the scalogram model for sociometric data

The Scalogram Model for Sociometric Data

PETER PARK

Uniuersity of Massachusetts

The Guttman scalogram model is employed in this paper to test the order assumptions behind the hypothesis of social status ranking in small communities; and, in doing this, certain measurement facilities of scalogram analysis are elaborated.

THE SOCIAL STATUS RANKING HYPOTHESIS In community studies of social status ranking which are exemplified

by the approaches of Warner and Hollingshead, social status is under- stood to mean an attitude of a person as perceived by the c0mrnunity.l The assumptions associated with this conception are that relevant members of a community can be placed into a meaningful hierarchical order in terms of perceived social status, and that a determinate number of social classes may be recognized and defined by equal social status ranks.

These assumptions are readily translatable as formal conditions of a quasi-series? which can be stated in terms of two general relation- ships, precedence and coincidence, symbolized by P and C, respectively. (“<” is a more familiar interpretation of P and “=” of C.) The conditions are as follows (reading aPb as “a precedes b” and aCb as “a coin- cides with b”): (1) Connectedness, i.e., if it is not the case that aCb, then either aPb or bPa; (2) P is asymmetric,3 i.e., if aPb, then it is not the case

* This research was supported by a Faculty Research Grant of the University of Massachusetts. A version of this paper was read at the Annual Meeting of the American Sociological Association at Miami Beach, Florida, on August 30, 1966.

1 Cf., W. Lloyd Warner and Paul S. Lunt, The Social Life of a Modern Commu- nity, “Yankee City Series,” Volume 1. New Haven: Yale University Press, 1941, p. 82; August B. Hollingshead, Elmtown’s Youth: The Impact of Social Classes on Adolescents, New York: John Wiley and Sons, 1949, pp. 27-28; Milton M. Gor- don, Social Class in American Sociology, Durham, N.C.: Duke University Press, 1958, p. 174, and, Thomas E. Lasswell, Class and Stratum: An Introduction to Concepts and Research, Boston: Houghton Mifffin, 1965, p. 75.

2 Carl G. Hempel, Internutione1 Encyctopedia of Unified Science, Volume 2, N o . 7, Fundamentals of Concept Formation in Empirical Science, Chicago: University of Chicago Press, 1952, pp. 58-62.

3The condition of asymmetry may be substituted by that of irreflexivity, but the former is more convenient for the purposes of this paper. See, Edward V. Huntington, The Continuum and Other Types of Serial Order, New York: Dover Publications, 1955, pp. 10-11.

34s

346 SOCIOLOGICAL INQUIRY

that bPa; ( 3 ) P is transitive, i.e., if aPb and bPc, then aPc; (4) C is sym- metric, i.e., if aCb, then bCa; ( 5 ) C is reflexiue, i.e., aCa; and, (6) C is transitiue, i.e., if aCb and bCc, then aCc. These conditions of order have been inadequately tested in the case of social status ranking in small communities because of inherent weaknesses in the methods employed.

Hollingshead’s study represents an explicit example of a typical procedure which can be characterized as the reputational method: It is essentially a sorting method of scaling in which selected members of a community (raters) are asked to arrange the names of relevant residents (ratees) in an hierarchical order in terms of social status by placing them in as many different classes as they perceive or are given by the investigator. The raters are usually selected on the basis of their familiarity with the community, and they in turn judge the social status of the ratees.5 The ratees are often similarly selected because of their social “visibility”-at least in the initial stages in which the general social status framework of the community is determined. Agreement among the raters as to the number of social classes and/or as to the assignment of the ratees to different social classes is taken, either im- plicitly or explicitly, as evidence that the community is ordered in a quasi-series. As long as demonstration is lacking, however, that the raters and ratees represent the community in some objective sense, the extent to which a community is connected in terms of social status is left indeterminate. Furthermore, the sorting method presupposes that the attribute being measured is orderable and imposes the transitivity conditions of order instead of testing it.6 It also leaves the asymmetry condition untested.

4 Hollingshead, op. cit., pp. 25-41. Among other studies utilizing this method either by itself or in conjunction with other methods are: W. Lloyd Warner, Marchia Meeker, and Kenneth Ells, Social Class in America: A Manual of Proce- dure for Measurement of Social Status, New York: Harper and Row, 1960; Harold F. Kaufman, Prestige Classes in New York Rural Community, Ithaca: Cornell Uni- versity Agricultural Experiment Station, Memoir 260, March, 1944; Otis Dudley Duncan and Jay 1%’. Artis, Sociol Stratification in a Rural Community. Pennsylvania School of Agriculture Bulletin 543, October, 1951; Edgar A. Schuler, “Social and Economic Status in a Louisiana Hills Community,” Rural Sociology, 5 (March, 1940), pp. 69-83; John Useem, Pierre Tangent, and Ruth Useem, “Stratification in a Prairie Town,” American Sociological Reuiew, 7 (June, 1942), pp. 331442; Cer- hard E. Lenski, “American Social Classes: Statistical Strata or Social Croups,” American Journal of Sociology, 19 (September, 1952), pp. 139-144; Thomas E. Lasswell, “A Study of Social Stratification Using an Area Sample of Raters,” Amer- ican Sociological Reuiew, 19 (June, 1954), pp. 31W13; Robert A. Ellis, “Social Stratification and Social Relations: An Empirical Test of Disjunctiveness of Social Classes,” Americun Sociological Reuiew, 22 (October, 1957), pp. 570-578.

5In deviating from this general practice, Ellis and Lasswell used samples of raters. See Ellis, op. cit., and Lasswell, “A Study of Social Stratification,” op. cit.

6 Warren S . Torgerson, Theory and Methods of Scaling, New York: Wiley and Sons, 1958, p. 53, and Clyde Coombs, A Theory of Dato., New York: Wiley and Sons, 1964, pp. 33-40,

SOCIOMETRIC SCALOGRAM 347

THE SCALOGRAM MODEL A formal analysis of the Guttman scalogram model suggests a more

rigorous method of testing the social status ranking hypothesis. Con- sider a typical scalogram analysis of an attitude based on responses to dichotomous items (stimuli). Represent respondents by a finite set, I, of elements xi, (i = 1, 2, 3, . . . n), and stimuli by another finite set, S , of elements yj, (j = 1, 2, 3, . . . m), and define sets G, such that G , = {x/xRyj) where the relationship R is interpreted to mean that x responds positively to yj. It is then postulated as a basic definition of the scalogram model that YlPyk if and only if Gi is contained in G, ( G j c Gk). And, the set S is simply ordered in the Guttman sense if and o d y if for any two elements y, and yk in S , Gi # Gk, and Gj either contains or is contained in Gk.7 This latter relationship constitutes the fundamental hypothesis in the Guttman model, and it embodies the transitivity condition of P. But in attitude scaling no direct comparisons are made between stimuli (or between respondents), and this hypothesis also serves the purpose of testing the necessary, but not the sufficient, condition of connectedness.8 Nor is the condition of asymmetry tested, since this is imposed by the asymmetric relationship between the respondent and the stimulus.9

The logic of the scalogram model makes it clear that, experimentally, stimuli can be represented by individuals as well as by attitude statements, depending only on the purpose of scaling and provided that the formal relationship R between the respondent and the stimulus is interpreted appropriately. Particularly when the same set of individuals serve both as stimuli and as respondents, a response can actually con- stitute a direct comparison of self with another person regarding some attribute. The data obtained by such a procedure would form a sociometric matrix which can be subjected to scalogram analysis.

In the sociometric method of scalogram analysis, as in the case of attitude scaling, the fundamental Guttman hypothesis tests the condition of transitivity for P, which is measured by the coefficient of repro-

7 For given any three stimuli, y., ye, and yt, if C. is contained in G. and G. in Gt, then G , is contained in Gt, from which it immediately follows that y,Py,, y.Pyt, and yrPyt; and transitivity holds among the stimuli. If, on the other hand, for some stimuli yu and yv, G. neither contains nor is contained in G,, then neither yuPyy nor yvPyu; and there exists no simple order. The definition of order among the respondents can be stated formally for ideal data as follows: Define difference sets GJ, such that CJ = Gj - CJ.1, wherey,.,PyJ. Then for x,zG, and x,!Gh, it is postulated that xp C xu if and only if g = h; and xpPx., if and only if G , 5 G h .

8 For a universally endorsed statement, y,,., G , = I, and G , contains all other sets CJ not equal to G, and I, regardless of its content. A universally rejected statement, analogously, is contained in all other sets G, # 0. Accordingly, the empirical procedure of Guttman analysis excludes stimuli of extremely high and extremely low marginal frequencies.

9 That is, where xRy means that x responds positively to y, yRx is empirically meaningless.


ducibility. Since the individuals who seme both as respondents and stimuli are compared with one another in this method, the condition of connectedness can be tested directly and independently of the fundamental hypothesis.1° Experimentally it is possible for individual a to place himself above individual b and at the same time for b to place himself above a, a situation which also makes it possible to test the condition of asymmetry. It can be shown that it is generally possible for response patterns to form a scalogram and yet to manifest this kind of inconsistency.ll Apparently these response reversals cause individuals a and b to be ordered one way as respondents and another way as stirnuli.l2 Consequently, the correlation between the respondent order and the stimulus order would provide an appropriate index of asymmetry which is independent of the transitivity condition for P.

The discussion to follow will describe a test of the status ranking hypothesis using the sociometric method of scalogram analysis.

The connectedness condition for the sociometric data can be stated formally in terms of the relationship R for the case of errorless data. First, define the relationship aR'b = -(aRb) to mean that a places himself below b. Then the connectedness condition is that if a and b are not identical, either aRb or aR'b, and either bRa or bR'a. Since, however, a and b are members of the same set, it is simply that for any elements in the set either aRb or aRb. On the basis of this, the connectedness condition can be stated for the relationship P. Define sets G'J, such that G'j = { x/xR'~J } . Then the connectedness condition for P is that for every j, GJ U G'j = I. With fallible data, it may be desirable to express this condition in terms of some numerical criterion. I t may be stipulated that N(Gj U G'J)/n 2 TI

for a single stimulus, and C N(GJ U G'j)/mn 2 T2, where N(GJ U G'j) stands for

the number of elements in Gj U G',, and TI and TZ are some arbitrary numbers, such as, .SO and 90, respectively. I t may be even more convenient to think of connectedness as a matter of degree, rather than categorically; that is, in terms

of more or less of the quantity, ,Y N(GJ U G'j)/mn.

.

m

j = 1

,

m

j = 1 11 For example, in the following hypothetical response patterns boRco and a b , .

and boPco as stimuli but b,Cs as respondents. And yet these response patterns form a rfect scalogram. (In the matrix below, the rows stand for respondents and the cocmns for stimuli, as in the attitude scaling method, and a "+" stands for the relationship R between the respondent and the stimulus, and the "-" for R'.)

a0 bo co Cl cz do

a0 bo ca do + + + + - t + + - + + + - + + +

- + + - + - - -

121n the following heuristic example, the response patterns form a scalogram with one error for the respondent b,. But bRds and doRbo, and coRdo and doRG; and b,Pdo are stimuli whereas b&do are respondents, and ePdO are stimuli while &Pco are respondents.


SCALE ANALYSIS OF SOCIOMETRIC STATUS RANKING DATA Data were collected from a small New England community which

had a population of 1,896 inhabitants comprising 564 households. Seventy-one families were chosen at random from a list of households. Sixty of these were initially judged to have resided long enough in the community and to be well known enough to act as stimuli. Fifty- one of the 60 also served as respondents, 9 families having been un- available during the data gathering period.

The respondent was presented with the list of stimulus persons during an interview, and he was asked to indicate for each whether his own social status was higher or lower than that of the other.13 The respondent was not given the option of equating his social status with that of the stimulus, this in order to prevent a rash of egalitarian responses which would have vitiated the study.l* For the purpose of soalogram analysis, a response placing the respondent above the stimulus was regarded as a positive response, and one placing him below as a negative one. It was found to be logically consistent a d useful to interpret self-comparisons, which would signify equality of social status, as positive responses.

Although several individuals were eliminated from the random sam-

do + -t- + + 4 f +

e4 + + + + + + + + - - - - en In general, however, the relationship between R and P with respect to the condition of asymmetry does not seem as simple as might be suggested by this example. With fallible data, a violation of asymmetry for R between elements n and b (i.e., aRb and bRa does not necessarily lead to a violation of asymmetry for P involving the same elements (i.e., aPb and bPa). Rather, it appears that a lack of asymmetry for P is a function of the frequency of such inconsistencies for R involving not only a and b but other elements as well. A consideration of the relationship C further complicates the matter.

13 The respondent was not directly asked to put himself above or below another member of the community, so that the task of personal comparison would seem less odious. He was asked instead to state how in his opinion the community would place him with respect to the stimulus--higher or lower in social status. This is not the same, of course, as asking the respondent to make direct comparisons. But to the extent that it is assumed that the individual's perception of his social position relative to the rest of the community influences his behavior, it would appear that there is little difference of practical significance between these two experimental procedures.

14 In the case where the respondent was inclined to give a response of equality, he was urged to take into account the smallest differences which, in the eyes of the community, would put him above or below the stimulus.


ple at the outset, as noted, because they were considered to be too new in the community, the remaining respondents and stimuli could not always make meaningful comparisons with respect to social status. Of 3,009 possible responses (excluding 51 self-comparisons) 799, or 26.5 per cent were left blank. It is clear that not all of these blanks signify that the respondent was unable to evaluate the social status of the stimulus in relation to his own. Undoubtedly some of them represent genuine status equality and others the respondent’s unwillingness to place himself above or below a fellow citizen of the community. It is difficult to assess the extent to which the blank responses reflect such technical difficulty, but the field experience would indicate that it did not exceed 50 per cent of the cases. Thus, a conservative estimate would have about 87 per cent of this community connected in terms of social status ranking.I5 Whether or not social status ranking satisfies the other criteria of order is a different question, which can be answered by scalogram analysis of the sociometric data.

Individuals who either cast or received more blank responses than non-blank responses were excluded from the ensuing analysis. This exclusion left 51 stimuli and 42 respondents, of whom 39 served in both capacities. The stimuli were ordered according to the proportion of positive responses to the total received and a selection was made of 11 stimuli which were separated from each other by at least five per cent in the proportion of positive responses received, and which were relatively free of blank responses. All of the 11 stimuli also served as respondents. The sociometric matrix for the 42 respondents and 11 stimuli was analyzed by the scalogram method. The stimuli are ordered from left to right in this matrix, which is reproduced in Table 1, in the order of the proportion of positive responses received; and the respondents are ordered from top to bottom, in terms of actual or assigned perfect scale types.16 A “+” signifies that the respondent is placed above the stimulus when these represent two different individuals and that they are equal when they denote the same individual; a “-” indicates that the respondent is placed below the stimulus. A pair of parentheses stand for a blank response, and the sign enclosed by the parentheses shows the “dummy” response which was substituted for purposes of scale analysis. Blanks were filled in with +’s and -’s to minimize scale errors for respondents. When either a + or - could

15 100% - K(26.58) 5 87% 16In attitude scaling by the Guttman method it would be considered a good

practice to eliminate stimuli 01 and 35 with marginal frequencies of less than .20 and stimuli 33 and 20 with marginal frequencies of over .80 because of the weak connectedness criterion. In the sociometric method, however, the stimuli are linked by a direct experimental procedure, and hence this rule of thumb is not particularly pertinent. But here, as in attitude scaling, it is still necessary to separate the stimuli by some distance in order to reduce errors resulting from random reversals.

SOCIOMETRIC SCALOGRAM 351 TABLE 1

RESPONSE PATTERNS OF 42 SELECTED RESPONDENTS TO 11 SELECTED STIMULI

Respondent Stimulus Number Scale Er- No. 01 35 03 32 23 11 19 13 02 33 20 Type rors

'01 + + + + + + + + - + + I 1 1 38 - + + + + + + + + + + 10 0 54 - + - + (+I + (+) + + (+) + 10 1

"35 - + + + + + + + + + + 10 0 "03 (-1 + + + + + + + (+I + + 10 0 08 - + + - + + + + + + + 10 1 37 - - + + + + + + + + + 9 0 5 1 - - - + + - + + + + + 8 1 2 4 - - - + + + + + + + + 8 0 0 7 - - - + + - + + + + + 8 1 3 6 - - - + + - + + + (+I (+) 8 1

"32 - - - + + + + + + + + 8 0 ""11 - - + - + + + + + + + 7 1

1 4 - - - - + + + - + + + 7 1 + + ( + I + - - + 7 2 4 3 - - - - + + - - + (+I + 7 2 1 5 - - - - + - + + + + + 7 1 + - + - + + 6 2 + - + + + + + + 6 1 + + - + + + 6 1 28 - - + - - + + + + + + 6 1 2 6 - - - - - + + + + + + 6 0 + - + + + + + 5 1 + + + + + 5 0 0 g - - - - - -

+ + + + + 5 0 0 5 - - - - - - + + + + + 5 1 34 - - + - - -

1 6 + - - + - - - + + + + 4 2 2 5 - - - - - + - + - + + 4 2

+ ( + I + + 4 0 17 - - - - - - - + + + 3 0 39 - - - - - - - - + + + 3 0 42 - - - - - - - - + + + 3 0 53 - - - - - - - - + - + 3 1 50 - - - - - - - - + + + 3 1 423 - - - - + - - -

45 - - + - - + - - - + + 2 2 2 9 - - - - - + - - - + + 2 1

- (+I 1 0 30 - - - - - (-1 - - - 0 0 12 - - - - - - - - - - -

52 - - - - - - - + + - - 0 2 0 0 10 - - - - - - - - - - - 0 0 04 - - - - - - - - - - -

019 - - - (-) - - + - - - - 0 1

""13 - - - - - "002 - - - "20 - _ _ _ _

""33 - - - -

Positive responses received + total responses received.

Positive responses + total respondents .049 .143 238 -317 .439 ,512 .575 .643 .725 .795 .875

.048 .143 .238 .310 .452 .500 .595 .643 .738 .810 .881 Note: Single and double asterisks designate respondents who also served as stim-

uli, the latter being those whose scale types were determined in line with their positions as stimuli.


be assigned to a blank, one of them was picked at random. Adjacent blanks were assigned the same signs, provided that errors were mini- mized; and ties were broken by randomization.

Respondents with quasi-scale type response patterns (i.e., those con- taining errors) were scored in the usual manner; that is, they were assigned to the closest perfect scale types, subject to randomization when two or more possibilities for the same number of errors offered themselves. In the case of the 11 respondents who also acted as sti,m- uli, however, the error types were scored so as to make the respondent order as congruent with the stimulus order as possible without intro- ducing extraneous errors. The quasi-scale types scored in this manner are denoted by two asterisks in Table 1; it can be seen that these respondents could have been assigned to other perfect types without increasing errors, but the resulting order among the respondents would not have agreed as well with the order among the stimuli. The rest of those respondents who doubled as stimuli are designated by single asterisks.

Reproducibility was calculated for the response patterns of Table 1, ignoring blank responses; and a coefficient of .93 was obtained.17 The correlation between the respondent order and the stimulus order for the 11 individuals was .59 by Kendall’s Tau. A Tau of this size signifies that in about 20 per cent of the pairs which could be formed out of the 11 individuals there were contradictions between the respondent order and stimulus order. In other words, the asymmetry condition is violated in, about 20 per cent of the test cases. This can be ascertained directly from Table 1. For instance, individual 19 precedes 13 as stimuli, but the order is reversed when these individuals are viewed as respondents.’s (It is to be noted that Tau would be 0 when the asymmetry condition is violated in 50 per cent of the cases.) Spearman’s Rho calculated for the same data was .70, which is appreciably greater than the Tau of .59. This difference indicates that the inconsistencies in social status order are restricted by and large to reversals between neighboring ranks.lg

The stimuli selected for the foregoing scalogram analysis represent discrete points separated by certain distances on the presumed social status continuum, and as such they can be regarded as marking arbitrary

17 It is also reasonable to count the blanks as full responses and to assign a half

18 For these individuals it can also be seen that 19R13 and 13R19. 19 Both Kendall’s Tau and Spearman’s Rho measure rank order correlation,

which is particularly appropriate for assessing the degree to which the stimulus order agrees with the respondent order. The former, however, is merely sensitive to order reversals, whereas the latter wei hts the rank differences involved in the reversals. See, Maurice G. Kendall, Ran& Order Correlation Methods, New York: Hafner, 1955, Chapters 1,2, and 3.

error to each. This accounting system yielded a coefficient of .92.

SOCIOMETRIC SCALOCRAM 353

class boundaries.20 It would be more meaningful, however, to define social classes as equivalence classes and to ascertain whether or not order exists among these classes and whether or not individuals can be ordered in terms of them. This can be accomplished conveniently by applying the H-technique to the sociometric data of social status ranking.

The 39 stimulus persons who also served as respondents were accordingly combined into five contrived items in such a manner that the relative proportions of positive responses were similar for the stimuli in the same contrived item and markedly dissimilar for those in Merent contrived items. The distribution of the 39 stimuli among the five contrived groupings is indicated in Table 2. The response to a contrived

TABLE 2 RESPONDENTS' SCALE SCORES

BY MEMBERSHIP IN CONTRIVED ITEMS

Scale Contrived Item Score I I1 1Zl IV V Total

0 1 2 0 0 0 3 1 0 1 1 0 0 2 2 0 3 13 2 0 18 3 0 1 7 2 1 11 4 0 0 1 2 0 3 5 0 0 1 1 0 2 Total 1 7 23 7 1 39

.95 .8C.71 .65-.27"O .20-.09 .03 *P = proportion of positive responses received. O * The stimuli in this group were scarcely separable from one another in terms of

the ratio of positive responses to total respondents and hence were allowed to form a single contrived item of a relatively large interval.

item was scored either positively or negatively depending on the ma- jority response to the stimuli comprising the contrived item. Blanks which outnumbered both positive and negative responses in a contrived item were filled in to minimize errors; the others were ignored. The coefficient of reproducibility calculated for the resulting H-technique response patterns was .99. Nevertheless, Kendall's Tau between the stimulus order arad the respondent order calculated for the 39

Range of Po

20 Scalogram analysis was also carried out on the larger matrix of 42 respondents and 51 stimuli, and a coefficient of reproducibility of .86 and a correlation coefficient of about .SO were obtainer. While producing a result in keeping with the findings on the reduced matrix, this analysis assumes the 51 stimuli to be simply ordered, and hence, it is not very pertinent in the present context, where the status ranking hypothesis is stated for a quasi-series.


individuals was only .39. This finding indicates that in about 30 per cent of the possible pair comparisons, the asymmetry condition is violated. Spearman’s Rho, however, was found to be .55. Here again, the difFerence in the coefficients signifies that the indeterminacy of order results primarily from exchanges of ranks which are not far apart. It can be seen from Table 2 that the subjects are distributed in a band of cells along the main diagonal, and that the cells in the upper right and lower left corners are empty; these latter cells represent order reversals involving ranks which are widely separated.

To summarize the results, social status ranking in this small community satisfies the condition of connectedness to about 87 per cent of the perfect situation. I t also results in linkages which are apparently transitive and meet the requirement of asymmetry for the relation- shop of P to some extent.2’

DISCUSSION AND CONCLUSION The sociometric method of scale analysis provides a method of test-

ing the social status ranking hypothesis in a much more rigorous manner than is possible by variants of the sorting method. One reason for this, which has been elaborated upon in this paper, is that the conditions of order vis-a-vis social status are tested in a fundamental sense. Another reason is that the sociometric method, unlike the typical application of the reputational method, has the respondent evaluating his

21 It is pertinent to ask whether social status ranking satisfies the conditions of order better if socially more “visible” members of the community are used as stimuli. In the course of the field work, residents of the community nominated 27 persons whom they considered to be representatives of different social segmentq of the community. These names were presented to the original 51 respondents, who cast 151 blank responses out of 1,325 possible ones (excluding self-comparisons), or 11.3 per cent blank responses. If, again, about half of these non-responses are at- tributed to the technical difficulties of the data gathering procedure employed, it may be estimated that about 95 per cent of the community is connected in terms of social status ranking when the ranking is confined to better known members of the community - a result which compares favorably with the 87 per cent connectedness for the community represented by randomly chosen stimuli.

Four of the 51 respondents who cast more blank responses than either positive or negative ones were eliminated, and eight were selected from the 27 nominees. The eight were separated by at least 5 per cent in the proportion of positive responses received, and they included all the nominated stimuli who were also initially chosen as respondents. The scalogram analysis of the resulting sociometric data, by the procedure explained above, resulted in a coefficient of reproducibility of .94. However, Kendall’s Tau between the stimulus order and the respondent order for the six individuals for whom comparison was possible was only 60. An H-technique analysis was also carried out on the sociometric matrix of 47 respondents and 27 stimuli which were collapsed into 5 contrived items. From this analysis a coefficient of reproducibility of .97 resulted, but Kendall’s Tau between the two orders for the same six individuals was .51.

It thus appears that the condition of asymmetry for social status ranking is not appreciably better satisfied, even when the ranking is confined to more “visible” members of the community.


own social status in relation to the community.22 This experimental procedure would appear to be a crucial element in testing the assumption (which is no less widespread for not being stated explicitly) that social status iduences the behavior of a person through his perception of the relative positions which he and other relevant members of the community occupy. The findings of the present study, which experimentally took this assumption at face value, reveals that in a small community of about 600 households, an adult member of a family can compare himself meaningfully in terms of social status with about 87 per cent of the other families. This figure, which might appear high, would no doubt dwindle rapidly as the size of the community in- areases.

Individuals may be able to compare themselves in terms of social status, and yet there may not be a consistent hierarchy of social status which orders the community in a meaningful manner. The scalogram analysis of the sociometric data presented in this paper does not give a clearcut answer to the question raised by the social status ranking hypothesis. The scalogram obtained from the analysis had high coefficients of reproducibility. But to the extent that correlation between the stimulus order and the respondent order was only middling, it would have to be concluded that social status ranking results in a less than perfectly consistent hierarchy.

Some remarks of a qualifying nature are in order. The procedures for sociometric scalogram analysis adopted in this study tended to favor the social status ranking hypothesis. For example, blank responses were filled in with dummy responses to minimize scale errors instead of resorting to such alternative methods as randomization; and quasi- scale types were scored to make the respondent order as congruent with the stimulus order as possible without incurring additional errors. The data gathering procedure, on the other hand, involved self-evalu- ations; and personal modesty, or a lack thereof, might have contributed substantially to the inconsistencies of social status ranking. These inconsistencies appear to embrace ranks, however, which on the whole are close to each other. It might thus be said that a rough outline of a social status hierarchy is discemabl-ne which makes gross distinc- tions in status ranks but is less sensitive to finer differences.

An instructive feature results from the application of scalogram analysis to sociometric data. It concerns the relationship between the universe of content and the items which represent it. In attitude

22The community prestige score of Duncan and Artis is in part based on self comparison of a similar kind. See Duncan and Artis, op. cit. Self-classification, whereby the respondent is asked to place himself in one of several social classes, is, of course, a logically different procedure. See, for instance, Richard Centers, The Psychology of Social Classes, Princeton, N. J.: Princeton University Press, 1949.


scaling, this relationship is stated in the haziest terms, largely because the universe of content refers to the set of all statements relating to the attitude in question. Practically speaking, this set is infinite; and its membership cannot be determined empirically. The scale items, or the statements on which scalogram analysis is actually d e d out, are considered to be a sample of the universe of content; and if the items form a scalogram, the universe of content representing the attribute in question is said to be scalable. But such a generalization is of limited value, since there is no objective way of deciding whether or not the items actually represent the universe.23 In the sociometric method, by contrast, the universe of content refers to a set of denotable individuals-for example, a community; and the scale items can be represented by a sample of elements from this set. The findings resulting from this procedure can be generalized to the universe directly, subject only to the usual limitations concerning inferences from a sample.

23 Cf., Torgerson, op. cit., pp. 331436. 37 (Spring, 1967)

the scalogram model for sociometric data

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