scale pairs by Kammann's (1968) associability
IPating method; i.e., ask S3 to rate, 1 to 10, how likely it
“mould be that a given pair of words would be used together
it) a sentence. Other §S would be asked to write ten
S<Dlutions to the sentence problem, and different gs could

Luse each set of four words. Since quality has already been

105

shown to be determined, at least in part, by the use of
word pairs over position. One could also use the beta

weights obtained in the present experiment to estimate

what quality ratings would have been had the present

judges been used again. This would save paying the judges.

Unusual Meanings

 

It was hypothesized that learning unusual meanings
(a) would increase the use of unusual meanings, but (b)
that use would not increase over the response sequence.
Thus, it was expected (c) that mean quality would be
higher for that group, but (d) that quality would not
increase over the response sequence. The data provide
partial confirmation of these expectations.

The data follow the results with word pairs almost
exactly. Learning unusual meanings increases their use in
subsequent solutions and increases mean quality. The
obtained unusual meanings, like word pairs, follow an order
of emission which goes from conventional meanings to idio-
syncratic meanings. The number of unusual meanings increases
over the response sequence and solution quality increases as
well. Thus, the interpretation of this data will closely
follow that for word pairs, with the exception that unusual
meanings serve to increase quality.

The term associative strength refers to the position
of a particular response in a response series for an indi-
vidual S, or the frequency of occurrence of a response in a

group sample. The data for unusual meanings in Group TUM,

106

like word pairs, shows that common meanings are given before
unique meanings in the response sequence. Thus, one could
say that the associative strength between a word and a
conventional meaning is greater than between the word and a
unique meaning. The quality rating is also a function of
the commonness of the meaning. Conventional meanings are 1
rated lowest, common unusual meanings are rated somewhat 3‘
higher, but the highest rating comes from unique unusual i
meanings. As a rule conventional meanings are given first,
then learned or common unusual meanings, and finally unique
unusual meanings.
"Meaning" as used in the present experiment has two
meanings. The first refers to the conventional dictionary,
or denotative, meaning. The degree of commonness varies
a from the usual ppppe as a "four-legged mammal" to the unusual
"slang for heroin." A second form of meaning is the unusual
use or function of a word. Examples would be to use pgppy
as a person's name or to use a noun as a modifier in a name

as in Lake Estates.

 

From the list of obtained unusual meanings in Group
TUM it appears that there are more of the latter type of
meaning. The high correlation between quality and unusual
meanings indicates that the judges thought both types of
meaning were clever and that both types of meaning were
better than conventional meanings. It is at this point that

the use of "associative hierarchy" and "associative strength"

107

as used with word pairs seem somewhat inappropriate.
Perhaps this is because the established language habits
which result from word pair hierarchies are intuitively
recognizable. With word pairs a hierarchy can be based
on the frequency With which words appear contiguously in
everyday speech. These concepts, however, should apply
to potential associations as long as there is some
probability that the response will occur. Furthermore,
the data show similar response patterns in word pairs
and in unusual meanings.

The unusual uses problem presents a similar situa-
tion. In this problem SS are required to write several
uses for a common object such as a brick. In general,
uses which are familiar and can be readily recalled are
rapidly produced. After the familiar uses are exhausted,
however, more unusual uses are produced at a slower rate.
Thus, obtained latency curves negatively accelerate and
uncommonness increases over the response sequence. These
results have been interpreted (e.g., Christensen, 23 pl.,
1957) to indicate that less common uses have a lower
associative strength to the object, and it usually takes
several responses before one works down the associative
hierarchy to unique uses.

Turner's (1967) data show the progression from common
to uncommon uses as a divergence from the uses and prop-

erties one usually associates with the given object. He

108

was able to classify the uses of a brick, for example. The
first responses were "engineered uses," or what a brick was
designed to do, e.g., to use in construction. These are the
uses with the greatest associative strength. Later the
responses used the physical properties usually attributed to
the object, "compositional uses," for example to use a
brick as a paperweight. The most uncommon responses, and
the ones to occur latest in the production sequence, were
"shape-quality uses" where the use was not based on the
concrete limitations of the original object. Commonly these
would be transformations of the object, for example to crush
a brick for a filter in a moonshine still. In other words,
the solutions followed an orderly sequence of getting
further and further away from the object as it is commonly
used or perceived.

The unusual meanings obtained in the present experi-
ment follow a similar pattern. The first meanings which are
usually given are conventional ones. If §S learned sentences
with unusual meanings, conventional meanings may be replaced
with unusual meanings which were learned in the sentences.
The unusual meanings which occurred later in the response

sequence represented transformations 0f the learned meanings.

 

For example, Lake Park was learned and reflected in Horse

Lake, Lake Happy, Lake Happy Horse, which were progressively

 

 

less common. The transformed meanings could have arisen,

because §s could not correctly recall the learned example.

109

The infrequent use of most learned meanings seems to indicate
this, rather than the knowledgeable transformation of learned
meanings. As to why the use of unusual meanings increases
over the response sequence, the best explanation is that they
should appear as clever to Ss as they do to judges. As a
result they should try to recall the ones they learned or to
transform the ones they have already used. In any event,
unusual meanings should be more reinforcing than conventional
meanings.

The validity of describing the sequence of unusual
meanings as an associative hierarchy may also be seen in the
solutions of Group TR Ss. In this group Se learned sentences
with conventional meanings for the words to be used later in
solving the sentence problem. As a result this group used
less unusual'meanings than Groups NC10 and TIR which had no
interferring learning. Furthermore, the frequency of unusual
meanings did not increase over the response sequence. It
seems that learning these sentences limited the associative
hierarchy to a few very dominant responses. As a result
mean quality is slightly lower than other groups.

The connection between solution quality and the use of
unusual meanings is rather straightforward. In every condi-
tion quality is highly correlated with the use of unusual
meanings. The experimental treatment was able to increase
the mean frequency of unusual meanings and to increase solu-

tion quality. Regression analyses consistently showed that

110

unusual meanings predicted quality. Furthermore, as quality
increased over the response sequence, the use of unusual
meanings and their uniqueness increased.

In Group TOP the relationship between quality and word
pairs was somewhat confounded by concomitant increases in
sentence length and complexity. In Group TUM there are also
increases in sentence length, tOpic freedom and decreases in
word pairs. In the latter group, however, the use of unusual
'meanings contributes to solution quality so disproportion-
ately that it must be concluded that the increase in quality
is almost strictly due to changes in the use of unusual
meanings.

As an experimental treatment learning sentences with
unusual meanings was able to produce rather large differences
due to the importance of unusual meanings in determining
solution quality. On other measures Group TUM used as many
word pairs as Group TR, and Group TUM solutions had more
topic freedom than other groups. Neither of these variables
confounded the results. If this treatment were to be redone
without learning sentences, the methods mentioned for Group
TOP could be suggested. Paired-associate lists would be
unable to convey a meaning, because they lack the context of
a sentence. On the other hand, words could be rated for
meaningfulness by Kammann's (1968) method. Ss would be asked
how many ways a word could be used in a sentence. Using

groups of high and low rated words, groups of §S could

111

produce ten solutions to the sentence problem. The data
would be simply how many unusual meanings were used for
each group and whether the use increased over the response

sequence.

Instructional Effects

 

It was initially hoped that instructing S5 to
produce five or ten solutions might illustrate some differ—
ences in solution processes. Under standard instructions
there were no differences observed between Groups NC10 (ten
solutions) and Group N05 (five solutions). Mean values
based on all solutions were identical for all response
measures. Comparing just the first five solutions of each
group produced no significant differences either. In fact,
for quality the regression lines were almost identical. In
all respects it appears that under standard instructions the
first five solutions are alike whether produced as the whole
task or as half of the task.

Using simpler problems other researchers have found
that higher productivity is associated with more high
quality solutions, but also lower mean quality (e.g.,
Gerlach, e; pl., 1964). Johnson, Parrott and Stratton (1968)
found, on the average, that producing one solution was better
than producing many and that mean quality correlated nega-
tively with the number of solutions produced. In a more
controlled study Johnson (1968) found that this is, in part,

dependent upon how many good solutions are possible. With

112

the conclusions problem there are a few perfect solutions
(about 10). If Ss are restricted to produce 1, 2, 4, or

6 solutions, mean quality decreases as a logarithmic
function of the number of solutions produced. What appears
to be happening with this problem is that Ss persist with a
single way of looking at the data. By approaching the data
from several different perspectives better solutions could
be obtained. In the sentence problem the biggest decrease
in quality was between Ss producing one solution and Ss
producing more than one. With this problem there are many
more good solutions possible.

The present results with the sentence problem extend
these data to the five and ten solution case. Although
five solutions have a slightly higher mean quality, the
difference is not statistically significant for standard
instructions.

Criteria-cued instructions produce a significant
decrease in mean quality from five to ten solutions. These
solutions, however, do not differ on any other response
measure. Ss producing five solutions were given ten minutes,
and Ss producing ten solutions were given fifteen minutes
to finish. It is possible that with more time per solution
five-solution Ss were better able to use the criteria-cued
instructions. Another possibility is that both ten-solution
groups show no increase in quality after the first few

solutions. This could be due to fatigue or lack of time, as

113

Ss were informed of the time after the session was half
over. Or Ss with criteria-cued instructions could just
be more conscientious for the first few solutions.

When the first five solutions are compared, there
are no differences between producing five or ten solutions.
For quality the first three solutions of Group CClO lie
exactly on the regression line for Group CC5. All curves
match each other embarrassingly well.

Comparing these groups on response measures over the
response sequence gives some insight into why quality
increases over the response sequence. Whereas Group CClO
does not increase in quality, Group CC5 does. The increase
in quality for Group CC5 is uniquely accompanied by signif—
icant increases in unusual meanings and decreases in the
use of word pairs. The importance of these variables was
verified by Groups TOP and TUM.

The comparison of mean quality between groups with
and without criteria-cued instructions shows criteria—cued
instructions did not increase mean quality. Furthermore,
quantity instructions did not affect quality. The four
groups did not differ on any other response measure either.

1. , (1968)

Every study reviewed and the Johnson, e3
studies have shown that criteria-cued instructions are a
most influential variable. Why did they have no facili—
tating effect in the present experiment? One possibility

would be that the criteria-cued instructions did not

114

accurately reflect the judges' criteria. The data show
that the present judges did weigh response measures
differently than the original judges. In fact, the
original judges used the criteria-cued instructions as a
basis for the first Rating Guide. This could easily be
tested with different instructions.

By specifying the number of solutions to be produced,
the effects of criteria-cued instructions could have been
reduced. Other studies have allowed S5 to produce as many,
or as few, solutions as they desired, and under criteria-
cued instructions usually fewer solutions are produced.
Specifying the number of solutions to be produced could
emphasize quantity to the extent that quality will be sacri-
ficed and the criteria-cued instructions ignored. It could
be that fifteen minutes was not sufficient time to produce
ten solutions that met the criteria (at least in Ss' mind
this may be true). The result of emphasizing quantity and
providing inadequate criteria would be to reduce the average
quality level to that of the standard instructions. This
could be tested by intentionally varying the degree of
accuracy, or adequacy, of criteria—cued instructions under
fixed or undefined quantity instructions. In this way the

quality-quantity tradeoff could be better specified.

CHAPTER V
SUMMARY

In an effort to investigate processes involved in
productive thinking, this experiment tested the response
hierarchy theory of problem solving with a problem
requiring subjects to write a series of sentences. This
theory predicts that under free responding instructions,
as more solutions are produced, the solutions will be less
like initial solutions and will be judged to be of higher
quality, i.e. more clever, etc. The quality dimension
will be based on criteria which reflect prior learning.
Since the sentence problem requires subjects to write many
sentences which include four given words, there could be
associative hierarchies involving pairs of the given words
and word meanings. The theory would predict that strong
adjective-noun associations and popular word meanings would
appear early in a series of solutions. Remote associations
and unusual meanings would appear later and should be corre-
lated with high quality. Under instructions which restrict
responding by specifying criteria for high quality solutions,
early solutions should be the same as later solutions in all

respects, i.e. there should be no response hierarchy.

115

116

The present experiment used two naive judges to
evaluate quality on a scale from one (low) to seven
(high). Interjudge reliability was .86. With criteria-
cued instructions and noncriteria-cued instructions regres-
sion analyses indicated that quality could be predicated by
the number of word pairs (negatively correlated), unusual
meanings, and sentence length. Quality increased over the
response sequence for noncriteria-cued instructions when
subjects wrote five or ten solutions, but not with criteria-
cued instructions and ten solutions. Average quality was
not significantly affected by quantity or criteria—cued
instructions.

The experimental treatments involved subjects learning
six sentences prior to producing solutions. These sentences
included word pairs, unusual meanings, relevant words with-
out pairs or unusual meanings, or irrelevant words. Results
for subjects learning irrelevant sentences or none at all
were identical. Learning word pairs increased the associ-
ative strength between the learned adjective-noun pairs such
that (a) more word pairs were used, (b) learned pairs
shifted upwards in the associative hierarchy such that they
were given more frequently and earlier in the response
sequence, (c) sentence length decreased, and (d) mean solu-
tion quality was lower. Learning sentences with relevant,
but unpaired, words increased the use of word pairs, but

relative position of pairs within the associative hierarchy

117

did not change from that shown by control conditions. Also
both conditions increased the associative strength between
the words and their most common meanings, so that less
unusual meanings were used. In both conditions quality
increased as more remote associations were used. Learning
sentences with unusual meanings also increased the number
of word pairs used, but the nouns acquired more new and

unusual meanings. As more solutions were produced, unusual

 

meanings became more unique, hence quality increased over
the response sequence. Mean quality for this condition was
higher than for other conditions, because unusual meanings
were more highly weighed in judging quality than other
variables.

These data were interpreted to be consistent with the
response hierarchy theory and the general View that crea-
tivity involves a process of breaking up old associations
and forming new ones, i.e. a divergent process. To the
extent that externally or internally produced instructions
provide cues to high quality solutions, the response hier-
archy may be by-passed or may remain covert. Then no low
quality solutions will be recorded, and no response hier-

archy will be apparent in the solutions.

BIBL 100 RA PHY

118

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APPENDICES

123

APPENDIX A

124

APPENDIX A

A QUANTITATIVE DESCRIPTION OF RESPONSES

TO THE SENTENCE PROBLEM

The purpose of this study was to determine the
relative contribution of a wide variety of descriptive
variables to the quality of a solution to the sentence
problem. Based on the introductory discussion and upon
the Rating Guide, 16 variables were derived which appeared
to quantitatively describe how one sentence could differ
from another. This number was reduced to the nine used in
this study after correlations showed some variables to be
repetitious or not at all correlated to solution quality.

The solution scores on these measures were factor
analyzed to indicate the underlying relationships between
the measures. By this method several independent measures
were found, and their relative contribution to solution
quality was ascertained. Furthermore, the relative contri-
bution of position in the response sequence to quality and

to other quality-related variables was ascertained.

Method

Subjects
The S were 40 students of Introductory Psychology

at Michigan State University. They were tested during

125

126

the Fall term of 1965 as part of a larger experiment

on productive thinking.

Materials

 

From the several problems completed by each S the
sentence problem was selected for analysis in the present
study, because it was most amenable to quantitative
description. The instructions for this problem were:

Below are four words. Your task is to write
sentences using all four of these words.
Write as many sentences using all four words

as you can in the time allotted.

The four words were: happy, expensive, horse and lake.

 

Procedure

 

As Ss entered the lecture hall for class the booklets
containing all problems were distributed, and Se were
instructed that this would be an experiment and not to open
the booklets. On signal everyone worked for seven minutes
on each problem, and on completion the the booklets were
collected. For each problem Ss wrote as many, or as few,

solutions as they desired.

Results
The obtained 215 complete solutions were typed, coded,
and independently judged for quality by two judges on a
scale from 1 (low) to 7 (high). Interjudge agreement was

.89, which is acceptable. The basic criteria were "the

127

sentence should contain all four words, be well-constructed,
and the given words do not appear obtrusive.
The following response measures were used in this

analysis and defined in the previous study: quality, word

 

pairs, unusual meanings, tgpic freedom, complexity and

 

 

length. The following response measures were only used in

the present study. Word moves--number of moves from the

 

word order as given in the problem (range of possible scores

= 0-3). Number of responses--number of solutions written

 

by S in seven minutes (2-20). Position--ordinal position
of that solution in the whole response sequence divided by
the quantity, number produced + 1 (.15 - .99). Each Solu-
tion was scored on each variable.

The solutions were initially factorized using the
Factor A program for orthogonal factors and secondly by the
Factor C program for oblique factors. Both programs were
furnished by the Michigan State University Computer Center.
Guttman communalities and Kiel-Wrigley criterion of "three"
were used. Quartimax and varimax rotations were computed
and were identical for the two-factor solution. Table A1
presents the correlation matrix which was factor analyzed.
Note the correlations between quality and the other
variables.

Table A2 presents the factor loadings for the three-
factor varimax solution. Factor loading below .20 are not

given.

128

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129

TABLE A2.--Factor Matrix for Varimax Rotations with
Intact Sample.

 

 

 

Response Measure Factor 1 Factor 2 Factor 3
Quality .42 .60 .34
Complexity .73 .29
Length .79 .27
Number of Responses -.51 -.21
Word Pairs .28

Word Moves .66
Unusual Meanings .69

Topic Freedom .67

Variance Accounted 19.4% 14.7% 15.0%

For (Total 49.1%)

 

130

The sample of 215 solutions was randomly split in
half and factorized using the same options as above.

Table A3 presents the last varimax factor matrix obtained
for both samples. Only factor loadings above .20 are
given. Consideration of the deviation of these factor
patterns from that obtained with the whole sample must

be tempered by the fact that samples of 100 will inherently
be less stable than samples of 200 or larger. Thus, the
difference may be attributable to the unreliability of the
measures and to the instability in the analysis of small
samples.

As suggested by Cattell (1965) and Armstrong and
Soelberg (1968) the factor loadings on every variable
(regardless of size) were correlated between split halves.
The product-moment correlation was .75 and the Spearman
rho coeffecient for ranks was .71. Thus in spite of the
inherent instability in the small samples the factor
patterns obtained were reliable, at least in the test—
retest sense.

Quality loading on all factors suggested that the
factors all referred to the same concept and would be
correlated. An oblique factor analysis was executed using
the three-factor varimax matrix as input. The resulting
factor matrix is given in Table A4 for factor loadings
above .20. Factor 1 was correlated with Factor 3 at .233

which was the highest correlation obtained between factors.

131

 

 

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132

TABLE A4.--Factor Matrix for Oblique Rotation with

Intact Sample.

 

 

Response Measure Factor 1 Factor 2 Factor 3
Quality .36 .55 .26
Complexity .70
Length .76
No. of Responses -.48
Word Pairs -.71
Position .28
Word Moves .63
Unusual Meanings .69
Topic Freedom .66
Variance Accounted

For (Total 43.2%) 17.1% 14.0% 12.1%

 

133

Removing the restrictions imposed by orthogonality did not
change the factor patterns, except to reduce all the
loadings. With the same factor space as the orthogonal
rotations the oblique rotation was able to account for
somewhat less variance in a three-factor solution which
suggests that more factors would have been drawn off had
this solution not been limited to the input communalities
based on the three factor varimax solution. It would be
recommended that the principal axis factor matrix be the

input in further oblique factor analyses of this data.

Discussion

 

It is apparent that the factor patterns presented by
the orthongonal and oblique analyses are reliable in the
test-retest sense. Because of the stability of the
analyses, it is possible to interpret factors in terms of
the questions initially posed. The factor patterns indi-
cates that each variable relates to the quality of solu-
tions to this productive thinking problem. Thus, the
variables are interpreted to contribute to quality in
three unique ways.

Factor 1 is composed of variables which represent
quantitative and structural properties of the solution:
position in the response sequence, number of responses
produced, and sentence length and complexity. This may be
called "verbal structure creativity." The negative loading

of number of responses indicates that fewer solutions were

134

conducive to higher quality. One way, then, to produce
good sentences would be to concentrate on a few solutions
making them long and complex. Sentences may get longer
as more are produced through a building from one sentence
to another.

Factor 2 has the highest loading on quality and is
related to only two response measures, unusual meanings
and topic freedom. If one of the given nouns is the
subject of a sentence, it could be said that the noun
"dominates" the sentence. To use another noun as the Sub-
ject or direct object would turn the topic of the sentence
away from horses and lakes, and the given nouns would
become buried in the sentence structure and be less obtru-
sive to the reader. Similarly, to use a given word with
an unusual meaning is also to diverge from the structure
inherent in the problem as stated. Because of the high
loading of quality on this factor, I would guess that these
are the solutions which appear to be out of the ordinary--
they are the obviously creative responses. A solution
exemplifying this factor would be, "When Happy, our horse,
won the Concord Lake Derby, my father no longer grumbled
about how expensive it was to care for him." This was
rated "6." A reasonable label for this factor would be
"ideational creativity."

Factor 3 is drawn from the first factor as illustrated

in the difference between the varimax and quartimax solutions

135

and is conceptually related to the same variables. The
highest loadings on this factor are the number of word
moves and number of old pairs. Quality as a result of
these variables would be due to the random scrambling of
the given words to achieve some unique sounding sentence.
It is a superficial form of creativity, and quality is
easily reduced by the appearance of old pairs. Getting
at quality in this way could be called "superficial

creativity."

APPENDIX B

136

APPENDIX B
MEMORY TASKS FOR GROUPS TOP, TUM, TR, AND TIR

The format and instructions were the same for all
groups which had memory tasks, only the sentences to be
learned were changed.

Instructions for the memory tasks:

This is a short memory experiment. You will proceed in
this fashion: (1) Read one sentence from this page.

(2) Try to remember this sentence long enough to write
it down on the next page. (3) Do this from memory--do
not look back at this page when you are writing! Follow
this procedure for each subsequent sentence.

 

Instructions on the following page:

Record the sentences you have memorized on this page.
Do not look back at the other sentences until you have
finished the one you are working on.

At the bottom of this page were the instructions, "Stop!
Do not go on until you are told to do so."

Memory task for group TOP--1earn old pairs:

1. Because it was a hot day, the happy horse
enjoyed the cool water of the expensive lake.

2. The happy horse lives in a beautiful red barn
right next to the expensive lake.

3. The elf made the happy horse into an expensive'
lake. '

4. If you lived on an expensive lake, would you
like a happy horse playing in the water?

5. The happy horse trotted full speed along the

side of the expensive lake with a rider on his
back.

137

6.

138

The happy horse jumped into the expensive lake.

Memory task for Group TUM--learn unusual meanings:

1.

2.

I had a happy summer horseback riding at our
expensive lake-front cottage.

At Lake Park today a horse named "Happy" won
an expensive purse.

Looking at the expensive lake-front cottage my
not-so-happy father gave a horse laugh.

At Happy Horse Dude Ranch on the lake my sister
spent an expensive summer just horsing around.

Heroin, sometimes called "Horse," is expensive
to purchase at Happy Hours Resort on the
lakeshore.

Horse, my little brother, was happy to just
sit in the lake making gentle waves with his
expensive hat.

Memory task for Group TR--learn relevant sentences control:

1.

6.

Memory task for Group TIR--learn irrelevant sentence control:

1.
2.

The horse was happy by the expensive house near
the lake.

The horse was so happy as it pranced by the lake
in its expensive attire.

Watching the horse standing by the lake was not
an expensive way of being happy.

The horse swam the lake to get to the expensive
fodder and then was happy.

The happy jockey of the horse that won the race
bought an expensive house on a lake.

Although it was an expensive ordeal, I was happy
about buying the horse and the lake.

Money alone can buy big things full of noise.

Leave my money alone unless you want by big dog to
make a noise at you.

{me-:1.

139
I'd give all my money to get away from all the
noise of this big party and be all alone.

Alone, the man stole the money without a noise
as big as a squeak.

The big wad of money sat alone on the table in
the noise-filled room.

Alone in a big city with no money, I was afraid
of each noise.

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