EVALUATION OF SOME MATHEMATICAL
MODELS USED IN THE INVESTiGATIONf
OF iN‘T’ER-PERSONAL RELATlONSHIPS

Thesis for the Degree of M. A‘
MICHIGAN STATE COLLEGE

Charies Harty Proctor
T950

 

 

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THESIS

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Charles Harry Proctor

Submitted to the School of lraduate Studies of Hichigan
State College of Agriculture and Applied Science
in partial fulfillment of the requirements
for the degree of

MASTSQ CF ARTS

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x'nt of Sociology and Anthropology

1950

PREFACE

Evaluation of theories is a highly cuestionahle and some-
what "unscientific" undertaking. Any techniques which nirht
he thought to serve this aim may in turn be "evaluated". The

oroTIem is very similar to the atterots to prove the validity

(J

of induction. Always, the nrin isles of induction are called

upon to prove their own validity.

A technicue for evaluation can, however, he orooosed if

.~

the ultimate "ends" or "goals" of a theory are stated or can

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be reasonably assumed. As these ends of science hecome more
and more adequately articulated, the task of evaluation will
become amenable to solution.

It will be the ourpose of this thesis (after deciding

st "ends") to develon some technioues for

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uoon certain mod

validation. The.

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techniques will then be apolied to two

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more mathemati-

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theories, 3h pole's interaction schema an!

are attempts to "mathematize" some asnects of a social science.
Although these theories are not representative of either what
is being done or what may he done in the area they may help

to point uo certain general consequences of msthsmstizeticn.

In addition, hese particular theoretical systems deal with

the small or primary :roun. This field of inter-narconal re-

(3

lolory, if the

letionshios may he found to nermeate all of so

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conjectures of tneor in this area are oon°irmed. Thus,

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one of the purpose: will to invostijete the tenabilitr of

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sucn conjectur-

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Cne word of caution is necessary.

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all Jujfiments of value must be made rslftivs to +hsse trohlems.
The strortly “olcmic ton; of too thesis can then he erolained

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rest a acknowledgment is due Dr.

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Thu author realizes
Leo Katz for a basic reorientation toward the statistical
portions of sociometry. Another pervasive influence was con-

tributed by the book, Structure of Social Action, (Kclraw

 

Hill, 1937) by Tallcot Parsons, which, althouth not cited in

‘A\ -‘< t- "\ ".v\ . 10" 'VI ‘3 ~‘. I. 4' i
“a text, has Lean res lonelhle for a i:r_,e snare oi the

II

III

‘TA‘LC CE SCTTSNTS

Introduction and Methodology. . . . . . . .

Ghanple's Interaction 30*

p. Satirical Constructs and their Scorjiza
definitions 0 O O O O I O O O

f -F‘ L. N A » yv A fi’<-y-\ ‘. (— 1 fl . fl 4-
v. deletions setween thlIlCd oorst:ucts.

3. {Isles Of TltCIcrvo o o o o o o o o o o o o
SOClODeth. o o o o o o o o o o o o o o o o

A. In I‘OiUCthn. o o o o o o o o o o o o o
0. Statistical Analysis. . . . . . . . . .
C. Eatrlx Analy318 o o o o o o o o o o o o

0. Conclusions . . . . . . . . . . . . . .

12

17

IV Technical note. . . . . . . . . . . . . . . .

A. Expected Frequency Distribution for Fair deletion

- C

r. i

o. {rehability Distribution for O, l, ...,

nfi

Choices when d - l. . . . . . . . . . . . . . . .
o. Frequency Distribution for a Posteriori Inter- an

Within-Class Choices. . . . . . . . . . . . . . .

D. A Posteriori Distribution for Choice Statuses . .
V Summary and Conclusions . . . . . . . . . . . . . . .
IV Conjectures on the Broader Asnects of Inter-personal

Theor)’. O O O O O O O O O O O O O O O O O O O O O O O

UT

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I Introduction 3nd Eethodology

A scientific theory may be regarded as a "tool". he
evaluation of theories can nroceed on a basis similar to the
process of evaluation as used in econom c analysis if this
"analogy" is accented. The analoiy is deemed ascertable as
a convenient first aorrorimation in evaluation nrocedures but

its difficulties will soon become annarent. In economic

ir snnlication is

 

inexoensive and the result? are desirable. Cne can make a

1 Although sucl a statement is evtremely broad, its elabora-
tion would require more space than is necessary for the our-
pose of drawing our analogy.

 

similar and more specific statement, in terms of tSBOPleF,
such as: theories have hivhest value insofar as their cooli-

1

cation requires a minimum of time, training, ~no exnense, and

i

insofar as the resulting explanation and/or orelictions are

abl\

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detailed and widely aonli
The two main variables, then, are (l) anolication, and (2)
resulting exolanations, which corresoond to the "means" and
"ends" in an economic analysis. An attempt will be made in
this section to find catezories by which these two variables
can be described. That is, the possible "values" (in the math-
ematical sense) of these variables will be specified. But

been comoleted the problem of comparing

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after this analy

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these "values (renresentina different

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various combine

theories) has not been solved. As a matter of fact, it does

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ct seem possible at this time to qive a go
(r mem.beri ng that this problem of value is a moot question

iffioulty will be avoided by melting

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even in economics). This
only tentative statements corceriin< the value of a theoretical
system as a whole. The problem of specifying the categories
of the two variables can, however, be attempted.

he most adequate ch51 racterization of a theory in terms

of "application" and "resulting explanations" would have to

be done as a result of actual use of the theory. After trving

(I)

the theory in many instances, som judzments would become
possible. This prooc dure is cuii etedious, and if by oore;ul

results could be obtained,

'"5

examination of the th-ory, e simila
the empirical tests would not be necessary.
It is hy.oth oecsted th1t. such a procedure of examination

al test s. This

0

can be developed to replace el -borete expiri

U.)

T tieo reti-

V

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(I)
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procedure consists of delimitin: three main tree»
cal structure, namely (1) coordinating definitions, (2) logical
consistency of the total the orv, and (3) levels of interration.
Coordinating definitions describe the oner *ions by which
”raw” data are carried into concepts or, better, empirical

2
constru0ts. 'Tney are OI tne iorm: 11 (sucn and such

a. DO

raw

 

2 To examine Trcoordinating; def nitions" is similar to, but
less inclusive, than examinin ctbouolosy

 

data) is observed, then (such and such eonirical construct)

exists. For example (from sociometry), "If Bill says he would

like to work with John, then Bill 'chooses' John." "Chooses"
or "a choice" thus becomes and empirical construct. For any

coordinatirg definition to be adeouate it must transform raw
experience into some symbol so that no ambiguity in interpre-
tation arises. Coordinating definitions will be useful focal

points by which to examine the variable "means", alluded to

in the second paragraph.

Coordinating definitions to be valuable must:

(1) be "operational" or "objective" (i.e., different
investigators should be able to apply them and make transfor-
mations of the same "raw" data into the same symbols),

(2) be efficient (i.e., should not demand extensive
clerical or mechanical manipulations),

(3) be such that the te minology of the conceptual system
should not bias interpretations (i.e., a term widely used in
other theories should not carry any inapplicable meaninms when
used in the theory in question),

(4) minimize "feed back" (i.e., the operations should

q

not eact uoon the zroup to any appreciable extent).

-J

Logical consistency will be a comparatively simple problem
if mathematical models constitute the theoretical structure.
In the course of writin: the tiesis however it was found
a , 9

that what at first aopeared to be a model was actually a series

of empirical :eneralizations. Due to this fact, the theories

were never
Aformally re rarined for 10 wi a.l cons -istency. The problem of

logical consistency is still overly simple, because the theories

3

to 1‘e examined here show no elaborate lomical development.

 

3 The ease n for this will has ome apparent when we examine
the are; "levels of integration". It will be seen later that
theories of only a single level, preclude elaborate theoreti-
cal structure, and the two theories which will be examined
consist of only one w all developed level. Al hough the areas,
logical consistency and levels of intezration, are disjoint,
most of the discussion of lorical consistency will be carried
out in terms of levels of integration.

‘ *3

 

H

m of examination 0: models is still a nart of

1')“

The pro 1

(1)

our job of finding ca te ories to characterize the ends of

our mean-ends schema. Even if the theories to he considered

nematiccl models can be noted:

some of the a vantages or positive values are:

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or in lo fli al treatment is, while not quarantee-

to the syntactic than the sematic level. That is, relations

 

between the concepts, as defined by the functions in the model,
are stated in logically complete and simple fern. This allows
efficien tand effective criticism of the mo e1. -hat is, with
many socioleical theories one may not the venue feelin: that
something is wrong but to pinpoint the difficultv is impossible
(in many cases, for instance, 1~cca=1se of implicit biaoes).
(2) nfirmat ion or disconfirmaticn cecomas more precise

A V D , -.~ . 1" ‘ N R o g ‘. L ‘. n-‘ . "'
ooniirmation oy the use c: jPObgbillbgfiS imolies this type of

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4 Freund, John ¢.,."Cn toe CO"f1VEEtLO¢ of oci'rtific licories ,
Philosophy of Science, 17:1:f7-94, 1930.

 

 

 

theory while even the qualitative criteria can be more easily

 

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5 hack, newis unite utnguPUCtLCCS and Inferred entities ,
"i. . i H 1 C 5' ,.
railoscpny of ocience, l7zlz74-c6, 1;,o.

 

 

 

a ' ‘ "
(3) The use of an 'universol" larfuaie sucn as mathe-
matics allows a decrease in ambiiuity amen: the initiate as
well as a procedural familarity with such techniques among the

uniniatiated. This applies for instance to clerical help who

-

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can handle mechnical formulae vithou

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t- mathematical backzround.

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(4) An une<nlored fund of models are waiting toAuti-
lined, along with a tradition in mathematics of being a-”

fy and develop new ones(models) which mixht result in the

.4

0

Some of the disadV~ntases are:

a!

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(1) Lost discourahing is the fact that this is a type

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of theory construction d--andin; extensive researcu. Sociologi-
cal or inter-persona theory may not have, as yet, reached that

e of evolution whici would allow mathematization. It is

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quite obvious that the mathematizat ysical sciences was

-nd theoretical dis-

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possible only after a fund of empir
6

coveries had accumulated.

 

.5 Merton, Robert K., Social Theory
Free Press, Glencoe, 111., p. 85, 1959.

 

(2) A concentration uoon formalization has the notenti-

ality of "drying up subject matter so trw t n aw discoveries
become difficult. This means a preoccupation with syntax can,

when the investigator ias only limited time, exclude an inves-

(I)

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tiration of s ntic or, especially, nrajmatics.

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(3) Under the name of "mathematical models", many equations
and statistical "sliezht of hand" techniques may be forced into
a theory. This constitutes a danger because the mathematically

unsophisticate may erroneously res pe ct such theory.

w 1 '
Insofar as any given matnecat ice 1 mode el maximizes tne 'ad-

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' and minimizes the disadvantazes it can be considered

vantages
"valuable".

Levels of integration will be examined from two viewpoints.
The fir st concentrates upon a narticul.r theo cry, and the resulting
levels are comparatively uniquely determined. The second
approach consists of arbitrarily delimiting levels which are
applicable to any sociological theory.

The first approach consider. that those relationshins which
exist between the empirical constructs of any theory constitute
the first level of integration. They might be called the class
R1. It may then be found that betweenmembers of the class R

l

lation hips consti-

(I)

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certain other relationshirs exist; the as r
tute part of the seconc level of integration, or Lelon: to 32.
Cthe r members of 32 might be the relationships between some 31
and an npirical construct. The other levels are added in the

fig:

 

7 by this aeproaoh, the resulting levels are
narticular theoretical st ucture, i.e., A 0
correspond by content to the R of another then

3

 

To use an ex mple: a social psychological theory in which

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the unit of analysis is the inoividuO 1 may be ex+en oed up'

 

of behavior symbolized

8 "Unit of analysis'r f c o in
cts. In the _ollowinv case it is the

re
by the empirical constru
individual's (social) be

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ynamics by defining the concent, groun

into the field of group
as so.ie narticular relationshios of sneti al nosition, psycho-
ical inter -reaction, etc. of cert ein ind ividue This

concept "group" may then be utilized to investigate (i.e., to

give meaning to) some inter—grouo conflict, cooneretior, or

other situation which will be interor eted as indicative of a

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peculiar in3titutional structrre. It may also be conven ant

to consider certa' structures

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as consiutive of certain "mentality". "Mentality", in turn, may
be a useful concept by W”lCl to inrestirste nrevicusly unstudied
institutional structures. In this hierarchy we can discern
four levels of intezretion: R1 - "individual", R - "small
grouo , 33 - Win tituticn" and R4 - culture .
Although in this thesis series of levels will be discerned
by the above method, the rcsultin: levels in the exarnle intro-
duce another technique. It may be more convenient to consider

the previous four levels as a reference 8081;. Then a socio-

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the tynes of social behavior, both investigated and hypothece ate
he theory can be compared to this we ale That is, any theory

losous or identicel to our "institutional

in

utilizing a concept an
structure" will (to this extent) automatically be assigned to
the third level. This technique is useful when the first method

annot be asplied, (for inst oce , when an author incomrletely
states his theory).

The difficulties of this latter procedure immediately

raises broader questions: Cf what use is this concert "levels
of integration"?, Are these f our levels delimited bv any so

called na-u ral law of social behavior? The delimitation of

H H

"ends" or scale

levels allows rough decisions to he made on the
which a theory may attain. But there is no natural law involved
in the choice of four levels; as a matter of fact such an ar—
bitrary scale contradicts, in a sense, "natural laws". All
social behavior is "naturally" explained as nart of a sinzle
usefulness" of these levels

system, not four levels; but the

is a more imoortant criterion.

The levels of integration in s taeory are directly related
to both the "comnleteness" of exnlanetion and the "wideness" of

aonlica tion. By comrleteness is meant the erount of detail in

heory can ade o.et ely exolain. By

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"wideness" is meant tne diversity of situations i'nich the theory
can exolein. These two characteristics are not indeoendent.
They are (over a collection of theories) in a rou 3h masher

inv: rsely rele ted. In addition this inverse relationshin is

due to the differing levels of in stration of the theories. A
greater number of levels imnlies more "comnleteness" while a
lesser number imolies more wideness.

Due to the vagueness in determination of ell three character—
istics, (completeness, wideness, and number of levels), the
relationshins are very rough. Put to understand why the rela-
tionshio should hold, consider an examole of a low level theory,
physiologi. thsiolo:y onerates in sociolo:y by setting up

ch detailed ex-

go

broad limits to behav or, but can not score

to

planation. It has the characterists cf wideness but not com-

sleteness.

r.

PhysiolOgy is, however, diiferent from our other levels,

 

 

 

in that, its field of investigation is ”closed". The relation-
9 We rust keen in in; that toecroticf steuetures are "closed",
not the e“pirical date or behavior.

 

shin within physiolozy are a large extent indenendent of hither
levels. It will be found thet the relationshirs within inter-
personal theory are far from indenendent of our arbitrary higher

levels.

In the following discussion we will consider only two tyres

o
*e

of theories with respect to levels integration. These tynes
are "horizontal" and "vertical" theories. Horizontal theories
exolein all of R1 as the result of only a sinr.e integrating
concept. That is, all relationshins between ernirical constructs

reflect one orincitle, or are given "meaning by only one syn-

-10-

thetic concen . Vertical theories, on the other hand, contain
any levels, and for socioloty the admit that analysis can he
extended, eitler up or down, to new levels.
dy the previous discussion, horizontal t.eories will he
chars cter rizel, if they are 10 icelly well conct.ructed, by a

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mideness but a lan of co m l ,eiess . Vertical theories,

then, will be relative y "some see", but lsckin: in wide

 

 

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acplicatility.
13 This conclusion is "2113 or sociolor'ce theory only {t
the ore sent time. It is a corms ohse rvetion th relatively
' .
'ccm: ete theories are very restricted in errliccticn. This
is partially a result oi American sociolory' 5 concentration on
crly on "ociety. Cn the other hand, anthronoloricel senereli-
73 ions corehle .f wide aonlieahilitv vive only a limited er—
lcrc‘ion of erv social situation.
Now to su series this sftennt to characteri7e "means"
erd "ends".
\ H H H - H g ~ _ H , r H ‘ o
(l) reluatfl , i.,_ns luxgnr 4,1u;IJJ: cecrdinatirrg

H V '1 II H w H .
(2) valu ole ends irsly valuaole lotica consistency

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as a va Huab e mathematical

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ness of exnlenetion is to ca valuasle the theory should he

resoecitvely horizontal or vertical.

A few more points concernii: soecificelly the field of

-11-

_'

inter-personal relationships need to he mentioned hy wev of

n of this field is liehle to he

0

introiuction. Any definiti

disproven by the existence of some theory nurportir; to he

a)

inter-personal hut lying outside, to son extent, of our def-
inition. he that as it may, we will consider any theory inter-
personal if:

(1) its fie d of investigation is the social oehavior of

mail, homo-

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individuals insofar S;

fin ‘ .-, fl +1 ‘1 . ~w o
closed witn ies ect to one aoove aenaVior.

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that to sol

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system . Tnet is, to some extent the theory should reflect

tne fact that these small grouse ere orteriems". Chenple's
ll
tired interaction schema deals first with pairs of individuals.

 

 

 

ll Eventually the schema is extended into all areas of Lehavior.

 

Since this area both fits under the above definition and is

mathematiéal we can justifiably examine Chaople. Sociometry,

on the one hand, is difficult to consider as a sinrle theoretical
system and on the-other it is practically impossible to hother

examining each and every research work done under the name,

U)

ociometry. For sociometry, then, we will first look at the

c+

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cry 9 mathematical portions which will lead naturally to

.-

consideration of the principal theorists, horeno and Jennings.

-12-
II Chaople's Interaction Schema

A. Field of Investigation.

Since this oarticular theory was desirned to renlace the

1 ' [a _ ..fi " .°
"guess worn' oi current social nthro 01 r its domain of ir-

o
‘<

9)

 

l Chaoole, Elliot D., "Reasurin; human Relations: An Intro-
duction to the Study of the Interaction of Individuals", Genetic .
Psycholo;y monograohs, 22:1:3-147, 1940, no. 5, 6.

 

 

quiry is ohe whole of human social behavior. Actually the mathe-
matical model is concerned with the non-symbolic nature of "inter-
action", (i.e., eliminatin: content) where there is face-to—face
contact between nerticioants. ‘urthermore, the more nrecise
etnirical generalizations concern the

oenavior of only two or

three individuals at a time.

B. Empirical Constructs and Their Coordinative Definitions.

(U

Cheapl- has great respect for tne empirical, observational,
atural science anproach. Thus there is no need to so into

all of his definitions but just a few words, by way of exaonle,
about one of the most debatable, "origination".

"Given two individuals,we observe that one of the two
manifests the first unit of action which is then followed by
a unit of action manifested oy the second individual. The
first unit is regarded as the stimulus and the second unit as
the response. The distinction between the two is that the
first action is not nreceded by an action of the other indi—
vidual ... It may be regarded, therefor, as an origin or ini-
tiation of action to which theacticn of the second individual

2
is the term_nus or resoonse.

 

-13-

n1

This is rather an abrupt introduction to onsoole's opera-
tional outlook but serves as an examole of his orientation.

All phenomena studied are related to the observational nrocedure
and in this case we see a distinct bias for the laboratory situa—
tion. All individuals are under such close scrutiny that the
"minute muscula.r activity" of one in N_vidue l which is then

followed by some change in behavior on the part of another in-

nd termed an "origin of action"

on

dividual can be recorded
Even more Chaople does on to es that althouth an individual
9 v _.
may be manifesting muscualr activity the imoortant observational

3

point is to record the changes in nattern of this activity.

 

3 Ibid., D. 27.

 

It is the initial change in nattern on the part of one individual,

 

immediately followed by a change in the activity nattern of an-
other individual, which determines "origination"

Although "pattern" annerently caused no trouble to Chaonle's
oservers, the criteria of an onerational science would not ad-
mit sucn conceots as natterg. This is an intuitive notion which

is subject to analysis just as is inb3PRCthu. In the assign-

ont of ori ins ion of action it

B
U)
K I)
E};
:3
’)
<1
)
d
\<‘,
i-J
,4.
p‘J
.)
..J
k
r+
)
1
Cf.
(+-
,_)
(D

H.
(D
O

oneratioial procedures would rive way to observational
It is too difficult a task to re thoroughly objective.

In addition it does not seem olausible that the notion of

 

follow says all that is imrlied. Two individi els m.s LV be worl-
io; at adjacent machines, one may leave his machine, immediately
afterwards the other may also leare; does tris constitute a

1

stimulus and a reset nse? Unless the observer also noticed that

-14;

they both went in Opposite directions or that the whistle

blew just previously, he may be inclined to say so. This
example paints a black picture but more subtle judqments on
the part of the observer are not eliminated by the elaboration
of "recipes".

In this section the primary goal is to develop a nota-
tional system capable of exhibiting the empirical generaliza-
tions. This notational system is not Chapple's and consequently
one must be:n15uard against constructing a "straw man".

First we observe action on the part of individuals and
discover that for purposes of this theory it can be character-
ized by five dimensions, (1) who is acting, (2) who stimulated
him, (3) who does he in turn stimulate, (4) how long does he
act, (5) during what space of total time. All of this infor-

mation is embodied in equation(l).

n2 EU n2 2}
(1) 21 = Z 1‘ (t)
n Zk 212k
1 t, : n1
where 21 represents the individuals who are (is) acting,

23 represent the individuals who stimulate(s) 2i,

(0

2k reoresents the individuals who 21 stimulates,

no ‘13
2:1 represents the length of time :Ei aot(s)

under the above conditions,

and ml, to n represents the Space of total time.

2
239 Si, and Zk are generalized notation which will be

 

.3

:15;

replaced with specific letters if single individuals are in-
volved. 2E3, say, may be composed of individuals a, b, c,
and d, either of the four or any combination of the four may

be stimulating ‘zik:and satisfy the meeninz of‘ fiij.

fégjii (t) can be considered a function of time which, when
1 k

the described action is goinq on, takes the value 1, and 0
otherwise. The summation can be over any desired intervals
which are usually one second.

Now before we write any equations more concepts are await-
ing definition in our notational system.

(a) uuration of event p = hp - Bp,

7. <. . ‘ Q P 1 -
where Bp is the value of t satisiyingz‘> £12k (t) - l, i being;
anyone of the Iik,
(2k)
such that f t-l = O
<2k><2i>‘ ’ '

and Ep is the first value of t following Bp satisfying

f(Z k)
(2' k) (2k)
(A-k)

such that fk(A-k)(t-l) = l. for all i = l, 2, ..., E - B ,

where A = (:Ek) and k is one of the (iik), with the general

(t) = 0.

condition that the total membership of the event, (2k), appear
as either a stimulator, actor, or respondee.

(b) Mean duration of 1's actions for event p = M10

E k ‘
where M '-'- p 12

11’ Bp 2k

ni

p

where nip is the number of 1's actions in event 0, or the

it:
number of times finzzk (t) Jumps from O to l in the duration

-15-

of the event p.
(0) Mean duration of i's action for any given number, n, of

actions within event p - Sin’

, a 25k
wnere Sin - 1

th'

n

 

where h is the time at which i started his first action, and

g is the time of the last second of this nth action with Bp - h,

g-fl‘p'

Chapple computed consecutive Sin's for n = 5 in pair
events (2k = i + k), that is, he summed the durations of 1's
first five actions and divided by five, summed the durations
of i's next five actions divided by five, etc. He then
noticed that adjacent values were approximately equal which

led him to define the "slope".

(d) 1's slope (between t = u and t I v) - Si(v-u)’

v 22k

1
81(V-u) ' LEE-Q 9

where 5r equals the number of 1's actions between t = u and
t = v,

r being the number of S '3 combined;

15
u is the time at which the series starts and v is its
end point.

(e) Adjustment between i and k between the time t = H and

 

t = s = A n ,
lk(u-H) G 2k
25k — (G-H)
where A n H ER 2
ik(q-H) G 23:
25k
H :Ek

where Zk = k + 1.

-17-

o. Relations Between impirica Constructs.
Althcu h Chapple has devised, or rather suggested various
other measures, the notation has already become rather involved.

he poirt of diminish-

Shapole's determinentel abstraction is: interaction can

be considered as a process in equilibrium. As defined by

-

‘

V 0 3 O ' O
Cnasole eouiiiorium implies that, '...within definable limits,

L A

the relations of individuals are constant. ... an individual or

a group, regarded as a system, returns to these constan values
after the impressed force is removed;" intense or lasting

4

forces may produce a permanent chanse in the system.

 

4 Ibid., p. 37.

 

Thus he expected these indices or concents to show some
consistent relations with each other, both over a series of

events and, esne

(J

ially, within anv sin le event as the individ-

‘.

uals adjust to each other. There arose one hyn'thesis, (H),

\I

and three empirical :eneralizations, (E

this attezpt to demonstrate equilibr.um.

C
l 1 AJ Eni i

where O a is i's total number of criminatiors,
i zJ
0 q is i's total number of terminations,
2J1
and C is a constant.

This states that i's originations minus his terminations are

-18-

equal to a constant value. This constant value is a result of
1's previous conditioning, thus should remain the same for
broad intervals of time.

(El) For a series of pair events, (EERZ‘ i + k),

Min = c} for all p.
"(g 1‘:
a. k p
(E2) Within pair events,
v 25k
1
Y . S -
£11 105 i(v-u) + K21 %:;£;E ’

and for the same pair, 1 and k, this equation remains valid
within a series of events.

(E3) For successive intervals of two minutes the index

Aik(120-O) gradually becomes stabilized at a small positive
constant, Aik’ or Aik(lEO-O) = Aik(24O-120) - ... - Aik’

for individuals 1 and k who "adjusted" to each other.

Also in the nature of an empirical generalization the
frequency distributions of duration of actions and durations
of events are in the form of a J-curve which can be fitted by
the exponential function, dF = a e-deT given by Chapple,
which becomes dF = a e‘aTdT, where T is the duration of either
actions or events and F is the frequency of such actions or

events. The constant a will differ for the two cases (actions

and events).

D. Mathematical Model.

The first and most obvious fact is that we actually do'

-19-

not have a mathematical model. We cannot discuss questions of
syntax but only coordinative definitions. The emphasis which
Chapple placed on operational definitions was reflected in the
complex notational system which was necessary to represent the
nuances of these definitions. What good is a notational system
without any possibility for systematic analysis?

The "interpretations" which Chapple advances to explain
El, E2, and 33 are simply that these uniformities prove the
fact that interaction is "in equilibrium". It appears that
his principle of equilibrium is capable of the most indefinite
extension. Any uniformities at all can be used to prove its
existence.

This is not the traditional use of the equilibrium con-
cept in, say, chemistry. There the basic nature of any equili-

rium of ionization concentrations can be derived a priori

from the various amounts, the ionization and reaction properties
of the compounds in solution. No such simplification has been
achieved in the area of interaction. The fact that this in-
determinant situation does not approach the natural science
goal does not preclude that possibility, but does indicate the
need for more analytic theorizing. Statements of empirical
uniformities do not constitute a theory, logical interrelation-
ship has yet to be added.

If we were to argue the adequacy of this demonstration
using Chapple's criteria the conclusion would be more flatter-

ing. The important point to Chapple is the formulation of new

-205

and refined concepts using accurate, sensitive measuring in-
struments. By generalizing the empirical findings new theories
are born. But the point here is that in empirical generaliza-
tions one can find no assurances that the final theory will
meet the criteria of sufficiency and adequacy either as a
theoretical structure per se or as any explanation or solution

to practical problems.

To demonstrate this, look at (E1), (E ), and (E ). Each

2 3

generalization contains experimentally independent concepts.

(El) concerns a series of pair events, (32) deals with variable

periods within an event, (E

3

tervals, while he also gives distributions covering both, series

) refers to equal, two minute, in-

of actions and series of events. None of them are derivable
or explainable on the basis of a compact number of postulates,

nor do they appear capable of becoming postulates themselves.

E. Uses of Theory.
The most important contributions of this theory are

I . "5, . ,
'suggestions . These suggestions allowed tne construction of

 

5 Merton, Robert K., Social Theory and Social Structure, The
Free Press, Glencoe, 111., 1949, p. 91.

 

an empirically based social anthropolosical theory. This

 

6 Chapple, E. D., and Coon, C. S., Frinciples of Anthropology,
Henry Holt and Co. New York, 1942.

 

theory examines "set" events (involving more than two persons)

”with the purpose of defining some ordination of individuals.

~21~

With this theory, we are going outside the previous bounds

of our delimitation of "interpersonal" theories.7 But since

 

1? See above p.11.

 

this notion of hierarchy or ordination is so important both to
the sociologist and the mathematician it will pay us well to
examine Chapple on this point.

First he extends the notion of "origin of action" to all
events, separating those in which one member (1) of a pair
originates (component i) from those in which the other member
(k) originates (component k). The ratio of these componentS“
ngives a basis for ordination in pair events.

Extending this to the set events we get: "a hierarchy is
made up of individuals in interaction in which some individuals
originate action for others who in turn originate for their
group, and so on, depending upon the extent of the hierarchy."

As a result of this Chanple finds that institutions are
characterized by three broad levels or classes. Class A are
the originators; those individuals who serve exclusively as
the initial stimulus leading to interaction among any subgroup
of the institution; Class C, those individuals wig) exclusively
and the interaction by an action which serves as a stimulus to
no one; and Class B, individuals who in some situations or
events originate, and in others terminate action.

If we define "originates to" as "includes" would it be
possible that we do have a hierarchy or a partial ordering of

the individuals in an institution?

i n
Say 1 23 ("1 includes 3") if and only if g fi1.23(t)>0’
1

where n1 and n2 determine a time span which should cover a
week or so, and 2E3 is a subgroup of the institution, I, con-
taining J.

Does this definition satisfy the three properties of reflexive-
"ness, antisymmetry and transitivity? Reflexiveness: for all

i, i = i. This may be considered correct from the standpoint

1 8
that i responds to his own stimuli. Antisymmetry : if i g 3

 

8 Head, 3. H., Eind,;3elf, and Society, The University of
Chicago Press, Chicago, 111., 1934.

 

 

and J Z'i then i = 3. Since no criteria for identification or

equivalence have been set up we may accept this statement as

a definition (otherwise we will have a quasi-ordering).

Transitivity :if 1 = 3 and j = k then 1 - k. This is one point
9

at which the ordering breaks down:

 

9 Another definition of inclusion to avoid this bottleneck
would be: i = j if all the individuals to whom j originates
are included in the group of individuals to whom i originates.
This is simply set inclusion and does give a well-ordering.

 

n2 1

i Z " plies f (t)>0
3 1m, ‘ggr 1:53
1
n
3% k means that 2fJ (t)>0
Jiik
t=n1

where Zk is some subset of I containing k.

These two conditions do not necessarily imply that 1:; k.

It is difficult to understand how Chapple uses "hierarchy"

without the rationale to determine one. Even more basic than
these formal considerations are the observational difficulties
of determining oriqination which have been discussed above.
This theory's applicability to practical problems has
apparently been demonstrated by Chapple's success in the area

_ 10
of industrial labor relations. His basic principle for solu-

 

10 This impression was gained by the statement by Dr. Kimball
that Chapple claims wherever an industry has taken his advice
their problems are solved, otherwise they remain.

 

tion of any maladjustments is to restore the system to equili-
brium. There may be alternative theories having this principle
as a conclusion, but it, in itself, is innocuous. The faCt
that there should be some stability in human relations is per-
fectly admissable.

But the fact that this stability should be defined by (El),
(E2), (E3), and (H1) is not completely assured. Ask any in-
dividual, i, when he felt most "happy" and he is not likely to
say, "I was interacting with k, our A = O, my K and K

1k 11 21
were stable, and C: = ." He will be most likely to describe

U1 lb:

some incident in which he was enjoying an unusual experience,
and his description will be in terms of the "content" of this
experience.

2
or more accurately, physiological phenomena. There is no

[*1

l)’ (E ), and (33) are concerned with physical phenomena,

criticism of this approach as long as it does not claim to be

an attem t to describe all of human social behavior with the

use of only physiological data. But when Chapple takes up the

7.21;;

question of content and the analysis of symbols by use of these
11
physiological phenomena he gets into difficulty.

 

ll "measuring Human Interaction", op. cit., p. 111-127.

 

Humans run their lives with a value-attitude system which may
be possible of analysis down to a conditioned response to some
physiological interactional situation, but, after this situa-
tion has produced the value-attitude system, humans run their
lives by this system and not by the original interactional
situation.

Thus, Chapple's theory is an example of operationalism
to the point of diminishing returns and a challenge to the
emergent nature of social behavior which illustrates that
physiology is a helpiul tool but a poor master of sociology.
However, it will be recalled that it is not the whole of soci—
ology, but the field of interpersonal relations in which this
theory was to be Judged. By these standards it becomes more
adequate and with its strong empirical demonstration takes its
place as an important contribution.

In terms of the points of attack set forth in the Introduc-
tion we find that:

(l) Chapple's coordinating definitions were precisely
stated except for parts of "origination".

(2) There are two levels of analysis, with one member of
R2, "equilibrium", giving "meaning" to all the empirical
generalizations in R1,

(3) The application of the theory requires extensive

clerical help and statistical manipulation and is chiefly use-
ful in "suggesting" social anthropological analytic techniques.
Chapple claims that the theory will predict interactional be-

havior, and the suggested theory has apparently been used with

success in labor relations.

-25-
III Sociometry

A. Introduction.
Unlike Chapple's system sociometry has no unified theoreti-
cal structure, one will almo.7 t he re to be imposed. All that

1
J. ' 1
exists is a collection of "post factum hypo heses'. This state

 

l Merton, op. cit., pp. 90, 91.

 

q

of aff air rs has result as from sociometry's preoccupation with
very practical problems, and has been fostered by its compara-
tive success in this field. Eoth being.supported oy and also
su uppo ortin:,these two conditions,has been the basic technique
of sociometry whichkonsists of asking persons what they want

and then ttempting to satisfy these needs.

in

As an answer to a decided lack of theoretical precision,
mathematical models hrve been proposed. We will be dealing
here with two ma in types which are statistical analysis and

2
matrix analysis.

 

2 Sociometric technic cues may arbitrarily be divided into iour
ain areas: (1) sociograflconstruction, (2 ) "traditional"

index construction, (3) statistical test is and (4) matrix mani-

pulations. The irst two have no+ been 'maihematize d' adequately

enou:h to examine here, but the influ— an e of these two areas

permeates much of th e discussion on the latter tw wo.

 

The empirical constructs of socicmetry are largely similar
for both t pes of analysis. This is due to the fact that the

.i l

D;

(D
:5
1“?

ess

in

eta are mostly the tvee of expressed pre
or attitudes on the part of each individual tower; a situation
involvi ng ir t:rac*ion with some other individual(s). These

attitudes are elicited by the sociometric questionnaire, con-

..27;

taining the questions which verbally create some interactional
activity and which ask the respondent how he would (does or
did) feel about interacting with certain other individuals.

These two areas are separated only by the nature of the
theoretical structures. Actually the terms are misleading,
since statistics plays an important role in matrix analysis,
while matrices are utilized in statistical analysis. The two
areas refer to two developmental stages in sociometric theory,
statistical analysis being the earlier and concerned primarily
with testing certain a priori distributions while matrix analy-
sis is a comparatively recent innovation,.usina certain metric
manipulations and at the present time produces primarily a
posteriori hypotheses.

Some basic empgiCal constructs are;

(1) Choice -- an expressed desire on the part of a
certain individual to interact with some other individual.

(2) Rejection -- an expressed desire on the part of a
certain individual to avoid interaction with some other indi-
vidual.

(3) Criterion -- that specific interaction situation-
which is provided in the sociometric questionnaire as the basis
for choices and rejections.

(4) Test population -- all the individuals to whom a
given sociometric questionnaire (i.e., by specifying the cri-
terion, number and types of choices and/or rejections) has been

administered. These individuals will be identified by numbers,

(1), (2), ..., (it).

-28-

To be able to mean the most and talk the least we will

introduce the matrix of choices, C

c =/§/013/§/

where Cij = 1, if individual (i) chooses individual (3),
3:

C13
013 = -1, if (i) rejects (3).

0, if (i) is indifferent to (3) or if i

To include more information, the values 1, O, -1 can be replaced
with finer degrees of choice or rejection, the matrix may be-
come rectangular if there are more different individuals chosen
than choosing, etc. In almost all of the following analysis
we will deal with a N x N matrix, the same individuals doing
the choosing are the only possible recipients of choices, and

we'll use primarily the values 0, ard l for We will also

013'
deal with Just a single criterion and reouire that each
individual make exactly d choices.

It is then possible to consider the total information

present by specifying values of c for all i, j = l, 2, ...,

13
N. This total information will be called the "total choice-
pattern". The 1th row of the matrix will (i)'s "outgoing
choice-pattern" and the (i)th column will be (i)'s "incoming
choice-pattern".

The matrix can be examined for peculiar structure and the
following list gives some of the more important focal points

of configurations. The column sum for the itn column gives

(ilLs "choice status" (the row sums are all equal to d). If

-29-

'
(i)'s choice status equals zero we will se', (i) is an 'isolat

If 013 = l and c.,i - l we will say the (i) and (3) form a

"mutual" pair; if cij a l and = O, we will say (i) and (j)

c

31
form an "unreoiprocated pair; and if c.l = O and Cji = O, we
will say that (1) and (3) forr'ian "indif

and c = l and c, - l and . . . and c = l we will say that
xp tf

3k
I 1 i o p i
a 'cnain' ex13ts between (i) and (f) oi length equal to the
numoer of choices involve . f 013 = l, and i is a member of

some subgroup (a) while (3) is not a member of (a), then c
is an "inter-class" choice, if (3) is a member of (a) c will

1 H . ' ‘
as a witnin—class' Choice.

3. Statist cal Analysis.
To develop any statistical techniques it is absolutely

h

refeience or hypot he see. an
the basis of these hypothe as all +he pcssi“le samples which
might arise are divided into c_aoses which are ordered on the
basis of their probability of occurcnce. Thus, if an observed
sanple b. lcn . to soze class (of possible samrles) which has

a very small probability of occurcnce, the by“0t38r‘
rejected.

a.

In the case o: sociometric statis miaht define the

( 9'
r.»
C)
U)
(D

future total cno ice-

in

population to consist of all the past an
patterns produced by a diven sociom trio cuest‘onro re. In

L

this case any tiven administration of the Questionnaire will

yield only one value, hardly enough measurements to constitute
a +est. However, it is p as ble to direct attention to some

particular characteristic (or confiruratic n) of the c

matrix which will yield s'

3
(D
5
r+
CO

choice matrix. In addition it will 3 dossi‘le to derive
cateiories or values of such chariot ristios such th“t, if this
hs'act ristic of a :iven ice triT falls in e c rto‘
category or has a certain value some hvootqese“ con be rejects
Instead of hecomin: ties u? in tstraotion", consider
th1t ell of t4? rossiolo tot l cnoioe—rsttsrro constitute a
cless, S. SsCi srecific total choice-pattern is sssooiated
hlth one elezeat, o of S. TPen tor HO, w ice st“tes: the
probability 0. occur n for any ele: c, P(c) ecuals 1

different total

fferent

1.4....

restrict attention to

each individual receives, we can

thet any individual will receive

Which turns out to be the resoective
6.1
..s. .

'—1

pension K-l-d

N—l

*-

To derive the

-el assumi
H a ll

equally lixely .
ioice

“
a,
UL

derive

ition thet every

Since

matrices, H results.

0

only the number of choices

from Ho the orobability

N—l ch-i

0‘3

(D

ble

chosen by a rarticuler (j)

quals d , of not beinz c osen, equals N-d-l, then, since, the
N-l K-l
umhor of oossiblo mexs of hein' chosen k tires eouals N- ,
,
a

the rrobability

wh ch is

“’1 te

the k r“ o? the pre-

21

vious binomiel. By only the use of H in relation to total

0
choice patterns v: c n errive at the ssme resolt, which is not
surprising.

23

Although it would be desirable, a test has yet to be de-

 

2a A teszt of the choice status of just one indivndusl at a time
is a ”rough” Jay of testin: HO. If the choice stetus of one indi—
vidual sllo«s Ho to be accented, there are still 3 great number op
oti e1 non- anion configurations ,ossible. This is true of any of
the tests, however, but seems esoec ielly rue of this nerticuler
test. This introduces some orob e2s woich the author is not cec-

able of resolvin.{, but cen only su33est. There is obviously some
”dependence" of these tes tt, i. e. a rejection of H for some he rti-
cular confiruret' on rey be associe ted wi h rejectign in ano her
confi“uretion.

 

‘

signed for (18 frequency distrioution of choice statuses for the

whole grouo. It was at first susoocted thet some nrobsbil ity dis—
tribution of the voriance for this distribution could be worked out

by combine toriel techniques. But the rrobier

’3‘
( D
O
’3
(D
'n
c+
O
O
O
3
F3
J
H
(O
.14

u.

(in e.merner similar to derM. in; the nrobebilit

~<:
( 21
f.“
(O
(+-
H
C.
—+
H!
O
:3

for mutual choices with d>'l).
With a similar er3u2ent we can psrticularize Ho to arrive
at an exoected frequency distribution of pair relations (mu-

tual, unrecinroce te d, indifferent),3 inter-class and within class

 

3 See below p..51

 

4 1:
choices a nro obeb ility distribution of O, l, ..., N-l-d isolates,“

 

4 Loornis, C. r., "Foliticel and Cccunetional Ciee1rares in
Hanoverie n Villsae ,Germany", Sociometrv, 9:4:316-3 33, 194s.
5 Katz, Leo, The Di strioution of t‘e Number of Isolates in a
Groun, Institute of Statistics, inivereity of North Carolina,
himeo. Series 36,1950.

in

 

 

O, l, ..., ed inter-class choices where a = number of

 

5 idwsrds, Daisy, Ste e:rkey, "The Constant Frame of Reference
'ProiL m in SociO2etry”, Sooiometry, 11:4:372-379, 194E.

 

 

individuals in sucgroup (a) , and O, l, ..., N mu tusl cooices
2

-32-

(when d = l)7. In addition, the non-random factors operating

 

7 See below pp. 51-53

 

in the case of the choice status distribution can be, so to
say, partialed out (by a posteriori restrictions on column
sums) and a distribution for inter- and within-class choices

can be devel ped.8 Also an-a posteriori distribution-for choice

0

 

3— See below p..53

 

9

statuses can be developed.

 

9 See below p..54

 

' associated with a rejection of th- parti-

The "meaning'
cular null hypothesis is, as alwats, relative to the theoreti-
cal structure which attempts then to explain this peculiar
phenomenon. The selection of the above points of attack on a
choice matrix have, obviously, not been chéEEen by some whim
of the statistician. The configurations have definite meaning
to the sociometrist.

Two ineffectual (from the standpoint of this thesis) types
of theory have currently been used in the analysis of socio-
metric data whenever this data shows itself capable of reject-
ing some set of the null hypotheses. These will be called the
horizontal and more-horizontal approaches. The first theory
is traditional sociometry, represented by Moreno, and the second
is the type of theorizing found in the numerous research articles

in Sociometry which are 99 44/100% pure empirical generalization.

 

H
\N
\>1

'1

In the first type any rejection of the null hypotheses

10
can be explained by a single high level abstraction called

 

10 The terminology, here, is remarkably confusing, in that,
this "high level abstraction" is as far as content is concerned
part of a "low level of integration" (i.e., physiological pro-
cesses constitute a level of integration under psychology while
they are a lower level of abstraction). Level of abstraction
is more akin to a set inclusion property; processes (loosely
speaking, events or ob acts) which constitute a himh level of
abstraction are more genergl or simple and include, as special
cases, complex processes of the "lower" levels. Level of in-
tegration refers to a pattern of information which on a high
level gives adequate explanation to most complex phenomena or
processes and special cases of this total information will
explain simpler phenomena or processes.

 

"spontaneity", "tele", or "God". his is seen clearly in an

. 11 n
italicized quotation from fiho Shall Survive: back of all

 

 

Publishing 00.,

P"
CO
(D
\D
J
(D

11 Moreno, J. L., Nervous and hental D
Washington, D. 0., 1934, p. 159.

 

teractions between individuals there
must once have been and still are two or more reciprocating
physiolorical organs which interact with each other".

The second type is evinced by a long list of research
designed to explore some peculiar confisuration of the choice

matrix. In reality the term "theory" is used very loosely in

 

12 Some of the articles are:

Choice status:

Kuhlen, Raymond G. and Bretsch, Howard S. "Sociometric
Status and Personal froblems of Adolescents", Sgciometry, lO:
2:122—132, 1947.

Young, L. L., "Sociometric and Related Techniques for
Appraising Social Status in an Elementary School”, Sociometry,
10:2:158-177, 194 .

Northway, Mary L. and Wimdor, Blossom T., "Rorschach
Patterns Related to the Sociometric Status of School Children",
Sociometry, 10:2:186-199, 1947.

 

~34-

Seaman, Melvin, 'A Situations 1 Approach to Intra—aroup
Negro Attitudes" Sociometry, 9: 2- 3:199-2 06, 1946. (Used, in-
stead of soc ie 1 status, the near-sociometric scale of the Chic
Social Acceptance Scale)

rankel, Esther B., "The Social Rela+ionshins of Nursery
School Cdildren” ,Sogigmetry, 9:2-3:2lC- 225, 1946.

Northway, Fary L., TTS-c-J'ciometry and Some Challenzina Prob-
lems of Social Relationships", Sociometrx, 9: 2-3 W1 M197 1946.

French, Robert L. and Fensh, Ivan n., "Some (elatiorsnins
Between Inter-personal Jud gments and Sociometric Status in a
Colle e 3rouo", Sociometry, 11:4:335 345, 1949.

Crossman, Beverly, and Wrighter, Joyce, "The Relationship
Between Selection- Rejection and Intelli enc ea Social Status,
and Personality Amongst Sixth Erade Children Sociometry, ll:

4:346-355, 1948.

 

 

 

 

Isolates:

McClelland, F. M. and Ralliff, John A., "The Use of Socio—
metry as an Aid in Promotin;; Social Adjustment in a Ninth
Grade home- room” Sociometr J. 13:2:147-153, 1947.

 

hutuals:.
Deutschberger, Paul, "The Tele-Factor: Horizon and Aware-
ness , Sociometry,10:3:242-249, 1947,

 

 

Inter- class:

Faunce, Dale and Bee :le, J. Allan, "Cleavaqes in a Relative-
ly Homogeneous }rouo of Dural Youth" ,Sociometry, 11:3:207-
216,1948.

Becker, Myron 3. and Loomis, Charles P., "Measuring Rural
Urban and Farm and Non-Farm Cleavaaes in a Qural Consolidated
School", Sociometry, 11:3: 246- 261, 1948.

Criswell, Joan H., "A Sociometric Study of Race Cleavare
in the Class room" Archives of psychology, No. 235, New York,
1939.

Lundberg, George A. and Beazley, Virainia, Consciousness
of4gind' in a College Population" So ciometry, 11:1- 2:59- -73,

19 .

Loomis, Charles P., "Political and Occupational Cleavages

in a Hanoverian Village, }ermany" ,Sociometry, 9: 4 :316-333, 1946.

 

"In

 

 

reference to this more-horizontal type. A set of empirical
generalizations can hardly be called a theory, but it depends
entirely upon the definition of theory. In this sense a theory
would refer to a group of relationships obtaining between em-
pirical constructs derived from a collection of raw data in some

restricted area of inquiry.

In the more-horizontal tyne most of the "hunches" prior
to research are implicitely formed, consequently a more impor-

tant characteristic is the post factum nature of all the R1.

‘ H
Jennings, although securely packed up by "psuedo-confirmatory

data, is a prime example of this tendency to post factum
13
theorizing. To this extent, then, she is subject to attack

 

13 Jennings, H. H., geadershin and Isolation, Lon3mans,

Ereen and Co., 1950, Second Edition. The set R is extended
to cover a wide range of behavior, nevertheless she is weak in
both "depth" and "hei3ht" analysis. Many of the correlations
which she discovers are spurious: p. 53. while "what is done”
becomes, "wiat should be done".

 

 

by theorists who would claim such research yields only "sug-

l4
gestive" hypotheses.

 

14 Merton, op. cit., pp. 90-92.

 

Having carried out a polemic argument to this over exa33er-
ated conclusion, it mi3ht prove valuable to discuss just what
implications are justified as a result of statistical analysis.
First, it seems a legitimate assertion that rejection of a
hypothesis per se does not become an important indication that
choice behavior is non-random. It is more important as an in-

dication that with this particular criterion aspects of signi-

 

ficant choice behavior become apparent. Another focal point

of any rejection is the particular confi“uratien heinl sub—

jected to test, but this area has received extensive attention

1

judging from the literature.

To introduce some m asure of svstematization, consider

"1 ' s
the dimensions' or variables wnich must be eventually inter-

4

m

up described in extra-sociometric

0

related: (1) g ture of the gr

, (2) criteria, (3) conficuration,

\/

terms (by control variable

(4) rejection or non-rejection of H [Where X is some parti-

OtX

cular configuration(si]. To confirm any proposition for socio-
metry, deductions from the proposition should be capable of
Specifying the first three variables and correctly predicting
the third.

While the last three variables are straight forward, the
first is very complex, as a matter of fact to specify it would
require most of sociological theory. We now have a hint as to
the role of sociometry. Sociometry gives a picture of small
group behavior which can be explained by interrelationship
between group structure and the variables or concents of psy—
chology, sociology and anthropology. The concepts of these
three areas enter into our four dimensional schema by way of

15

"nature of the group". It may, how-

the amorphous category,

 

15 To avoid spending too much time on such a ridiculously com-
plex problemwe will only observe a few of the variables to be
specified when describing the nature of the :roup: age, sex,
race, and occupation comoosition, individual's reasons for mem-
bership (to increase conomic, social, or political class posi-
tion, artistic or pure friendship motives), group ioals or
normative systen, size of group, frequency of meeting, past
history, etc., ad nauseam.

 

ever, be valuable to notice which areas the sociometrists have

favored.

lize

H

\D

although sociometry does not attempt to speci n
psychological theorizing, this position is almost inevitable
To a large extent the explanation of the interrelationships

between, (1), (2), (3), and (4) turns out to be psycholoqical
reasoning. This orientation is dictated by the nature of the

raw data. Each individual chooses some other individual and

these actions are first seen as due to some individual "reasons".

It is quite possible to ask each individual why he makes such
and sucdfi choice with the response becoming a psychological
datun. An analysis of these reasons becomes an integrative
portion of heory on R2. Consequently many empirical generali-
zations have been constructed to relate particular aspects of
group structure to (extra-sociometric) psychological variables
which relationships are then explained in psycholorical terms.
There is, however, another level possible and that would
be a "social system", a concept on the third level of integra-
tion. The development on this third level would certainly
allow sociometry a more important place in sociological theory,
but various difficulties must be overcome. The basis for any
hope in this direction lies largely in further development of
matrix analysis which attempts to get at total group structure.
The previous discussion concerned with theoretical consid-
erations can not become an excuse for avoiding a discussion of
substantive theory. The previous four dimensions, waiting to
be explored under riaorous and precise experimental corditions,

may have to remain neglected for too long a time. But since

this thesis is not backed by original data he only way out 13
to look at the research and attempt to fit it in, deriving our
levels of integration as best we can and demandina certain
minimum statistical considerations.

The contribution to substantive theory which will be con-
sidered is the research of Moreno and Jennings. As was mentioned
above Moreno is a horizontal theorist, but he has set forth
various propositions capable of test. To quote again from
Moreno:

"Tale is the factor responsible for the degree of social
gravity operating between individuals and groups of individuals.
It is responsible for the degree of reality of the social con-
figuration above chance." This corresponds to our previous
conception of the horizontal theorist in that every sianificant
deviation from chance indicates to him "tele present". But
Moreno does so on to define tele more completely as closely re-
lated to the number of mutual choices, and we will accept this

,
more restricted definition.

 

 

15 Paul Deutschberger also following Moreno states, "The tele-
factor may then be isolated as the characteristic ability of
the given individual to create and to enter into mutual social
relationships, ("The Tale-factor: Horizon and Awarenes ",
Socicmetry, 10:3:242-2fl9, 1947, p. 243).

 

 

It is a major contribution of Jennings, however, which
allows us to relate tele phenomena to the previous dimensions.

Her argument, restated, would become: If (1) the particular

3rouoin3s under investigation are not desitned soecifically

for objective, articulate-, m-co ni_tic

W‘

or designed for the individue l or rersone 1 side of 3ainin3

co.- oanionship or "acc eptance" (recs ivin: 3ositive affect);
and (2) the criteria are uns stru ctured interactional situations

which are cond ucive to accomolishinent of these personal ends;

O

I]

(I)
9

and (3) we concentrate uoon investigation of neir relati

.L

the result of a statistical test of pair rel tions will be

03

rejection of the null hypothesis. If the first two conditions
do not obtain, testir 3 the pair relations will not necessarily

imoly a rejection.

Frankly, I have not been able to find confirmation of
these hyootheses. Jennin3s uses only the comparison of ner

cents, Deutschber3cr's research design is not enplicahle, and
17
maucoros does not nresent the relevant data. If, however,

k

 

l7 Deutschber3er and haucorpst, Paul B., "A So ciometric In-
quiry in the French Army' ,§ggiogetry, 12:1-3 :46-83, 1949),
have, nevertheless, derived certain internal pronerties of
the tele phenomena such as; correctness in indentification
by (i) of other oersons chc osin3 (i) is directly associated
Wl th the intensity which (i) chooses them (Deutschber3er)
and is asrociated with the number of mutuels in which (i)
en3a3es (haucoros).

 

18
we acce ~pt Jennin3' 8 results as conclusive does there exist

 

18 Not too dangerous en accents nce jud :in3 from the ori3inal
data, Jennin3s, op. cit., p. 238- 244.

 

an explanation for this phenomena? Jennings aroears to favor

some va 3ue traditional sociolO3icsl exolanation for the latter,

-40-

19 -
or socio group, phenomena while she turns to Roreno for an

19 Cp. cit., p. 278.

 

, , 20 n
explanation of tne former or psyche3roun, behavior. moreno

offers the explanation, previously quoted, on terms of physio-

 

20 Cp. cit., p. 575-7.

 

logical ultimate causes. Jennings then confuses the issue by

explaining relationships between an individual's choice statuses
I . .,

and 'mutual statuses" in the two cases as cue to the prior and

more pervasive psyche3roup structure, with only the residual

differences being due to some institutional or structure factors.

 

2l Cp. cit., p. 290.

 

Thus we have an elevation of the psychegroup or its index,

I
the mutual choice, into a realm of the "most powerful" and 'best"
22
type of group structure, both from Moreno and Jennin3s.

 

22 Moreno, J. L., YT-Sociometry and harxismw, sociometry, l2:
1-2:1c6—143, 1949, p. 14o. "The world is full of isolated
rejec ed, rejectih3, unreciprocated and neglected individuals."
These individuals are in psycho103ica1 misery.

Jennin3s, on. cit., p. 276.

 

"hen, we have dealt with the naive empiricism of Jennin3s

and the mysticism of Moreno the systematization of statistical

\D
H

sociometry be3ins to f. l apart. Te still have the unmanageable

numerous articles in Socioaetry, but it does not seem valuable

 

to attempt a synthesis here. the only way out is to 3st back

on the mathematical theme, and investi3ete those few extensions

21

-41-

of structural analysis which purport to descri:e the total

group.

C. Matrix Analysis.

One of the most prev- lent phenomena of inter-personal re-
lations and yet one of the most difficult to determine has been
clique structures or subgroupings of the original group. The
sociosrrem aopro nhas attempted to study or at least determine
clicue as but h s developed intde n art rather than a science.

‘
Into the breach comes matrix analysis with answers as to how
clioues shall be determined and studied scientifically.

There are two main types of solutions, one developed by

23 24
Forsyth and Katz, and the other by Perry, Luce, and Festinqer.

 

'1

23 Forsyth, b. and Katz, L., "A Natrix Arproa ch to the Analy-
sis of Socio. metric Data: Preliminary Report" ,Sociorn-_t§1, 9:
340- 47, 1946; and also Katz, L., ”On th e latrix Analysis of
Sociometric Data" ,Sociometry, 10:2:233- 41, 1947.

24 Luce, R. and Perry, A. D., "A he thod of Flatrix Analysis of
Group Structure" "Psychometrika, l4: 2:C j5-116, 1949.

Luce, R. 0., "Connectivity and 3enera.li7ed Cliques in So-
ciometric }roup Structure" Esrchometrika, 15:2:169- 90, 195 .

Festinger, "The Analysis of Sociograms Using latric Alqe-
bra" Huma- Relations, 2: 2 .153- 56, 1949.

Festinger, L., Schachter, S. and Back, K., Social F
in Informal 9roups, Harper and Bros., New York, 1953,

 

 

 

The first technique consists of mechanically permutina the
ori3inal choice-rejection (-l's allowed) matrix until the con-

dition, z Zc'.’1j(i--j)2 equals a. minimum, is satisfied. .A
25

simple solution toJ this problem has been intimated by Criswell ,

 

25 Criswellfi H. H., "Sociometric Concepts in Personnel Ad-
ministration , Sociometry, 12:4, 1949, p. 299.

but as yet has not been published.

The resulting matrix (if cliques are present) will show

clusters of + 1 choices alon: the main diagonal and the - 1's

(0

'

will be shoved into the corners off the main die3onal. Th -e

clusters of y l's indicate that the individuals are choosi

:3
04

"into themselves" with qreater freouency than "outside them-

*‘5

selves", and if the cluste s can be clearly boxed off the in-
dividuals involved are said to form a clique. The cliques
fart‘est from the center of the matrix are placed there because
they have ne3ative or indifferent choices going to and/or
coming from other individuals (principally those on the other
end of the main diagonal). Thus we have some measure of "social
distance" by using the final ordering of individuals. We also
have a measure of social distance between cliques by the same
principle. Those individuals near the center of the final
array are the most generally accepted individuals for the total
group while those individ als near the center of their cliques
are most accepted by the clique.

This picture of the group structure provides a two dimen—

H

sional picture, "social distance and "cliques", but is very

cumbersome to obtain. An extension to this technique has been
26

suzgested by Katz which involves factoring the choice matrix.

 

26 Op. Cite, p. 2400

 

This implies that the group will show two structures,one for

outgoing choice-patterns and one for incoming choice-patterns.

=43-

Since the individual could be expected tochoose himself, the
communalities could become equal to 1.

The factorial structure for the outgoing choice-patterns
and the incoming should show the same reference vectors and
similar factor loadings which would indicate pure cliques. Any
deviations from this ideal setup would show a lack of cleavage
even if in both structures well defined clusters of individuals
segarate out, but the group would also show a "disc ganization"
if thes two structures refused to coincide. It is possible

27

(says Dr. Katz) to arrive at a single factorial structure.

 

27 Since this would .ecessitate a symmetric matrix it appears
the unreciprocated choices could become 1/2 or in general a
new c could be defined _ _ . ,

13 ’ - 011 031. This, however, is

5
not what Katz had in mind. ‘3 2

 

 

Considering that we have this new sinile structure it
would yield to(o) many interpretations. The cliques could
easily be defined as those individuals havinq hith loadirjs on

a Iticular reference vector. The relationships between

e

cliques could be examined by the angles between ref
I1 ~ H a . —
tors ('oistance oetveen defined proportional to the "angle
1 I - ' 1 'I a
between"). Tne 'leaqers' of tne cliques are those individuals

1 . 1 a _ u v
having the hi nest loadings. The 'carriers' of information

The individuals who have the largest communalities will be most
If \\
"integrated" (i.e., they don't have towater-down their choice

output or intake because they missed mutuality).

 

-44-

H
:5
(D
(.0
r 0
(i)
L:
O
(D
O
' J3
<4
(+-
in
....a
7"!
H0
5'5
'\ 4.’
(a
C
c ‘J
O
(I)
{D
{u
P‘h
q
(1)
'( 3
O
‘1
i")
' 3
(a
O
H)
(3
A
,i
(...
LY
I
H
(n

th

2
see this let 0 be the i, 3 element of C , then,

13
011 013 * C12 C23 + °'° ‘ CiN CNJ '

which equals the number of three person chains connectin: i and

j (these are called chains of "length 2"). Since c . either

1J

O or 1, a contribution of l to 033 will only result if, for

some (k), 01k = l and CkJ 3 1 or (i) chooses (k) and (k) choeses

(J). Elimination of redundancy in chains oddength greater than
28
2 is laborious but possible.

 

28 Katz, L., An Application of Matrix Alaebra to the Study of
Human Relations within Crranizations, Institute of Statistics,
University of North Carolina himeo. Series, 1950.

 

This technique seems limited to a study of communication
29 30
processes. However, communication is by no means unimportant.

 

29*"Cliquesrr can also be determined but we will not :0 into this
application since the definition of a clique is almost too re-
strictive to be of great value.

30 See Festinger, Schachter, and Back, op. cit..

 

There does seem to be some possibility of extending its use
H q .. ...
into influence" studies where indiv1duals choose others as
' 3
'having 'influence' over me" or "under my 'influence'" in whicn

case the chains would become hierarchies of power. Cne impor—

tant twist is its use in determination of "carriers" or indi-

-45-

viduals who can spread news quickly. To find these individuals
2
3 is

n x I: _‘ '1" m " r -. , f,
+ x» + ... fCPPQu.3DJ.VdUMQ sole ,nliVAdu l

C"
:4
(U
(D
C
B
(J
‘-
C)

nae filled in his row with entries mreettr than zero he will
communicate to every nem :er of th groun in at least the number

of stees corresponding to the lest newer of 0 required.

p-J
(U
i
1
cf
*3
H
N
"3
)
‘3
>3
0
x')
O
:5!
...4
O
'3‘
’0
;s‘
l )
C
,4
D:
t-
(D
"3
1'".
(D
H:
H
4

Th

l-"

a)

1‘9 8

0

11

(D

1170"

mentioned, since a report on it appears in Sociometny.

 

. , T -, . T A, or"
31 CerVirxa, Jleoimir, "A Dimen31onal neory of Irouo ,
Document 253 American Documen etion Institute, Washin. ton,
D. C., to: reoort by S. C. Dodd in Sociore try, 11:1- 2:133-7.

 

 

 

...-m _-..__ ———---.~——~..—_--_ .—

Cervinka allows his matrices to lead him around to such an

 

extent the information he demands is rrectically imoossible to
obtain and the manipulation, consequently, becomes far too

cumbersome. fie does manage to sugrest the extension ofmacrices
out beyond the test to; lation into other ar reas. That is, in-

stead of an N by N matrix we have a N by N + M waere the extra

h variables are attitudes toward ideas or objects outside of the

()1

test population. This exte sion seems capable of yiel in:

f O
P‘}

valuable info: mat i.n by, say, fac torinz thi. I by N + M matrix
(usinm col -uznn intercorrels Mtions) T: ien t‘ie attit .ud variables

could be seen in relation to clique formation, etc.

D. Conclusions.

*1 v 1 O " V "
how that seeiometric theory has been “resented, some attempt

c+

ct o cordi-

(L)

C)

will be made to sum ma rize its properties with resp
noting definitions and le rels of integration.
\ '1 fl 0 O
(l) Coordinating definitions for soCiometry :ooeer quite

adequate. There is, sometimes, a difficulty

-AS-

in naming indices. The name of an index carries the implica-

tions of the originator, and sometimes these are debatable.

For instance, what we have called "choice status" is also termed

J.
L)

tus . This latter concept has dec ded resonances

in

social s

5L3

of meaning, that re not at all aopliceble in most cases. But,

since we do not deal in indices excent in matrix analysis, it

is only for this area that the definitions are debatable.

- I w w
(2) Levels of inte ration has been 'over-hasheo , out a

.T.
-‘
~J

?

summery may help. Do mathematical models exist for sociometry;

1 1 ~ .
the metastatioal manipulations are merely "tecnniques'. As a
matter of fact, no theoretical system exists for sociometry.

Sociomecry is a technique, abolicable to investisations on

any level of integration, and the data can be explained on any
level of integration. Cur substitute theorat cal schema suffers
from this same malady, "uneven erphasis uoon exper mentation

and data collection, without the theory to back it us."

If we might be allowed another cnonce, there is the nos-

sibility of interpreting sociometr c data by use of

 

 

tendency to be organicmic and a type of analysis evolved from
ohysiology should show some correspondence w th Koreno's inter-

pretations. In addition analysis of the arious levels of in-

f!

tegration can be separated in discussion 01 the "unit subserved

33

by the function".

-47-

 

:1

 

33 Ibid., p. 31 where merton mentions concents of rsychclogi-
cal fur ction,;roup fun notion, so: stal function, CU1+LUPE1'fUKC-

" _"7‘ ‘- ~ " A“ Pfi‘
tion, etc. . 'ne orresoondence netween these "echoests are
our four levels is not fortuitous but rrstifyinr.

The mechanical 10% a 3r;njin* out a norcdivm for the
functional ac’lysis of co ionetrio dots would then, tart sene-

7’1 . J- , ‘ I“ ‘H
pron matr A analys

I . 1
'carriers', etc.

II) hotivation or
individuals in the test

analyzing choice

tegrative) level, but are

QualifiC?

tion.
III) Functions

The

1)

n-zo nin;: srstem for
whic the conii ;'ura-
tion?1 or i on has
function.

Psychological Level:
First the structure

or model of personality

is we have

"reasons"
no ulation cons stitute v lid data

behavior in

of each particular

choice status niera

which lead to re-
These

eananes

l 1 . ‘ '3 i.
f‘“ “(3 f“ i C V' f“ '_'.v f" ’, .- V‘ ‘
lel‘iK/v ..Ie'..z-u‘iuf NIEJ $3.4qu6

for choices as resorted by
when
terms of the ;,ycn-lo’ic -l (in-

Tful fo- ther levels

see nin

only with

structure:

Functions.
a) For the psychological level a hifih
choice s atus manifestly indicates that

the nerson receiving it is socially ac-

should be constructed
for each individual,

then the neculiar choice

hyootheca+ 31. In

this conne m‘ion it seems

advisable to use a basic

H v. ,
(a la narci-

'U
m

I"

(D
O
:3
y.)

lity
ner) so that functio

can be imputed (to the‘
statues

choic ) having

(D

more :jeneral a7plica-

bility.

ian schema would allow

{D

asier interpretation,

dvnani-

U

m
r40
*3

‘00 3.

”'5

-sy-
chology fits ee.sily in-
to the functional or

organismic agproech.

cented an nd will derive the conse-
ouent increase in security (i.e.,
his 6:0 is validated) but a latent
function may he that this individ-
ual is increasi1*lv motivated to
leintain his oosition with resultin:
instability in his oerconolity.
The low man on the choice status
unfortunate nosition. Kon- acce otance
by a group will naturally lead

to some tyre of rersonslity dis-
organizatio if the individual
values highly oarticication in the
oarticular criterion. The effect
of the non-random choice status

uoon t‘: individual rersonalities

u)

!

must, of course, always be judged
relative to the particular person-
ality structures and to ,he criterion.
But since a "basic" personality
structure would ordinarily demand
some social activity, frustra-
tion of this "desire could be ex-
pected in the case of the under

chosen.

-49-

Interpersonal Level:

The mall informal grouns

CO

to which this term refers
are in actual practice
the most important (on
the basis of permanency
and intensity of their
existence) subgroups of
some institutional struc-
ture(s), they are esigned
to afford the membership
almost nure companionship
and thus demand only that
they be maintained, and

that there be some min-
. I
imum amount of 'meeting

of minds".

b) For the inter—nersonal level
a high choice status bestows the
role of leadershio or more accurate-
ly ind.soensability (i.e., in very
few interactional situations is

this individual omitted). This
will lend unity to the group if

the individual with the hifh social

(1)
*5

H
status r-oreseits", so to say,

the entire group. If, however,
there are two or three individuals

receiving hich choice statuses
and their "constituencies" are
mutually exclusive the result may
well be a dysfunctional cleavaae
the The under chosen

of group.

individual's frustrations may

result in his taking a dim view
of all group activities and thus

becoming a dysfunctional or damp-

enin" factor. The piling uo of

U4

individuals on particular choice
statuses may indicate a very demo-

cratic distribution of choices

‘

also may indicate cleavages

L);

f'“
2*

(which can be studied seoarately).

W:

This type of analysis must then be carried out for all
configurations over all levels of integration. The additional
points which herton requires (mechanisms, alternatives, limits,
chan e, validation, and imolications) can in like manner he

34
added. The theory may then hecome a leritigate nortion of

t

 

34 I will avoid the usual comment, "There's a thesis topic

here".

 

the social sciences, hut would it become a valu hie one?

l‘ ‘0

By our previous criteria of value, existin sociometric

if}

theory is not worth too much. It is not because of the ex—
pense and trouble associated with collectin: the data or in

the technioues of analysis. Actually it is in this area that

 

(+-
(f)
(D
:3
'I_Jo
Q
C
(D
U)

4' ~ 1 «r - ‘0 ‘ ‘.
sociometry is most valusole, e centin , gardens, fl?
‘1 m ~ n- v v‘-\ n 1‘ , , 1. s " w 1.. l‘ -
oi matrix analysis which oan, hovever, he seniled ty clerical
‘,'f‘. 1 .0 :V t .r': “w 1J1; fine a 4- an T" n g I? O, 1- ‘m ~ c n r“ a v»: Q A: A1 7‘. f“.
uric-IFS. in El :16;. ”V C.1..:\p L'O VL«’.J~-’.L ‘JP n Lit: 5.. vOjc 'C‘Ll'ui L2 ‘v -1“ --Cy
p ‘v a r-, ~ 3 ,~ .L .-\ ~.\ 0 V‘-
of tne emollnations and predictions W: e:e forced to defend a

p 1.: . -. at ~ 0 W. a. ...
rae oi theoretical riior whicntOCIOMetry cannot nro-

(a
0
‘b
(o
' 3
k
3
1
d.
3
I

would then be a cuick efficient techniou

'T,
./

IV Technical Note

A. 3xnected Frequency distribution for Pair Relations.

The orobability distribution for the comtinotion of

values (0, l) for and c s :iven in Table l. §ince

Cij 31 i

 

 

 

 

 

 

the total possille number of nsiro is Kgythe exnected fre-
c
l 13 o
2
l d g F-l-d
9‘1 ‘ (N- 1)
c
31 2
i dgN-l-dz K-l-d
O (K _ l)2 h-l
Table 1.

quencies are:

2
N d
mutual oairs,(2>(m) (013 = ch a l),

 

unrecinrocated Deirg, ('2) iii-$5.1 01.] = C- and ch = 1 or
Cij = l and ch = O
- 2
on N N-l-d
indiiierent pairs, 2 ‘E:§‘ (Cij = Cji = O).

2
The observed frequencies can be compared by )L test with. two

degre;

\l)

40f fr edom.

(D

_ h N
5.1 rrobability uistribution for O, l, ..., Mutual Choices
when d ' 2

l) The total number of choice patterns for the groun is

‘.

fl

N-l N v
given by (Ed ) which = (N-l)“ in this case (each individual

. N-l
can make d choices to any of k-l persons, Cd , and, since there

'1"-l

are N individuals, the Nth power of Cd qives the total number

of patterns for the group).
2) The number of choice patterns which include at least

' N-2 (

(N-l)‘ l mutual implies a pair of in-

one mutual choic = C
dividuals, and GI gives the number of ways this may arise; then
when d = 1 those two individual's choices are determined and

the staining N-2 persons have N-l possible ways to choose, thus

the (Ii-l)“-2 term).

3) The number of choice patterns which include at least

4 *-
2 mutual choices is given by 34 E;(Y—l)k 4 (when d = l, 2 ru-
2 N
tuals must involve 4 persons and these can arise in C4 ways.
“4
The pairina of these 4 can be done in :2 ways since both pairs
2
are determined then only one pair is assizned; as before there

are N-4 persons who still retain N-l possible ways of choosina).

4) By the same procedure we an derive the number of

N 5 C4 N-S
pattorns includinj at least 3 mutuals, 3g 04 _§(N-l) 3 4
N a 6 c4 N-8 2
mutuals, CF 3/ 34 _§(N-l) , etc., until some one of these
-- O 2

5) Then to derive the probability that exactly k mutual
choices will occur subtract the number of ways that at least
k + l mutuals occur from the number of ways that at least k

e the result by the total number of

Cu

mutuals occur and divi

choice patterns. Simplifyin: we get:

I
‘1

P [k mutu a1 8]
2(k t l) k + 2

(N-l) 2

N(N-l)...(N-2k + 1) 2(r-1)2—(t-eki(N—2k—1i

Fhe derivation of this distribution for d)’l requires

elimination of extensive overlap in choice patterns

a task requiring much patience and consequently not attempted
here. Since most questionnaires requiring d = l are useless
the only possible way to utilize such a distribution would be
to consider only those mutuals comoosed of first hoices.

C. Frequency vistribution for A Posteriori Inter- and Within-

class Choices.

This distribution beco me s a simole of a chi-sous

case

"S
(D

2 X 2 table

test for a

 

 

Ingroup (a 's in- Cutgrouo (bF's
coming choices. incoming choices
Ingroup (a)'s out- 3C a 32-h 30
going choices. ’ “ a
3% C n
1 _ v
Cut5rouo (o)'s v a b-b b

out-Io in.: choices

 

 

0
I
(3'

C)

 

 

 

 

No restrictions on the number of

KKK e

m s are necessary. Aejections
and s

'1‘
’4
(1)

term within br- ts is

(D

“2"44- ' "1‘.
l)_"‘ 4'i'1..v J

‘

CflClCeS which an individual

9
*3
.

av be analyzed simil°rily

enarately, with the ir t3 rpretioo remaining the same f

L‘ a 4.1.
T7'of’l- I" Lilgn

D. A Posteriori Distrioution for Choice Statuses.
A possible fit for the choice st tus distribution was

sujiested by rreenwood and Yule (.3T cu urnal of the Royal Statis-

 

tic cal Society, 83:235—279, 1923). The basic hyoothesis is

that perhaps each individual has a diff ercnt potentiality for
drawing choices; maybe this "drawing power" is distributed as
some binomial, and the whole function is poisson. We can then

at a distribution for choice statuses. This fit is

erved data collec ed on a group of hichiqan county

 

l Loomis,

C. E., “De onstration in Rural Sociolo y and anthro-
pology: A Case

Repo rt", fipplied Ant‘m rorolo v, 6.1.10-25, 1947.

 

 

Choice Cbserved G. and Y.
Statuses Frequencies Frequencies
O - 2 9 70299
3 - 5 12 16.313
6 - 8 20 17.381
9 - 10 17 13. 504
12 " 14 3 9055
15 - 17 11 5.972
18 " 7 70979
78 79.000
2 f
7L for a. and Y. - 11.08 P = .02 (4-d.o.f.)

Thus, although the 3. and Y. distribution is close tothe
observed, it does not yet fit. A more fortunate selection of

class limits would have Elven a lower chi-square.

K?

V Summary and Conclusions

To more systematically evaluate Chapple's interaction

schema and sociometric theory, a review of their properties

i

o ' o ' 3
in relation to the categories of 'anplicat1on' and resulting

|

explanations", as discussed in the Introduction, is in order.
Since it is the task of coordinating definitions to pre-

cisely determine which operations are to be performed in

C+

transforming raw data into a concep uel system or empirical
constructs, these definitions become the focus of an examina-
tion of esearch techniques. In both systems the definitions
are sufficiently adequate and objective. 'here is the possible
exception of Chapple's definition of "origination" and the

dubious, but unavoidacle, practice in sociometrr of naming

L'

indices with terms widely used in other fields.

a H , , 1
In tne area of the efficiency" of tne definitions, botn

a timing device and sociometry manipulates matrices, both r

(0

LL

1 .- I R- (“ ‘Pf‘ “ ’N T ‘ A A?" ‘
quirin5 cleric #ELJBJCS. it does 833m, however, that the s

This process involves the reaction upon the group by the collection

of data; that is, the group may actually change its behavior

ecause of the investigation. The passive nature of data
1

collection by the Chapole system would be an advantage

‘. 'T —— 4» '. D ‘ 1- -..
indiv1duals were not consc ous oi tne 0 server.

maximized if rejections are included in the questionnaire.
Such attitudes as are elicited by the sociometrio question-
naire are not widely considered as "public" property. If the
information is not kept conf dential, it has a tendency to
create jealousy, false security, or perhaps,_it is seen as
"votes" for which to "campaign". The usual assurances of
annonimity are never completely effective. Cutside of these

considerations the individual himself may become overly self-

conscious and create a false fron as a result of verbelizinm,
for the first time, his preferences. These difficulties are,

a5ain, common to most social research.

I 1 ~
'nure' theory in tnese

. r

ahen discussing the value of the
two systems it willbe wall to note that the emphasis has

shifted from the non-existent mathematical models to more

general "theory". It is very difficult to assess the scope

of application for these two theories. Both Chapple and the
prime representative of sociometry, Moreno, believe their
respective theories capable of providing the groundwork for
explanation of almost all social behavior. If they imply by

this that relatively comolete explanations of any social behavior
can be produced from either of these theories, such claims are
untenable. In all justice to both theorists, this is probably
iot their implication. They are stating, rather, that their

propositions will hold true for any social behavior.

The question now becomes one of eterminins the limits of

applicability for these two theories. __§ Chapple's theory

 

1 This problem of limits is still not adecuately treated in
most theoretical discussions.

 

is extended to all possible relevant measurements of timed

O

icovered which will

(

interaction, if some relationshios are di
1 _ I h
determine (i.e., within the system of timed interaction) 'chanres"

in equilibrium, and if this completed system is then brouvht

‘ o '1 '
into relationsnip with "social oeiavior', we could examine the

'l ' o n o
extent of the 'social behaVior" and be ml to describe the

$13
( )4
(D

U)
it)

"limits". At the pre nt time it is possible to make only

rough predictions of

m
:5

individual's favorable or unfavorahle
"reaction" toward conversation with another individual _§
both individuals' previous interaction behavior is krown.
This seems tdhe a more restricted aredof social behavior.

For sociometry these limits are even more difficult to
determine. Koreno does not use the sociometric ques.ionnaire

alone, and invariably those who do utilize many and voPlEd

O
i
H
C+
(u
‘3
...).
Q)
*0
:1
C
B
(7‘
(D
*‘5
O
H)
O
:3‘
O
H.
O
(D
m
U
G)
C+
U
0

For each poss ble form of

(‘u
H.
(J
(+
’—
O
D
C.)
[‘3
{.21
(D
>4
’{ 3
H
in
:5
91
Ct
Ho
0
:5
0
H3
L)
(l)
”S

e are, however, ce tain conclusions
possible in the f‘ce of particular socionetrically determined

. .a -' qp.+n- («A ".V .1 \f‘. m \
irouo structures. ouca phenomena

n , _ n ,_
.s favoritism , cleava~

i‘)

'V f) A A w 'w a _‘U_
sciation, cohesion, etc., can oe found to Le press;+ or

\ '1
l D

‘1 s A , A 4, L A 4. A 1“ .fl . 0+
o5etr". ouca consecueices have rot been inorou. lJ irreoci-
“‘ " " ‘ R D 4'“ ‘f‘ V‘\ f‘fi . fi * 1 ”‘A ‘pA‘L 3m o‘A-1 A)
.at d, but oerhros ti; -unc.-oo-l aoarodch \_ll -4 *4. a, o
-4
.33 L7 A ‘ T ‘« \ ~.. - ‘l ,1. L‘-,. A 1%., 1—... 1r. 1
to \A0 JLLV JFK-J. it .1... 44 Eaccd fi- ;._, -Afc--t t ‘5‘.» U- 6“; L. 11 L3 (111*;

a A - - ‘- - - 2. v- ‘f‘« a ‘- L '- ‘ . 1 3 1‘. ‘, '1‘ |~ -_' f' r ‘ ‘”
not he very extensive, out cdey viii or we ly hold true ioi

- v v . . - s + ~ "‘ r I" f. 0 ‘-~-. 1“
If... S L; ‘y‘r J 1’1 ‘3' 1 F ‘fi L} V. : 2-1) I»: U ; P3: OI! 1-. S .
l4 0 - u.. -
'T‘l— I‘ t‘ +~ ~ A s A ':11 1-.«1»: 1 g t, W‘Cv‘ 3
she iact JEU t.e:c consaqeahces xii n, u tr), ov r ”any

1,—- - p 1 V ‘,g A
svs*,”s sill :ervuu: a_l airle*siiors _ 202131 a a _ r.
,‘H\ O J_ o ‘A' a an: L 1_ L‘ b + A
leis Ale? easily into a “1 ri'us :31 i. igac is, \Cb; t- JLese

and a comparatively low level of integration. For systems
of this type it is oossihle to predict that the‘ will not be

A
x

C‘
J 4
n

C)
9'1

f " A. " D . n' ‘- erfi M 1 ‘
lie of complete explanations ior clearacivelv colpiex

data, but th'

(I)
H
*3

l
variety of social situations.
'To prove this proposition consider t1
the only member of R2 was a psuedc-physiolo ical concept

(equilibrium and tele). If this concept is a valid one then

it will operate in social science as does anv other physio-

logical concept: to establish broa’ lizits, but far fro“ a
complete explanation f social behavior. The fact that these

concepts (equilibrium and tale) are not true physiolcsical

concepts, but are actually sociological implies that they

..¢ ,

l
\ )1
\O

I

W " I .
operate similarily, but in a lesser dearee . That is, compared

to physiological concepts, they as eblish less broad limits,

and more complete explanations, but :aintain their same relative
2
. 1 . ! ~. , ,
pos1tion witn respect to "most' other socioloxical concepts.

¢

 

2 An empirical test of this property has been furnished by
the apparent applicability of the Chapple system (i.e., the

.‘

social antnropoligical one) in cross-cultural analyses.

 

1

As a summary statement of the value of tease theoretical

(D

sys ems, one must first propos that they become more lexically
unified as opposed to their present emphasis upon empirical
uniformities. Then, it is"lo:ical"to suppose that their con-

tributions will become widely applicable, and consequently,

"valuable".

-60...

IV Conjectures on the Broader

Aspects of Inter-personal Theory

In the course of the above development (of a technique
of eve «lue ation and application of this technique to two theore-
tica 1 eye wte s) the specific role of inter-personal theory in

sociolozy was not adequately delimited. Some attempt was made

D

by way of the paradi3m to define this role (i.e., as one of
the "on-going systems for which the configu1 ration or item has
function"). Nevertheless, some further discussion of this
role in terms of a sane a1 theory of small groups would be
helpful in ascertainin3 the specific "3oals" or "endS" of
inter-personal theory.

It has al eady been hinted that the goals of inter-per-
sonal theory are much more limited than any complete explana-
tion. An analysis of the inter-personal field will make this
clearer. In the small or primary 3roups, interaction between
members is not governed by the broad social norms, but rathei
by the principles of "ours sociability" (to use Simmel's term).
The rules of behavior are a p; oduct of, or contributed by, the
specific interactional situation; that is, they are (to a

greats

*5

extent than, say, institutionalized behavior) formed
"on the spur of the moment"
To understand this consider that:

(a) by the typi

al schema for "acquired rewardS" in-

O

dividuals learn to value associatin3 or interactinr with other

~J

individuals as an end in itself,

tutional structure it continues to onerate.
Admitting the existence 0:

as a "desire") we have now to specifr the tvoe(s) Oi small

group structures which will be iormed in the ahsence of insti—

tutional factors (e.$., grouns 01 persons occupying similar

statuse within the same or similar institutional soructures).

consider

0:

0‘)

e

The profiles, however, is not set up so that we n
only that there be some minimum of interaction which will

. u . .,
satisfy this 'desire” for sociability; and, teen, deduce certain

group structures which will maintain interaction. This and

"fully equipne " with other behavior

which we mentioned is
patterns. Ihot only do individuals associate a value with in-
teraction per se, hey also have developed beravior patterns
for satisfying such a value.

Thus we go back to social institutions to determine which
behavior patterns will be most likely brought forth in a situa-

‘

tion such as the small group. A set of benav or patterns called

Ho

' ' ' 1 w
'baSic oersonality' appear to answer our needs, these behavior
patterns are acquired by individuals all through life hut

primarily are formed in the earlier years uu to say, 8 to 10

(D

y are.

The small group structure if it actually deoends upon such

7'1
,4

behavior patterns will be relative to a given culture. .or

-62-

this society we could distinfiuish the authority pattern of

arent over child and insofar as this prevails predict sone

p
well de ined hierarchy of influence or power in the small
group. Ae could also predict that insofar as the society favors

a conjugal type family th-.t any "closely knit" group will be

c nperatively small; and insofar as group menhe rs come from

an "average” family they will form these "closely knit" groups.
The influences from the family are to a. apireciable

extent tenpe red by each member's experience as a member of some

children's clique or "peer group" Such experiences will have

a "democratic" influer ce. They predispose members to form

group norms after an aistre.ct principle of "justice", or "fair

play", which insists that every member has equal riahts, etc.

In like manner we could deduce other properties of inter-

personal relationships. Each of these properties then would

.I

[+-

have limited vali i y de:.ndin; upon the extent to which the

-

(

group members he J9 been subjected to the "common" cultural
norms.

éut the maintenance of a small group has certain unique

 

properties which will operate upon the members of such a group.

Each member in atte pting to keep the group aoin: (we have

\J‘S

seen hat each member is motivated) will be forced to modi fy
to some extent his cul+ urelly relative behavior patterns.
Such a principle gives rise to a group's "internal ovn nerisri
while the previously considered Fehavior patterns constitute
an "external dynamism". The fusion of these two variables

with a given social environment determines small group structure.

-53-

Ia o H
What has been termed 'oynamism is
1 ‘ -, ' w
tne present time) unoerstandable'. The

this lack of knowledge; for, although i

C

not manv iocial

1,.

.2

term, actually,

its meaning. It usually occurs when

relationships are not pacified, but

some uniformity of behavior.

Cne method of avoiding the ove

"‘ :
v‘vA‘.

"dyn mic" interpretation is to utilize

I . . ,
sonality' in comrination witn a

. . "
"requirements for maintaining a small eroup .

concept
w _ '
may tnen be found to form a 'first

1
structure.

’1

r-generelizat

series of deductions

in reality "not (at

term dynamism indicates

t appears to he a reputable

r
J

gupear to understand

variables and functional

ere there seems to te

tions of a

w I
the concept 'basic per-
concerning

Both of these

s will yield broad properties of group structure which

I
approximation' to this

 

 

 

1 Such a proce’urc is aain to the type of analysis af’orded
by the paraoi m for f notional aralyses.

The siecific contribution by inter-personal theory to this
methoq is in the descriotion and aralysis of "internal dipsticm"
or "requirements for "tinteinin; a small group". Such an
analysis, than, crn be concerned with deductions s*ch as, "stme
norms of interaction are necessary, among these: a relatively
stable tine at which interaction will take place, a relatively
well defined pattern of influence, some fethnioues by which
deviant nemhero "re "fenced" to corfor: or techniques by which
they can be clininsted fro: the jrcuo, etc."

Socioxetry (more th"” Chapple) atterrts to make such cor-

-64-

:1.

.3

01"

S
g

n:

01‘

C
5
n

.l

naopen

it is

an h,
when;

C‘

j

)-

“oeclori

.Ann-fl‘
-J‘.

+1
U-
:11

O 1', a].
.V ,1": t

’6 #1
.L ~_-.

A
xiv

s

inter-r-
V.‘

C
L ...
LU
wi
J
C
..L
o 1.

“Nu

Cu
.1

:u

07‘

.
..~

8
..L
H. ~
.7 J
3

a...

a.
i.
5‘.

nl

rl

3-
r".
..L

‘A

svrj
v

C...

.l

\A

..-.

E
1.1

n5

3“

S

.I
O
. .C

 

kt,“