UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

A technique for the measurement of realism in social situations McEachern, Alexander William 1950

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata


831-UBC_1950_A8 M23 T3.pdf [ 3.68MB ]
JSON: 831-1.0106930.json
JSON-LD: 831-1.0106930-ld.json
RDF/XML (Pretty): 831-1.0106930-rdf.xml
RDF/JSON: 831-1.0106930-rdf.json
Turtle: 831-1.0106930-turtle.txt
N-Triples: 831-1.0106930-rdf-ntriples.txt
Original Record: 831-1.0106930-source.json
Full Text

Full Text

A TECHNIQUE FOR THE MEASUREMENT OF REALISM IN SOCIAL SITUATIONS by ALEXANDER WILLIAM McEACHERN A Thesis Submitted i n Partial Fulfilment of The Requirements for the Degree of Master of Arts In the Department of Philosophy and Psychology THE UNIVERSITY OF BRITISH COLUMBIA APRIL, 1950 ABSTRACT A Technique for the Measurement of Realism i n Social Situations. by Alexander William McEachern. It i s suggested that i t might be useful to develop techniques which are specifically designed to examine the social aspects of experimental situations, i n light of the increased emphasis and recognition given social phenomena i n psychology i n recent years. For this purpose the author attempts to modify level of aspiration techniques for use i n sociometric situations. Concern i s mainly with the concept of realism, which i s operationally defined, on the basis of previous studies of the level of aspiration, as "that function of personality revealed by a technique designed to measure a subject's a b i l i t y to designate accurately his expected performance i n an activity i n which he has had some experience and consequent-l y some criterion on which -to base his designation." The attempt to measure this defined function i n social situations was undertaken i n the following way: 1 . Asking each individual i n a group to choose other individuals on the basis of a specified criterion. 2. Asking each individual to give the names of those individuals he expects to have chosen him. The individual's realism i s estimated i n terms of the discrepancy between the obtained and expected choices on the basis of three factors which were logrcally determined: Factor A, discrepancy between number expected and ob-tained; Factor B, discrepancy between correct expected choices and obtained choices i n terms of the actual names of the individuals involved; and Factor C, the discrepancy between the mean sociometric status of the individ-uals he expected to choose him, and the mean sociometric status- ; of those ABSTRACT (Cont.) who did choose him. The process of derivation of the totai R score i s summarized below: Factor A - expected - obtained Ttnrr) x 1 0 0 - can be either + ol> -. Ignore this 'direction' u n t i l the expression of the R score. - converted to sigma score i n terms of the distribut-ion of A within the group, by formula: A - M a - Z a Sigmaa Factor B _ correct expected choices 1 Q 0 Obtained choices - convert to sigma score Z D Factor C - (M e xp. - M o b t J x 100 - can be either + or -. Ignore direction u n t i l R i - convert to sigma Z c. score. R score i s given by the formula: W aZ a + WbZb+ wczc Ihere WA, Wb, and Wc are the weights derived from the beta coefficients obtained from the inter-correlations of the factors. Ineluded i n the expression of the f i n a l R score for an individual, are the directions i n which he tends on Factors A and C. This technique was applied to three groups at different age levels ( 7 - 8 y r s . , 2 1 - 3 1 y r s . , E>9-86yrs.,) for the purpose of determining whether or not i t was possible to obtain distributions of R scores for each of the groups; that i s , whether the function measured could discriminate between individuals. This purpose was f u l f i l l e d . Certain general indications are presented, having to do with the patterning of the positive and negative direct-ions on Factors A and C, various sociometric relationships, and a few others. There i s also presented empirical evidence which i s interpreted as a partial justification fofc the logical assumption that the technique i s measuring a 3. ABSTRACT (Cont.<) realism function similar to that reported i n aspiration studies. Implications and suggestions for future research are discussed under these headings: "Technique," "Levels of Aspiration," and "Sociometry. TABLE OF CONTENTS I INTRODUCTION 1 II HISTORICAL BACKGROUND 3 The Level of Aspiration k Individual Differences 7 III THE PROBLEM 10 Formulation of the Problem 10 Analysis of the Problem 12 IV PRESENTATION OF THE TECHNIQUE 16 Obtaining the Data 16 Tabulatimg the Data 18 Analysis of Data into Constituent Parts 20 Treatment of Data 21 V DEMONSTRATIVE STUDIES 27 Group I 27 Group II 33 Group III UO General Discussion Hi TABLE OF CONTENTS (Cont.) VI CONCLUSIONS ' . 5U The Technique 5U Implications 55 VII REFERENCES 60 APPENDICES Appendix A. Index of Tables 65 Appendix B. Derivation of Formulae for W 67 1. A technique for the measurement of realism in social situations  I INTRODUCTION Robert B. MacLeod, in a recant article ( 5 3 ) , has called social psychology the "new psychology" of today. This trend is exemplified by one of the more recent text-books in social psychology, in which the authors state that "as a basic science, social psychology does not differ in any fundamental way from psychology in general." ( 4 5 , p. 7) This social emphasis does not stem from a belief in the fundamentally more fruitful nature of the traditional psychology, but from the recognition of the social origins of personality, and the recognition that any experimental situation, whether i t have as its subject matter perceptions of colored paper or attitudes toward criminals, is a social situation since i t involves two or more persons; or in the case of a scientist making obser-vations upon himself, his subject matter can be considered to be social subject matter, his personality. While i t might be argued that this is an assumption accepted by a l l experimenters, and consequently nothing particu-larly new, i t is significant that the great majority of experimenters in the fields of motivation, perception, and learning, have ignored the commonly recognized social concomitants to the situations within which these phenomena are studied. It would therefore seem useful to develop and apply techniques which are specifically designed to reveal the social aspects of experimental situations, or at least, which take into account the social concomitants which we a l l recognize. It might be even more 2. useful to concern ourselves in part with the examination of behavior which is traditionally called social. An experimental technique which has been called the "door by which the- ego re-entered the cloisters of academic psychology" is that of the studies on levels of aspiration. (1, p.471) This technique has proven valuable in experimentation with the phenomena of motivation, learning, and perception. It would seem reasonable to suppose that i f i t were applied to behavior which is primarily social, then the scientist could obtain information having to do with the learning, perception, and motivation involved in these situations. Further, i t might be argued that a technique with this purpose could give insight into the concomitant social aspects of situations which are not ordinarily considered as essentially social. The problem undertaken in this thesis will be the conversion of the level of aspiration technique from one which is applicable to "individual" functions and tasks such as penny pitching, target shooting, and arithmetical computation, to one which is applicable to social functions and tasks: generally, to interaction among individuals. Following a brief review of the literature pertinent to aspiration phenomena, this problem will be more explicitly stated in terms of the possibilities revealed by this review. 3. II HISTORICAL BACKGROUND The level of aspiration concept, introduced by Dembo (10) in 1931, is concerned with goal levels and goal-directed behavior. The experimental results obtained by Dembo' have been reconsidered and extended by many other workers, until at the present time there is a considerable body of data bearing on the problems of that goal-striving behavior which occurs within a specified range of difficulty. Further, there seem to be emerging experimental data bearing on the common factors which determine the level of aspiration phenomena with reference to other fields and problems of psychology. In Figure 1 is presented a typical time sequence of events in a level of aspiration situation. (47: p.334) TYPICAL TIME SEQUENCE 1 2 3 4 Last Setting of New Performance level of Performance 1 Aspiration 1 1 Reaction to new Performance 1 1 I Goal Attainment Discrepancy Discrepancy Figure 1. For example, we may consider that at Point 1 an individual has repeated six digits, and at Point 2 expresses his goal for the next t r i a l as nine, and at Point 3 repeats only five digits, so that at Point 4, his 4 reaction to new performance, he decides to try for only seven, lach point within the time sequence represents a situation that has characteristic problems. Two of these will be considered here: what determines a level of aspiration, and what are some individual differences apparent in the reactions to achieving or not achieving the level of aspiration? A. The Level of Aspiration It is apparent that each decision regarding a level of aspiration is determined by the subject's perception of his position on each reference scale which is relevant to his performance. It has been found, for example, that generally, the level of aspiration will be raised or lowered respect-ively as the performance reaches or does not reach the level of aspiration,.. (14). Frank (20) demonstrated that the level of aspiration is also affected by the sequence of tasks which are easy or hard: the height of the level of aspiration is usually higher when the "normal" task follows an easy task than i t is when folloxving a hard one. Certain general cultural reference scales have been identified which are particularly significant in light of the competitive emphasis of the western culture. In an experiment with f i f t h grade children, Anderson and Brandt (3) found that there was a consistent trend in which those subjects who find themselves above the average of the group tend to have a slightly negative discrepancy score, those finding themselves close to the average of the group tend to have slightly positive discrepancy scores, while those finding themselves below the mean of the group tend to have a very large positive discrepancy score. Similar results were found by Hilgard, Sait and Magaret (39) who worked with college students. These experiments suggest the existence of a frame of reference in which an individual places his performance on the scale formed by the performance of his group. , Chapman and Volkman (8) performed an experiment with college students for the purpose of demonstrating that knowledge of the performance of other groups which are more or less "prestigeful" has an effect similar to that of knowledge about the subjects* own group. They demonstrated that this was the case: subjects tend to have positive aspiration scores when comparing themselves with less "prestigeful" groups, and negative aspiration scores when comparing themselves with more "prestigeful" groups. Gould and Lewis (32), and Festinger (14) substantiated this finding in other experiments, which suggests the conclusion that there is a reference scale with respect to other groups which are viewed in a valuative way. Another possible frame of reference within which individuals to some extent form their expressed levels of aspiration has been demonstrated by Hertzman and Festinger (37). Subjects were told the goal discrepancy scores of the group, rather than the actual obtained scores. It was found that over a series of trials the subjects' aspirations tended to change in a direction which led to conformity with the aspirations of the group. Concurrently, however, these investigators found that the subjects' main conscious set was toward the performance of the members of the group, even though they were not told of i t . Thus, although there would appear to be a frame of reference identifiable with respect to group levels of aspiration its determining effect on the levels of aspiration of the subjects is not so significant as the performance of the group. Gould (30) has presented evidence which indicates that goal discrepancies are also related to, and therefore possibly partially 6. determined by, various factors in the socio-economic background of the subjects. Lower discrepancy scores were found for subjects with more favourable socio-economic backgrounds, while more difficult circumstances were related to higher discrepancy scores. This evidence is closely related to that presented by Sears (62) for his examination of the discrep-ancy scores obtained by children having.records of past academic success, and those with failure: those who had a consistent pattern of failing in school tended to have higher goal discrepancy scores than did those who had been relatively successful, and there was wide variability within the failure group while the success group fairly consistently presented dis-crepancies within the small positive range. Various authors have found that the nature of the task, and the specific question asked to elic i t the level of aspiration,affect the expressed level. This w i l l be discussed in more detail in Section III: The Problem. In summary we may l i s t the following determining factors, or frames of reference for decisions as to future performance: 1. Relation of new performance to level of aspiration. 2. Relation of the task being examined to other tasks in a sequence, in terms of relative difficulty. 3. Comparison of performance within group. 4. Comparison of performance with other groups with greater or less prestige value. 5. Comparison with levels of aspiration of other members of the group. 6. Socio-economic factors in the background of the subjects. 7. Nature of the task, and specific questions used to elic i t expressions of levels of aspiration. 7. B. Individual Differences There are certain problems apparent in level of aspiration s i t -uations other than those considered in the foregoing section. While i t is necessary that the investigator consider in what way certain variables affect the level of aspiration phenomena, i t is equally important, for example, to consider the extent to which an individual's expressed aspir-ations maintain a consistent relationship to the group within which they are being considered. Recognizing this specific problem, Frank (20) inves-tigated the consistency of the-goal discrepancy scores on one task from one session to another (correlations of from +.57 to +.75), and on two different tasks in one session (correlations of from +.50 to +.65). Gould (29), in a "similar experiment, obtained correlations which, while s t i l l indicative of a tendency toward consistency from one task and session to another, are lower than the results obtained by Frank. The discrepancy can be partially accounted for by the considerable difference between the sets of tasks used by Gould and Frank. Frank's were of a very similar nature to one another, while those used by Gould differed considerably in terms of- the nature of the required performances. Gardner (24), obtained results which'more nearly approach those of Frank (mean correlation of +.55). The results of Heathers (36), serve to reconcile those obtained by earlier workers. His experiment consisted in varying the three factors which had been identified in previous experiments as the most probable determining variables. These were: the units in which the performance scores were presented to each subject, the curve of the arbitrarily constructed distribution in terms of which the subjects are presented with "performance scores",? and the motivation of the subjects. His results generally support those of the 8 previous experimenters, indicating a high degree of consistency in the aspirations of the subjects under most of the varied conditions, but differentiating the extent of consistency on the basis of the three vari-ables considered. In an attempt to discover whether or not there were other signif-icant patternings of the level of aspiration phenomena, Sears (62) performed an experiment with children, which suggested certain patterns of behavior in aspiration situations. There are four patterns presented by Sears: a low positive discrepancy score - realistic and flexible (these terms are defined on page 11); a low negative discrepancy score - less flexible with a protectively low action goal; a high positive discrepancy score - very low flexibility; a mixed pattern - responses are highly variable. Hilgard and Sait (38) in a modification of the usual aspiration studies asked subjects to estimate their past as well as their future performance. They concluded that goal strivings influence not only the subject's expressed aspirations, but also his perception of the past. These influences are not consistent from individual to individual, but there are indications that there is considerable consistency in each subject's tendency to distort his perceptions from task to task. Generally, i t might be concluded that most of the experiments performed for the purpose of demonstrating consistent trends in the way in which a subject views his performance in an aspiration situation, have shown that for any particular subject there is a generally consistent pattern, although i t is doubtful that there are general patterns that can be identified as characterizing certain groups of subjects. While several investigators, among them Frank (21), Gould and 9 Kaplan (31), Gardner (25), and Sears (63), nave attempted to explain the variations in level of aspiration phenomena in terms of various person-ality characteristics or functions, the most recent formulation of an hypothesis capable of explaining certain apparent contradictions was made by Holt (41). In an experiment concerned with the solution of the problem of whether the level of aspiration was a motivational or. defensive function, he arrives at the following hypothesis expressed in the form of three pro-positions: (1) . When ego-involvement is minimal, levels of aspiration have l i t t l e motivational sig-nificance, being primarily rational judge-ments. (Supported by Bayton (5), Frank (£2) and McGehee (52)*. . . •-(2) . When ego-involvement is present, but at low intensities, levels of aspiration have l i t t l e defensive meaning, but reflect to some extent the intensity of motivation. (Bayton (5) ). (3) . When ego-involvement surpasses a certain limit, defensive considerations become paramount, and the level of aspiration becomes more complexly determined. (Holt (40) ). This hypothesis, while apparently the most acceptable, cannot be considered to have been proven simply because diverse experimental results have been reconciled with i t . However, lacking significant proof, i t can be considered as complementing the knowledge already amassed regarding the nature and function of aspiration phenomena. 10. I l l THE PROBLEM A. Formulation of the Problem It is apparent, even from this brief review, that aspiration studies have, taken many and varied forms. Their concern has been with various phases of the time sequence described on page three. It would be desirable to formulate a technique which could account for a l l of the . phases inherent in this sequence, but i t would seem more practical to concern ourselves with the primary phase of this sequence,which is the goal discrepancy score. (See Figure 1, page three.) In matters of level of aspiration this discrepancy .has been used to discriminate the more realistic individual from the less realistic individual. This conception of realism is borne out by a number of findings. Festinger (14) found that subjects who were asked "what would you like to get next time?" had a significantly higher goal discrepancy score than did those who were asked "what score do you expect to get next time?" Irwin and Mintzer (42) corroborate these-findings and make the suggestion that different attitudes, which may be interpreted as possessing different degrees of reality, are engendered by the two types of question: there is a wishful or unrealistic expression evoked by the former. Frank (21), Sears (62), Irwin and Mintzer (42) and Festinger (14) performed experi-ments which tend to support this suggestion in that they a l l found discrep-ancy scores which were lower in work than in play situations. Sears (63) has made clinical studies of selected small groups of children, in which he found that those who obtained high goal discrepancy scores tended to be lacking in self-confidence and school achievement, and 11. were rather free in admission of their incompetence. Another group, those obtaining low goal discrepancy scores, were characterized by their high level of confidence, achievement, and comfort in their achievement. These findings are interpreted as substantiating the view that realism as shown by low discrepancy scores is greater for persons clinically designated as "realistic" than for those appearing "irrealistic." Preston and.Bayton (58), in an attempt to control more adequately the attitudes of their subjects, asked them to state three levels of as-piration: the least they expected to do, the most they expected to do, and what they actually thought they would do. The "least" estimate was found to be unrelated to either of the other two, but there was a high correlation between the actual and the maximum estimates. In addition, the actual estimate was always closer to the maximum than to the least estimate. This suggests that even a statement involving a supposedly objective (actual) estimate, will in the absence of external controlling factors tend in the upward rather than the downward direction. On the basis of these experimental findings we may conclude with Lewin (47, p.345) that: The realistic attitude will produce a small discrepancy score with a level of aspiration that is flexible and responsive to changes in performance. The unrealistic attitude will produce a large discrepancy score with (a) level of aspiration which is unrespon-sive to reality influence, and may represent a wishful attitude toward the attainment of the action or stated goal. It can be suggested, then, that the following operational definition* will be useful in the construction of a modification of level *1. "If a scientist experiments with a conceived function and varies its form, he relies upon an 'operational definition', which links this function to procedures of creating i t or to procedures for testing its existence. The existence of the function is established by 'doing something with i t ' rather than simply 'looking at it'.»'(48,p.91 12. of aspiration techniques insofar as i t is consistent with experimental findings concerned with the concept. . Definition of Realism: Realism is that function of personality revealed  by a technique designed to measure a subject*s ability to designate  accurately his expected performance in an activity in which he has had  some experience and has consequently some criterion on which to base his  designation. The problem with which we will be concerned in this thesis may now be formulated in the following way: to develop a technique for the measurement of realism in social situations. B. Analysis of the. Problem Our problem resolves itself into two areas: the first, to select an activity which will be essentially interpersonal in nature; the second, to obtain a technique which wil l be capable of describing the obtained activity in terms which are comparable to those used in other studies on levels of aspiration, that is, a technique from which we will be able to obtain "measures" of both the aspiration level and the achievement level, and consequently of realism as defined above. The fi r s t area of the problem is comparatively simply solved. Any activity, the essence of which is interpersonal, will be an activity suitable to being studied by means of the technique, and capable of yielding results in terms of the stated problem. It is very likely, however, that the technique derived will be of restricted applicability, 13. and consequently wil l impose certain limitations on either the type of activity, or the setting within which i t occurs, or both. Let us consider, then, techniques for the assessment of inter-personal activities. These might be divided into two broad classifications: those concerned primarily with the extent and nature of interpersonal activities in which groups of individuals are involved. Those concerned with the assessment of individual activities, that is, clinical techniques, might well produce measures of the aspiration level of the individual with regard to interpersonal activity, but i t is unlikely that they could be modified to yield measures of the achievement level. On the other hand, techniques concerned with the assessment of group interpersonal activities, sociometric techniques, are capable of yielding measures of achievement level, and conceivably, with some modification, of yielding measures of the aspiration level of each individual. Sociometric data are composed of numerical equivalents of the choices expressed by members of a group for other members of that group. There appears to be only one limitation that this technique imposes on groups to which i t is applied, and that is, that the groups must be com-posed of more than two individuals. However, there are limitations imposed on the meaningfulness of the results of a sociometric study. One very important one is that there is no indication of quality or type or relation-ship expressed by an individual who says that he would choose another particular individual. A l l that can be observed in the group administrat-ion of this technique is the actual choice, and consequently each choice is treated as if it were equivalent to every other choice, and is allotted the value of one. With these limitations in mind, the kind of modification 14. required to meet the needs of a study concerned with levels of aspiration will be discussed. According to our definition of realism, we require a technique which w i l l permit a subject to designate his performance in an activity with which he has some experience. This technique f i l l s the requirements of the definition in the following three ways: 1. Since the measured activity, or achievement, is in terms of interpersonal relations, i t can be assumed that a l l individuals have had some experience in the activity. 2. It can be seen that there is some similarity between asking an individual to designate his performance at the present time in examining interpersonal activities by means of sociometric techniques, and asking an individual to designate his future performancein ar specific activity such as target shooting, since the designation in the fir s t case can be considered to be an expectation rather than an actual awareness. It is assumed for purposes of the problem with which we are concerned, that i t is justifiable to call the former designation a "level of aspiration", and consequently justifiable to consider the discrepancy between this designation and what is found to be the individual's achievement level a measure of his "realism" in social situations. 3. The designation, in order to be described as accurate or inaccurate, should be in terms which are the same as those of the obtained achievement level. This can be very simply accomplished by having each subject name the individuals that he thinks will put his name as one of the ones that they have chosen. 15 In summary, then, our technique will consist of the following: 1. asking each individual to choose a certain number of other individuals on the basis of some specified criterion, and from the data so obtained deriving for each subject a sociometric status or achievement level; 2. asking each individual to designate the names of the individuals he thinks have chosen him, and from these data deriving an aspiration level; 3. com-puting the discrepancy between each individual's achievement level and aspiration level, this discrepancy being considered a measure of the accuracy with which he designates his performance in this activity, or, by definition, his realism. 16, TV , PRESENTATION OF THE TECHNIQUE In Section III we have presented in essence the technique to be used to measure realism. Here we will outline, step by step, the specific questions asked to reveal the achievement and aspiration phenomena, as well as the proposed method of treating the data so obtained. A. Obtaining the data: 1. Sociometric data: Customarily, workers using sociometric techniques attempt to formulate a number of questions, each having to do with a specific activity, which, taken together, are considered to be representative of the types of activities in which the individuals of a specific group are most likely to have equal opportunities to participate. Each subject is then asked to select a certain number of individuals in response to the criterion questions. For example, there might be three questions to each of which the child is asked to reply with three names. (6, p.46) 1. With what children would you like to work best? 2. With what children would you like to play best? 3. What children would you like to have sit near you? The number of choices each child receives is then considered to be an indication of his sociometric status in the group. This type of question, and means of obtaining a sociometric status, have several limitations. First of a l l , the statuses obtained are literally "sociometric statuses" in that they are only functions of the questions asked. This in itself might not be a limitation, but since the questions asked refer to specific activities, we can conclude that the statuses obtained refer to these specific activities. 17. In the interpretation of sociometric results i t is frequently-assumed that the statuses are representative of "social" statuses and inferences are then made as to the extent and capacity for interpersonal interaction of each individual,with no specific reference to.the activities presented in the questions. If it is the purpose of the investigator to obtain "social" statuses in the broad sense, then it. would seem reason-able to ask questions, or even a question, which he considers to be evocative of responses with broader social reference. There is at least, a need for experimentation using the two types of questions to determine which is the more fruitful in obtaining general-ized social statuses, i f that is the purpose of a particular sociometric application. It is suggested, then, that since our concern is not with * any specific activity, but ostensibly with social interaction generally, a question such as the following would be useful in the general formulation of this technique: "Whom would you most like to be with most of the time?" The number of persons each individual is asked to name is determined in each case by the size of the group, and the extent to which social inter-action is present in the group. 2. Aspiration data: A number of questions have been asked by investigators in the past in eliciting the expression of the subject's aspiration level. Gould (29), Festinger (14) and Frank (22) have inves-tigated and compared the attitudes adopted in answering questions as to the aspiration level such as: "What will you do next time?"; "What do you think you will do?";_"What score do you expect to get?" On the basis of their findings i t appears that the questions involving "think you will 18. do" and "expect to do" educe the most realistic aspirations. It would seem desirable, since i t is our purpose to measure realism, defined as "ability to designate accurately", to ask a question which is most likely to engender a realistic attitude. Consequently, the following question is suggested as of the type which would accomplish this purpose: "Who do you think chooses you?" It is usually desirable to point out to the subjects, prior to asking this question, the basis and number of the choices each individual in the group is making. B. Tabulating the Data One form for tabulating results can be adopted with slight modi-fication from sociometry, and is illustrated in Table I. TABLE I Individuals are identified by the numbers at the head of each row and column. A l l choices made by one individual are recorded in the row opposite his number, and similarly, a l l the choices of individuals that he thinks will choose him are recorded in the same row. Choices are signified by unit symbols, and expected choices by zero symbols. Thus, an individual's social status raw score, or achievement raw score, will be the sum of the unit symbols in the column below his number; his aspiration raw score will be the sum of the zero symbols in the row opposite his number. This modi-fication involves only the addition of data obtained in addition to the TABLE I Sample Tabulation Chart of Sociometric Choices and Expected Choices Subject 1 2 3 4 5 6 7 8 Expected Choices (No.) Row X 5 4 4 2 5 3 I i 1 1 0 1 1 C ( ) 4 2 1 0 0 0 1 C 1 ( ( > 0 7 3 1 0 1 1 1 4 1 C 1 0 1 2 5 1 0 1 1 1 6 1 o x 0 1 1 3 7 1 c 1 1 0 2 8 0 1 1 0 0 C 1 4 Social Status Raw Score 4 6 2 4 3 2 1 2 2 0 . standard sociometric data, and therefore we may quote directly from Bronfenbrenner (6, p.28) with regard to the advantages of this form of tabulation: Since a l l data are recorded exactly as obtained the chart presents a complete summary of the test results, obviates the necessity of referring to the original questionnaires, and permits detailed analysis of a l l choices and choice patterns. C. Analysis of Data into Constituent Parts Consider, now, what we have obtained. ?Je have for each individual much more than simple numerical equivalents of the number of choices he reoeives and expects to receive. We have the actual names of the individ-uals who choose him as well as the actual names of the individuals he expects will choose him, and for each name involved in these expressed interactions we have an index of social status. It is possible then, to break down each individual's designation of his performance in this social aotivity: we may consider the accuracy with which the individual designates (a) the number of individuals who choose him, (b) the names of the individuals who choose him, and (c) the social statuses of the individuals who choose him. It is immediately apparent that an individual who can designate the correct number of individuals choosing him is.more realistic than one who cannot; and that, of two individuals, both having designated the correct number, the one who designates the correct names is more realistic; and again, of two individuals, both of whom have designated the wrong names, the one who designates names of individuals with indices of social status more nearly approximating the social statuses of those who choose him, is more realistic. In the next section we shall speak of these three factors of 21 number, names, and social status indices, as faotors A, B, and 0, respect-ively^ D. Treatment of Data 1. Factor A: The discrepancy between the expected number of choices an individual expresses and the actual number he obtains can be most simply expressed by the formula: expected - obtained This discrepancy can vary from 0 to (N - l ) . Since N, the number of indivi-duals in a group, varies from group to group, i t would seem more useful to express the obtained discrepancy of a particular individual as a fraction of the total possible discrepancy. That is; expected - obtained (N - 1) But it is usually more convenient to work with whole numbers, rather than with fractions, and we can very simply obtain whole numbers by multiplying the fraction by 100. Then the formula for the expression of an individual's discrepancy score on Factor A becomes: expected - obtained x  H (N - l) X l 0 ° ( 1 ) This expression has some limitations* It might be argued, for example, that an individual in a group of 31 who thinks that 20 will choose him while 15 actually do choose him, and obtains a score of firrt)*100 s 16-67 is more realistic than an individual who thinks that 6 will choose him while only one does, and obtains the same score. While this might be the case in activities which are less directly interpersonal in nature, i t is not 2 2 . necessarily the case here, and consequently we shall accept this score as adequately expressing the discrepancy, with reservations as to the inter-pretation put on any one score in comparison to other scores. Another limitation is that the expression can yield either positive or negative scores, depending on whether the individual has expected too many or too few choices. The quantity of his score is an expression of his irrealism, while the sign is an expression of the direction in which he tends to be irrealistic. It w i l l be seen later that i t is difficult to incorporate these obtained directions into the total realism score. For the moment, let us consider that each individual obtains the following: (a) a number, which can be between 0 and 100, and which is an expression of the degree to which he tends to be irrealistic in designating the number of indivi-duals that will choose him; and (b) either a positive or a negative sign, which is an expression of a direction in which he tends to be irrealistic in this function. 2 . Factor B: The discrepancy between the names of the individuals who choose an individual and the names he-expeots will choose him can be expressed, again, most simply by the formula: obtained choices - correct expected choices. It is reasonable to discard a l l the incorrect names in the computation in the score on this faotor, since these selections are considered in Factors A and C. Here again, the resultant score can vary from 0 to (N - 1). This expression is of very limited value in discriminating the accuracy of designating names of individuals, since an individual who was able to name fifteen out of eighteen individuals who chose him would obtain the same score as one who was only able to name one out of four individuals 23. who chose him. Consequently the following formula is suggested as having more discriminating value: j i * , a, correct expected choices ^jJ^JZ^ i&t^fL^ dbtained choices —^T**T- '.^  In order to obtain scores which will be easily manipulated the formula is modified as follows: so that 0 will be the score obtained by the most realistic individual measured on this factor, the expression is subtracted from 1, and the fractional resultant eliminated by multiplying i t by 100. The formula for the expression of an individual's discrepancy score on Factor B becomes: 1 _ correct expected choices X J^QQ (2) obtained choices 3. Factor C: Social status indices are expressed, in accordance with the technique of Bronfenbrenner (6 #), in terms of probability of chance occurrence. For each individual, then, we have an index which is somewhere within the range between 0 and 1. Since we have already expressed the dis-crepancy between actual numbers (Factor A), and that between actual names (Factor B), then we*mu^ t express here the discrepancy between social status indices. We require a representative social status index for the expected choices and for the obtained choices. The arithmetical mean is generally considered to be the most representative function of two or more numbers, and since social status indices are expressed in numbers between 0 and 1, then the formula for an individual's discrepancy score on Factor C becomes: (Mexp. - M o b t J 3C 100 Mexp, = the mean value of the social status indices of the individuals he expected to choose him. Mobt. = the mean value of the social status indices of the individuals who chose him. Here again, as in Factor A, this expression can yield either positive or negative scores, depending on whether the individual has expected to be chosen by individuals with social status indices higher or lower, respect-34. ively, than the indices of those who did choose him. As in Factor A, it is difficult to incorporate directions into the total realism score. Therefore, let us consider that each individual obtains a number between 0 and 100, which is an expression of the degree to which he tends to be irrealistic in terms of social status indices in designating individuals who will choose him, and a direction, either positive or negative, which is an expression of the- direction in which he tends to be irrealistic in this factor. 4. The Realism Scoret For each individual we have three scores. Each of these scores lies somewhere be/Cween 0 and 100, but, as we have seen, this is for convenience in manipulation only. A l l that we can say of these scores is that a score of 0 on any one of the factors indicates the maximum realism measurable on that factor, and as the scores become pro-gressively higher they indicate progressively less realism, or more irreal-ism. It is possible, however;, in any group, to convert these scores into standard scores, so that scores obtained are comparable from one factor to another in terms of relative standing in the group. These standard scores have two particular advantages: they save an extra computation in arriving at the weights to be given to each of the three factors, and they are readily understood by anyone with even a very limited acquaintance with statistical concepts and techniques, (66, pp. 40 ff.). Thus standard scores on the A factor will be given-by the formula: Sigmaa (4) And in the same way we can obtain Z b and Zc. Standard scores of this sort have one other important advantage: they can be averaged so that we have 25. a representative single score which has taken into account the three scores of the factors. However,- simply to average the three standard scores that any individual obtains in each of the three factors is to ignore what might be an important consideration: what are the relative weights that each factor should receive in order that its contribution to the resulting com-posite score is appropriate to the relative independence of this factor from the remaining two factors? A statistical technique has been derived which permits the allocation of weights to each of the factors in terms of, the relative independence of each factor in discriminating between members of the specific group with which we are concerned. (See appendix for derivation of formulae for the three heights) In consideration of this, the formula for E, the realism score, where WQ, Wb, and Wc, and ZQ, Z^ , and Zc, are the weights and standard scores of three factors, A, B, and C res-pectively, becomes: (67, p.15) wa* wb+ wc . 5. Meaning of the R Scores: The derived R scores may be inter-preted in the same way as any other standard score. That is, we can say, for a particular R score, that i t represents a position on the distribution of R scores for the particular group within which i t has been obtained. Whereas before the most realistic individual received a score of 0, now he obtains the lowest R score, or, since these scores are in positive and negative numbers, the largest negative score. Similarly, the largest positive score is obtained by the least realistic person in the group. It w i l l be recalled that factors A and C produced both positive and negative scores, and that the:' directions are not considered in the 26. calculation of the R score. If an attempt had been made to consider them in this calculation two chief difficulties would have been introduced. The fi r s t is that the zero point, which is the lowest raw score, would have become a point somewhere between the two extremes of irreallsm: i t would have remained at zero in the raw score form, but would, because of the nature of standard scores, become an indeterminate point in the stan-dard score distribution, except by reference back to the raw scores of each individual in the group. The second difficulty is that since there are two factors capable of taking on either positive or negative signs, i t is con-ceivable that in averaging the standard scores, i f the two were indicative of irrealism in opposite directions, the irrealistic indications of these scores would cancel one another out. For these reasons it seemed advisable to leave the-directions of irrealism until the final R score was obtained, and to include these with the expression of the score. Therefore, each score will consist of: (a) , a numerical expression of the position of that score in relation to the distribution of the scores of the group, or the weighed R score, (b) . a positive or negative sign indicative of the direction in which the individual tends to be irrealistic in the expression of the number of individuals he thinks will choose him, (c) . a positive or negative sign indicative of the direction in which the individual tends to be irrealistic in the expression of the names of individuals with social status indices different from those of the individuals who actually choose him. 27. V DEMONSTRATIVE STUDIES To provide illustration, the above technique has been applied to three groups. No attempt has been made to interpret the results obtained, or to compare them with other functions which might be considered to be correlated to the function measured by the technique. The purpose of these applications is to show-that i t is possible to obtain distributions of R scores within various groups. That is, i t is a function in which indivi-duals are measurably different. It has been applied to three groups at different age levels, whose bonds are entirely different, and who operate at different levels of integration.- Description of the groups is limited since i t is assumed that for purposes of demonstratidn, a knowledge of the age range, male to female ratio, and group bonds is adequate. A. Group I: Age Range 22-31 1. Constitution of group: this group is composed of nine in-dividuals - three women and six men - whose ages f a l l within the specified range. It is a group whose members are joined by common academic interests and vocational goals. 2. Obtaining the data: The following questionnaire was submitted to each member, with the request that he answer the questions in private and return i t to the investigator: This is a preliminary t r i a l of a variation of a sociometric technique. It involves the regular type, sociometric question - "who would you like...", as well as a "reversed question^ - "who would like .. you...". The.purpose of the addition of the reversed question is to determine in some way the "reality" with which individuals view their own interpersonal relationships. As yet no method has been devised to evaluate the "reality". This is our present 28 purpose. Even though the results will mean l i t t l e they wil l be confidential. The individuals who are members of this group are listed here: Please answer the following question, restrict-ing your choices to individuals on the above l i s t . Question: With whom would you most prefer to waste an hour in the coffee shop? Place them in order of preference. 1 2 , There are eight individuals other than your-self in this group, each of whom has made only two preferences. With this in mind answer the following question. Question: Who of these eight ppeople do you think has chosen you with whom to waste an hour in the coffee shop? 3. Tabulating the data: This has been done in accordance with the form presented above. 4. Treating the data: This has been done in accordance with the technique presented above. The results are presented in Table II. TABLE II 5. Discussion: Since we have obtained realism scores for each individual in this group we may conclude that the technique should be applicable at this age range and to groups whose bond is of a similar nature. Our method for arriving at R scores seemingly produces the expected results: individuals who are most realistic or whose expressed expected choices arS equivalent to their actual obtained choices, obtain 29. TABLE II  Results of Group I A. Calculations 1. Sociometric indices: (6) p « _A_ r 2 = .25 N-l 8 q - 1-.25 - .75 m = np - 8 x .25 = 2.00 d s jTnpq » V 8 x .25 x .75 » 1.23 a3= 3c2. z .75 - .25 = .4065 <s 1.23 No. of Choices Upper Limit Raw Score Social Status Probability Deviations Equivalent of Chance S L L-M L-M P s  • _ t f ; 0 .5 -1.5 -1.22 .102380 1 1.5 - .5 - .41 .361452 2 2.5 + .5 + .41 .679245 3 3.5 +1.5 +1.22 .884609 4 4.5 +2.5 +2.03 .969326 5 5.5 +3.5 +2.85 .993834 30, TABLE II (Oont.) 2. Raw & Z Scores on Factors A. B. & 0. Factor A Factor B Factor G ject Raw Z Raw A Raw Z 1 (+)25 +1.54 100 •1.13 U)44.8 •2.01 2 0 - .77 0 -1.21 0 - .69 3 ( + )25 +1.54 66.7 * .36 (-)ll.O • .03 4 0 - ;77 100 +1.13 (-)33.9 •1.35 5 0 - .77 33.3 - .45 0 - .69 6 (-)12.5+ .38 33.3 -.45 U)10 - .09 7 0 - .77 0_ -1.21 .0 - .69 8 0 -.77 33.3 - .45 - .58 9 (-)!2.5-.77 100 •1.13 (-)l.5 -..60 3. Derivation of Weights: (»Appendix';B) Where ; r a b - .48, r a c r .39 and r b c = .62 2's A .7558 .1348 .0372 .9278 a .9278 B .1857 .4293 .3487 .9637 .9637 C .0585 .4359 .6141 • 1.1085 f 0 sf 1.1085 3 W - ,3093 Wb = .3212 Wc = .3695 31 TABLE II (Oont.) B, R Scores and Directions: Directions Subject R Score • Factor A Factor C 1 + 1.58 + * + 2 - .88 0 * 0 3 + .60 + 4 + .62 0 -5 - .64 0 0 6 - .06 - + 7 - .88 0 0 8 - .60 0 - ' 32„ TABLE II (Oont.) (o) Histogram of Distribution  of R Scores: Group I o 3 a< 3-*I.9S (d) Soattergram of R Scores and Social Status Indices: Group I in « :9T-- 2 5 . W <D U 8 +*s-CO •H.25 Social Status Indices <0 1 z 1 1 1 z 7 4 '> 33. the largest negative score (individuals 8 and 7); individuals who are least realistic obtain the largest positive score (individual l ) ; those with intermediary R scores appear to have exhibited intermediary irrealism with respect to the choices they expected to receive*. B. Group II: Age Range 59-86 1. Constitution of group: This group is composed of 118 indiv-iduals, a l l men, whose ages f a l l within the specified range. These indiv-iduals are residents of a veterans* home, and are admitted because they require institutional care, although not constant medical attention. Some association with the other members of the group is inevitable, but beyond this, each individual is able to determine the extent of his participation in interpersonal activities. 3. Obtaining the data: A l l the individuals in the group were interviewed over a period of six weeks. While i t was found impossible to maintain a standard interview, each individual was asked the same questions. In many cases i t was necessary for the investigator to reassure and en-courage the men, but only two refused to participate in this study. The first eleven men were asked the following questions:. I would like you to give me five names of men that you would most like to be with most of the time, and then I would like you to give me a l l of the names of the men that you think would give your name as one of the five they choose. ,?* The questionnaire used in this study was devised and administered in strict accordance with usual sociometric procedures. After the adminis-tration, the investigator discussed with the members of this group the efficacy of asking .them to make choices in terms of a specific activity, for purposes of obtaining an indication of the general "social" status of the members of a group. It was concluded that a more generalized "social" question would be most likely to produce a more generalized "social" status. 34 o However, despite repeated explanation and encouragement i t was found im-possible to obtain an answer to this second request. The most they would give was the number of men they thought would choose them, without specify-ing any names. Consequently, the investigator rephrased the second request, and asked the remaining men: I would like you to give me the number that you think would give your name as one of the five they choose. 3. Tabulating data: The data were tabulated in accordance with the form presented above, except that there are no zero symbols entered in the rows opposite each man's number, so that the tabulation sheet yields only raw social status scores. The number of men that each man thought would choose him was placed at the bottom of the column below his number, so that an additional row of data was obtained which are the raw score aspiration indices. 4. Treating data: The data were treated in accordance with the technique presented for obtaining scores on Factor A. Thus, in this group, R is equal to Zg. TABLE III 5. Discussion: The R scores obtained in this group have an obviously different meaning from those obtained in the f i r s t study, or outlined in the development of the technique. They represent the accuracy with which an individual can designate the number of men he thinks will choose him: his numerical estimate of his raw social status score. This estimate can be given with very l i t t l e consideration: i t is very easy to 35. TABLE III RESULTS OF GROUP II A. Calculations 1. Sociometric indices: (6) P = .0427 q. B .9573 m e 4.9959 c e 2.1862 a 3 - .4184 No. of Choices Probability of Chance No. of Choices Probability of Chano s Ps. s Ps. 0 .008890 7 .872354 1 •040646 8 .935819 2 .120541 9 .970415 3 .259135 10 .987893 4 .433828 11 .995321 5 .615256 12 .998272 6 .766261 13 .999413 B. R Scores & Directions (R - ZQ) Standard Score on Factor A Standard Score on Factor A Subject Za Subject za 1 - .28560 26 — .28560 2 - .39984 27 + •08568 3 •5.04084 28 - .52836 4 - .15708 29 - .52836 5 - .39984 30 .52836 6 +2.87028 31 + .57120 7 +2.62752 32 — .39984 8 - .64260 33 — .64260 9 - .39984 34 - .28560 10 +1.65648 35 + .08568 11 - .39984 36 + .44268 12 - .04284 37 — .39984 13 - .39984 38 — .39984 14 + .44268 39 - •52836 15 - .52836 40 — .39984 16 - .64260 41 - •64260 17 - .39984 42 - .52836 18 - .52836 43 • .08568 19 - .52836 44 - .28560 20 + .08568 45 — .64260 21 + .08568 46 + .68544 22 +1.29948 47 - .52836. 23 •1.17096 48 ,52836' (did not respond to 24 + .44268 49 25 + .08568 Question 2) 36. TABLE III (Cont.) B. R Scores & Directions (R - Z„ Subject Standard Score on Factor A Subject Standard Score Za 50 - .52836 95 - .15708 51 - .15708 96 - .39984 52 + .08568 97 + .57120 53 - .28560 98 X (did : 54 - .28560 99 - .39984 55 - .52836 100 - .15708 56 - .04284 101 - .64260 57 - .15708 102 - .52836 58 - .64260 103 - .39984 59 - .39984 104 - .39984 60 - .64260 105 X (did v61 - .39984 106 - .28560 62 + .08568 107 - .39984 ' 63 4 .32844 108 +1.65648 64 + .44268 109 - .04284. 65 .-• - .15708 110 X (did 66 - .39984 111 - .64260 67 + .32844 112 - .52836 68 - .39984 113 - .52836 69 - .52836 114 - .39984 70 - .64260 115 - .04284 71 - .52836 116 X (did 72 + :. 08568 117 - .52836 73 + .08568 118 - .04284 74 - .39984 75 +1.41372 76 «. 52836 77 - .64260 78 - .28560 79 - .64260 80 - .15708 81 - .52836 82 - .52836 83 + .32844 84 - .52836 85 + .19992 86 + .32844 87 - .28560 88 - .52836 89 +4.55532 90 - .52836- , 91 . + .32844 92 + .44268 93 - X (did not respond) 94 • - .52836 (c) Histogram of Distribution of R Scores: Group III (a) Scattergram of R Scores and Social Status Indices - Group II >0 0-« TO 0 a-•. 6 4. 4 6 6 z 5 2 0 9 4 a ± 3 2 i z Z 1 3 i 1 i 1 i I 1 1 i 1 1 39 "think" that fifteen men will choose you, but a great deal more difficult to name those fifteen men* It seems reasonable to infer that in most cases both the estimates and the discrepancy between estimates and obtained choices will be greater where only a numerical expression is requested. Since the R scores here are expressed as standard scores, this limitation is to some extent taken into consideration. Even when the technique is used with this limiting modification, i t is capable of producing results which are mean-ingful in terms of the stated definition of realism. The largest negative standard scores are indicative of the greatest degree of realism, while the largest positive standard scores are indicative of the greatest degree of irrealism. It is conceivable that, under appropriate conditions, a skilled interviewer could obtain the expected choices in terms of actual names, even from the most reticent or apprehensive individual. Here, the inter-views had to be carried out in the rooms of the individuals, within hearing of some of the other occupants of the rooms. In some cases a l l the men in a room participated actively in each interview carried out in that room. Under better conditions, and with more interviewing s k i l l and experience, i t was felt that most of the men could have been persuaded to respond more adequately to the request for the names of the individuals they thought would choose them. If this is the case, there is no need to conclude that the rather significant, or direct social meaning of the questions will detract from the feasibility of carrying out experiments using this tech-nique. 40. C. Group III: Age Range 7-8 1. Constitution of the group: This group is composed of 25 children - 14 boys and 11 girls - whose ages f a l l within the specified range. They are members of a grade II class in a small primary school. The bonds that tie the members of this group can be considered to be similar to those that are operative in any schoolroom situation. They must work at least in proximity to one another, and their play activities in the school situation are restricted to other members of their par-ticular group. 2. Obtaining the data: The data were obtained in strict accord-ance with the technique presented above. That is, the investigator, after a few brief introductory remarks as to the nature of the investigation, presented the two questions to the members of the class. It was thought that group administration would produce results adequate for the purposes of a demonstrative study, although i t is generally considered that indivi-dual administration is more valid in sociometric techniques. The two questions were: I would like you to give me four names of children in this class that you would most like to be with most of the time. Now I would like you to give me a l l of the names of the children that you think would put your name as one of the four they have chosen. 3. Tabulating the data: Since the data were obtained in exactly the way that is presented in Section V, i t was possible to adhere strictly to the form presented for the tabulation of data. 4. Treating the data: This has been done in accordance with i l l . the technique presented above. TABLE IV 3>. Discussion; Here again, i t i s apparent that the technique distributes the R scores i n terms of the relative accuracy with which the individuals designate those that they think w i l l choose them. Since this i s the sort of group that i s most convenient and productive for sociometric analysis, i t seems reasonable to suppose that i t w i l l also be the sort of group to which this technique w i l l have the most frequent application. It i s therefore significant to note that the children appeared to be co-operative and conscientious i n answering the questions asked. D. General Discussion • Certain general indications are apparent i n a comparative exam-ination of the data obtained for the three groups. Particular note should be taken, however, of the obvious limitations imposed on any interpretation or generalizations made from these suggestions since the groups are highly selected, and in the case of Group I, at least, the numbers involved are so small as to make any statis t i c s almost meaningless i n terms of parametric interpretation, even though the numerical manipulations involved are quite meaningful and legitimate for purposes of obtaining and comparing d i s t r i b -utions of scores within the group. (a). The distributions of R scores for the three groups suggest that there might be a positive correlation between realism i n social situ-ations and age. Tables l i e , IIIc and IVc w i l l i l l u s t r a t e this point. The distribution of scores for school children i s sli g h t l y positively skewed, and the distribution for the oldest group i s considerably 42. TABLE IV RESULTS OF GROUP III Calculations: 1. Sociometric Indices. P - .1667 q = .8333 m = 4.001 <r = 1.822 3g - .6666 No* of Choices Probability of Chance S Pa 0 .005185 1 .059329 2 .213328 3 .431817 4 .647301 5 .807025 6 .904936 7 .957064 8 .981959 9 .992865 10 .997320 11 .999037 12 .999660 13 .999886 14 .999963 43. TABLE IV (Cont.) 2. Raw and Z Scores on Factor A, B, and C. Factor A Factor B Factor C Subject . Raw Z Raw Z Raw Z 1 T16.67 .61 66.67 -.01 +18.23 -.51 2 -41.67 3.00 71.43 .17 +32.99 .08 3 •16.67 .61 0.00 -2.51 +16.46 -.58 4 •4.17 -.59 100.00 1.24 +80.70 1.97 5 -12.501 .21 50.00 -.64 -23.52 -1.15 6 -29.17 1.81 63.64 -.12 -2.72 -1.12 7 -+.8.33 -.19 100.00 1.24 +90.30 2.36 8 0 -.99 66.67 -.01 -17.74 -.53 9 -4.17 -.59 50.00 -.64 +13.53 -.69 IP 0 -.99 66.67 -.01 +54.91 .95 i i - +20.83 1.01 0.00 -2.51 -15.93 -.60 ia •20.83 1.01 66.67 -.01 +11.89 -.76 13 -12.50, .21 66.67 -.01 +19.57 -.45 14 -4.17 -.59 66.67 -.01 +17.40 -.54 15, 0 -.99 100.00 1.24 0.00 -1.23 16 -16.67 .61 80.00 .49 +56.27 1.00 17 -4.17 -.59 95.00 .30 +42.64 .46 18 +4.17 -.59 100.00 1.24 •8.72 -.88 19 -.59 100.00 1.24 -80.70 1.97 20 --• : Q . ; : 7 -.99 30.00 -.64 +18.76 -.49 21 -16Q67 .61 37.14 -.37 -27.88 -.12 22 - 0 0 -.99 100.00 . 1.24 +47.31 .65 23 -12.50 .21 60.00 -.26 -20.78 -.41 24 0 -.99 50.00 -.04 +28.41 -.10 25 +8.33 -.19 66.67 -.01 +27.44 -.14 TABLE IV (Cont.) 3. Derivation of Weights (Appendix b) Where r at, - -.29 r a c s -.19 and r D C - +.46 then Wa = . 3 3 6 a Wb .33«»o Wc - ,5Z7i B. R Scores and Directions Directions Subject R Score Factor A Factor 1 +.04 — m _ 2 +1.09 _ + 3 -.83 +. + 4 •-t.86 + * 5 -.52 -6 + .20 — _ -7 +1.12 + + 8 -.51 0 9 -.64 _ + 10 - -.03 0 • 11 -.70 + _ 12 +.90 + + 13 " -.08 + 14 -.38 _ + 15 -.32 0 0 16 + .70 + 17 + .05 _ + 18 -.07 * + 19 +.86 — 20 -.71 0 + 21 +.04 _ _ 22 +.30 0 + 23 -.15 _ 24 -.58 0 + 25 -.11 + + 45. TABLE 17 (Cont.) (d) Seattergram .of R Scores and Social Status Indices: Group III Social Status Indices to 8 o - / . o r -.-7S-, - . V S T . 1 i z 1 1 1 1 1 1 1 1 3 1 1 1 1 ~ 1 1 46. positively skewed. While this comparison between groups is made on the basis of scores which have reference to the specific group within which they have been obtained, the implications of the suggested relationship are worth considering. If there is a developmental continuum of realism from childhood, through adolescence and maturity, to old age, i t might be suggested that an individual's perception of his social position in a group may progress through increasing degrees of accuracy, even after the decline of some other functions. (b) . There appears to be l i t t l e relationship between an individ-ual's social status and realism. Consider Tables (2d), (3d), and (4d). Even though a slight correlation would be expected between the distrib-utions of these scores, since the choices received by an individual (the basis of the social status index) are involved in some way with the scores on each of the three factors, the scattergrams suggest very slight co-relations between the two distributions. The only exception is Group I, in which N is too small to make any correlation obtained almost meaning-less in terms of generalized conclusions regarding such a relationship. It is interesting to note that in the older group (II) the most unrealistic individuals are at the same time among those with the lowest social status scores, although the most realistic individuals are distributed throughout the range of social status indices. However, this does not appear to be the case in the group of school children, where the two most unrealistic individuals are at opposite extremes in the distribution of social statuses. (c) . In both cases where the three factors were used, Factor A appeared to be the most independent. Further, the sequence of progression from most independent to the least independent was the same in both groups: 47 Factor A (the number), Factor C (social statuses), then Factor B (names). (The obtained coefficients of separate determination for themselves (given by Formula 3, Appendix&)are: Group I: Factor A .7558, Factor C .6141, Factor B .4293; Group III: Factor A .9372, Factor 0. .7894, Factor B .7558). Although no explanation can be given on the basis of the present studies, wider application of the technique may clarify this sequences 'possibly in terms of a common frame of reference for this function from one group to another.. (d) To supplement the information available in the scattergrams of the total R scores and social-status indices, three four-fold contingency tables were constructed, in which the relationship between realistic and irrealistic scores (defined by an approximate median) and high and low-social status indices (defined by an approximate median), on each of the three factors, were examined by means of the chi square technique. (54, pp 192-202). TABLE V / The only relationship which appears to be significantly differ-ent from that expected by chance, is that between realism and social status on Factor A: (less than one chance in one hundred). It can be seen, from an examination of this contingency table, that the relationship is in a direction which indicates that, in this group, individuals with low social status tend to be more irrealistic with-respect to the number of individ-uals^will, .choose them, than those with higher social status. This seems to be the situation that one would reasonably expect, since the more choices 48. TABLE 7 Contingency Tables of Factors A, B, and C with Social Status; Group III  FACTOR A: Realism-03 -p •p r CO 9 2 11 x 2 > 8.93 Social 3 1 1 14 p - <.oi Social 12 1 3 •. 25 FACTOR B: m Realism Status 4- 7 U . x2- .« 3ocial 8 6 14 P • <.70 12 13 25 FACTOR C: Realism ra P •p CD 6 5 CO •H O O CQ 7 1 7 11 14 P 9<D 12 IS 25 49. am individual receives, the more the error i s reduced than he can possibly make. (e) Since the directions involved i n scores i n Factors A and C have been ignored, except for their inclusion in the expression of the total R score, i t might be suggestive to examine how they relate to the realism function and social status indices. The terms expansive and recessive w i l l be used to designate the positive and negative directions, respectively, i n each of the factors (refer to Table VI). TABLE VI There i s apparently no consistent tendency for individuals in this group to make designations i n one direction or the other (Via). That i s , individuals who are expansive on Factor C are equally distributed over the expansive ahdrrecessive directions on Factor A. However, since there i s only one individual who is expansive on Factor A and recessive on Factor G, the tendency to consistency in this way might be suggested: i t would seem quite tenable that individuals who tend to expect more choices than they receive, w i l l expect then from individuals who hold a sociometrically superior position i n the group. (See Table VII, page 53). The chi square coefficient for the relationship exhibited i n Table Vlb i s quite significant, (less than one chance in one thousand that this occurred by chance). The suggestion implicit in this relationship i s that individuals with a low social status tend to expect feuer choices than they receive, while individuals with high social status tend to expect tVvere choices than they receive. This might mean that in the matter of placing 50. TABLE 71 (a) Contingency table of Expansive (+) and Recessive (-) on Factors A and C< Factor C Factor A + X p 2.42 .10 (b) Contingency Table of Expansive (+) and Recessive (-) on Factor A and High (+) and Low (-} Social Status Indices Factor A + -+ o io x 2 = 1 4 * 7 9 S.S. - . 12 3 P s .001 (c) Contingency Table of Expansive (4) and Recessive (-) on Factor C and High (+) and Low (-) Social Status Indices Factor C + + 3 7 B 2.08 9 6 P » .20 (d) Contingency Table of Directions, Expansive (+) and Recessive (-), on Factor A and Greater or Lesser Degrees of Realism on Factor A Realism •*-f 4 8 X 2 = Direction -'8" 5 P = .20 (e) Contingency Table of Directions, Expansive .( + ) and Recessive (*), on Factor C and Greater or LSsser Degrees of Realism on Factor C Realism + 9 3 X = 6 » 7 4 Direction 3 10 P - .01 .51, themselves numerically i n a social group, individuals tend««Ni^Jtfimthe mean. The relationship suggested in Table YIc is not very significant s t a t i s t i c a l l y . However, by inspection, one might be tempted to interpret this table as supporting the inference made on the basis of Table VTb: individuals tend toward the mean in designating their own position i n a group. The relationship represented i n Table Vie i s s t a t i s t i c a l l y s i g -nificant (less than one chance in one hundred of occurring by chance), and suggests that individuals who tend to' be r e a l i s t i c on this factor, that i s , expect to be chosen by individuals whose social statuses approximate those of the individuals who do choose them, tend to have discrepancies in the negative direction, that i s , expect to be chosen by individuals whose lower social statuses than those who do choose them. While the relationship re-presented in Table VId i s not as significant, the opposite effect seems to be at work. The realisticeare s l i g h t l y more expansive than the unrealistic. It might be inferred from these indications that Factor A i s a measure which produces results similar to those expected on the basis of previous aspir-ation studies. The r e a l i s t i c individuals tend to have low positive dis-crepancy scores, sli g h t l y expansive, while the unrealistic have "protect-ively low action goals," or are recessive. (See Page 8).- This inferred similarity would provide partial empirical justification for the assumption that the technique developed i n this thesis i s a level of aspiration technique. (f) In an attempt to answer the question, "do the unrealistic expected choices (not considered in Factor B) tend to go to higher or lower sociometric groups?" Table VII was constructed. The subjects were 52. divided into approximate quartiles on the basis of their social status indices. It appears that there i s a consistent tendency for these choices to go to sociometric groups (quartiles) above the group of the subject making the designation. Sixty percent of the subjects tend to go to groups above their own and twenty-eight percent do not give any incorrect expected choices. The other twelve percent are within the upper, two quartiles; eight percent i n the fourth quartile could not expect individuals i n a higher group to choose them. We might conclude on the basis of this table that there is a reasonably consistent ten-dency for individuals making incorrect expected choices to select i n -dividuals with superior sociometric positions. TABLE VII 53 TABLE VII Quartile Position of Incorrect Expected Choices i n Relation to the Quartile Position of the Subject making the Designation £ Relation of Incorrect $ Expected Choices No Incorrect ra Below Above Same Choices rH ^ | 5 (High) Q4 1 0 1 4 0 -P t o 0 <n 5 Q 3 1 1 2 o n S H Q2 6 £ (Low) Q 1 . 8 1 1 a? 1 i i . TOTALS 1 15 2 7 54o VI CONCLUSIONS A. The Technique The technique haa been shown to be applicable to three age groups including individuals with ages from seven to eighty-sir years. While the members of the groups were restricted to individuals who f e l l within the restricted bounds of the age ranges for these groups, i t would seem a valid induction that the technique will be applicable to any age group within these limits. We might therefore conclude that the technique will be useful in describing the realism function numerically, and even more useful where extending modifications are made. It appears to this writer that such modifications will have to develop out of empirical studies designed to delimit more accurately the nature of this phenomenan. Some of the more immediate needs are listed here: 1. Application of this technique to many and varied groups for the purpose of determining the extent to which the weights applied to each factor vary from group to group, with the objective of determining a general weight which can be applied to each factor. It would appear from an examination of the weights obtained for each of the factors in Groups I and III (Group I, .3093, .3212, and .3559; .Group III .3368, i3360, and .3272) that the weighting technique had l i t t l e significance in the deter-mination of the R scores for the individuals in those groups since the weights are nearly equivalent in both cases. It might be that there is no problem of weighting, since the weights are usually nearly equivalent. This will be amenable to investigation in any application of the technique. The solution of this problem will greatly facilitate the use of the tech-nique by eliminating a ^considerable amount of statistical manipulation 55. required to obtain scores for the individual members of the group. 2. Possible utilization of the mean social status raw score and the mean aspiration raw score in describing the relative realism of groups, or some other measure common to both groups, for the purpose of converting the R scores of the individual members of the groups into terms which are capable of comparison from one group to another. This might even be in terms of some individual measuring devices (performance on other tasks designed to measure realism in specific activities) which might be des-cribed as "linking correlates". 3. Incorporation of the positive and negative directions into the final expression of an individual's realism, so that comparison with other functions can be accomplished more readily, and in terns of more rigidly defined criteria. 4. Definition of units by which this function is measured, rather than the expression of an individual's realism in terms of his relative position along the distribution of the realism scores of other members of the same group. B. Implications 1. For research concerning levels of aspiration: ;;TheJ fi r s t '.logical step__in the incorporation of this technique used in level of aspiration studies would appear to be an empirical examination of the relationships between the phenomena measured here and the phenomena measured by other techniques. This could be accomplished by correlational analysis of the scores of a number of groups on this technique, and on usual level of aspiration techniques such as target shooting. Once this has been done i t would seem feasible to examine aspiration phenomena as manifested in '56. situations with more direct social meaning, in much the same way as they are examined in less meaningful situations. It is apparent that the similarity between the application of this technique and the application of level of aspiration techniques is a very limited one. There is no time sequence through which we measure the function of realism in social situations. It is, however, conceivable that in the evolution of a group of, say, school children, an experiment could be carried out making use of the various parts of the time sequence involved in most level of aspiration studies. That is, a sociometric test could be administered to a group at year one ( last performance ) and the results, or at least, some results could be communicated to the members of the group; on the basis of this knowledge regarding their position in the group,.the members could make an estimate of their performance in the specific social function under consideration at the next administration, say at year two (level of aspiration)}, a second administration of a sociometric technique could be effected at year two, (new performance), and the members of the group asked to make another estimate of their performance in this function at year three (reaction to new performance). This procedure would, then, be in effect a duplicate of the procedures generally used in level of aspiration studies. Any number of experimental studies could be designed, following the experiments on level of aspiration phenomena which are briefly reviewed in Section II: Historical Background. If the incorporation of this technique into the techniques used in aspiration: studies is possible, i t might be concluded that i t will be of value for future research in the same direction as that of aspiration studies generally. To quote from Lewin (47, pp376-377.) 5 7 . 1. One can try to understand more f u l l y the general laws of the level of aspiration. The analysis i s far enough along at present to encourage an attempt to determine quantitat-ively the values on the various scales of ref-erence. Such an attempt would give insight, for instance, into the factors which determine our probability judgement about our future, and would be of considerable value for the general theory of cognitive processes and perception. It would permit a quantitative approach to such divergent questions as a theory of choice and compromise; the effect of past experience and group belonging on certain aspects of cultural values, e.g., their distribution, interdependence and r i g i d i t y ; the factors determining the a b i l i t y to "take i t " ; and the problems of development ..and regression in regard to complying to rules. 2. It i s possible to use level of aspiration | techniques as an instrument to compare different cultures and to characterize their systems of values in a quantitative way. Similarly, these techniques may become progressively more useful for measuring individual differences of value systems and of other major characteristics of the normal and abnormal personality. 2. For sociometric application; It has been pointed out that there i s a considerable amount of information l e f t unconsidered both in the application of this technique and in the application of sociometric techniques generally. For example considering in Table 1, the row of data immediately below the row containing the numbers of the individuals comprising the group (Row X), What i s the specific meaning of the numerical values tabulated here? A consideration of how they were obtained w i l l perhaps make their meaning a l i t t l e clearer. The number of zero symbols, which represent expected choices, are summed for each column, and this total i s entered at the head of the column under each individual's number. That i s , they represent the number of individuals who expect that a particular 58, individual w i l l choose them: they are representative of relationships subsidiary to the primary relationships recorded as preference choices. Additional information about the interpersonal relationships involved i n the structure and functioning of a particular group i s avail-able i n far more complex " i n f i n i t e regresses" than those treated by Seeley (64); Rather than being able to make the comparatively simple statement that "A's popularity i s a function of the popularity of those who chose him; and their popularity is a function of those who choose them, and so ad infinitum," we are required to say that A*s popularity i s a function of those who chose him, and those he thought would choose him, and those who thought he would choose them; while the popularity of a l l of these individuals is similarly a function of a complex of choices and expected choices, and so ad infinitum. There is a spiral regression of choices and expected choices within the group, which starting with one individual extends through a l l of the members of the group and back again to the individual i n question to continue i n f i n i t e l y . The problem becomes considerably more d i f f i c u l t . However, we have obtained the information required to arrive at the popularity of each individual i n these terms (however adequately they represent this function), and therefore, the data which are pertinent to the description of the interpersonal position of that individual in a group. Whether this description can be more adequately presented numerically or diagrammatically remains to be demon-strated. This information would seem to be invaluable in "tracing internal structure of social groups and. delicate behavioral balances existing betxveen populations." (9, p.7). 59 One necessary step i n the experimentation process is the con-struction of a tool for examination of the phenomena being considered. -This thesis i s based on a conception of that step as i t i s related to studies i n levels of aspiration. However, the fact that this i s a necessary phase in experimentation does not imply the necessary value of an attempt to f u l f i l l i t : the foregoing has simply seemed, from a limited viewpoint, to be an informative means of making a tentative investigation in this area. 6 0 . VII REFERENCES 1. Allport, Gordon W., The ego i n contemporary psychology. Psychological Rev. (19U3) 50: 151-1+78. 2 . Allport, Gordon ¥., The psychology of participation. Psychological Rev. (191*5) 52: 117-132. 3 . Anderson, H.H., & Brandt, H.F., Study of motivation involving self-announced goals of f i f t h grade children and the concept of level of aspiration. J. soc. Psychol. (1939) 10: 209-232. 1*. Bavelas, Alex, A mathematical model for group structure. Apr>l:. Anthropol. (19U8) 7: 16-30. 5. Bayton, J.A., Performance as a function of expressed and non-expressed levels of aspiration. Amer. Psychol. (19U8) 3 : 271*. (Abstract) 6. Bronfenbrenner, Urie, The measurement of sociometric status, structure and development, Sociometry Monogr., No. 6: New York, Beacon House, 19U5. 7. Centres, R., & Ca n t r i l l , H,, Income satisfaction and income aspiration. J. abnorm. soc. Psychol, (191*6) 1*1: 6I1-69. 8. Chapman, D.W., & Volkman, J., A social determinant of the level of aspir-ation. J. abnorm. soc. Psychol. (1939) 3l: 225-238. 9. Criswell, Joan H., Foundations of sociometric measuremem. Sociometry, (19U6) 9: 7-13. 10. Demfio, Tamara, Der Arger als dynamisches Problem. (Untersuchungen zur Handlungs - und Affektpsychologie. X'Ed. by Kurt Lewin.) Psychol. Forsch., (1931 15: 1-lUU (cited i n 1*6)) 11. Deutschberger, Paul, The tele-factor, horizon and awareness. Sociometry. (19U7) 10: 21*2-21*9). 12. Escalona, Sibylle K., An application of the level of aspiration experiment to the study of personality. Teach. C o l l . Contr. Educ. (19U8) No. 937, 132 pp. 11*. Festinger, L., Wish, expectation and group standards as factors i n f l u -encing level of aspiration. J. abnorm. soc. Psychol. (19l*2) 37: 18U-200. 15. Festinger, L., A theoretical interpretation of shifts i n level of aspiration. Psychological Rev. (19l*2) 39:235-250. 61 . 16. Findley, W.C., A generalized procedure for constructing indexes of soc-i a l assimilation. Amer. Psychol. (19H8) 3: 267. (Abstract) 17. Finley, L.B., Age grade progression i n social attitudes and their pre-dictive value. Amer. Psychol. (19^6) 1: U50. (Abstract) 18. Forsyth, Elaine, & Katz, Leo., A matrix approach to the analysis of sociometric data. Sociometry. (I9k6) 9 : 31+0-3U7. 19. Frank, J.D., Individual differences i n certain aspects of the level of aspiration. Amer. J. Psychol. (1935) hi'. 119-128. 20. Frank, J.D., The influence of the level of performance i n one task on the level of aspiration i n another. J. exp. Psychol., (1935) 18: 159-171. 21. Frank, J.D., Some psychological determinants of the level of aspiration. . Amer. J. Psychol. (1935) U7: 285-293.. 22. Frank, J.D., A comparison between certain properties of the level of aspiration and random guessing. J. Psychol. (1936) 3: U3-62. . 23. Frank, J.D., Recent studies of the level of aspiration. Psychol. Bull. (19U1) 38: 218-225. 2U. Gardner, J.W., Level of aspiration i n response to a prearranged sequence of scores. J. exp. Psychol. (1939) 25: 601-621. 25. Gardner, J.W., The relation of certain personality variables to level of aspiration.' J, Psychol. (19U0) 9: 191-206. . 26. Gardner, J.W., The use of the term "level of aspiration". Psychol. Rev. (19H0) hi: 59-68. 27. ' Gildea, Margaret L.L., The social function and group therapy. Ment. Hyg. (1?U8) 32: 203-216. 28. Gould, R., Factors underlying expressed level of aspiration. J. Psychol. (1938) 6: 265-279. , 29. Gould,; R., An experimental analysis of level of aspiration. Genet. Psychol. Mooogr. (1939) 21: 1-116. 30. Gould, R., Some sociological determinants of goal strivings. J. soc. Psychol. (19U1) 13: k6l-h73. 31. Gould, R.,& Kaplan, N., The relationship of the level of'aspiration to academic and personality factors. J. soc. Psychol. (19U0) 11: 31-ii0. 62. 32. Gould, R., & Lewis, H.B., An experiemntal investigation of changes i n the meaning of the level of aspiration. J. exp.,Psychol. (19l*0) 27: 1*22-1*38. 33. Gross, Llewellyn, The construction and partial standardization of a scale for measuring self-insight. J. soc. Psychol. (191*8) 28: 219-236. 31*. Gruen, E.W., Level of aspiration i n relation to personality factors i n adolescents. Child Development. (191*5) 16: 181-188. 35. Hausmann, M.F., A test to evaluate some personality t r a i t s . J. gen. Psychol. (1933) 9: 179-189. 36. Heathers, L.B;, Factors producing generality i n the level of aspiration. J. exp. Psychol. (191*2) 27: 1*39-1*52. 37 . Hertzman, M.,-& Festinger, L., Shifts i n explicit goals i n a level of aspiration experiment. J. exp. Psychol. (191*0) 27: 1*39-1*52. 38. Hilgard, E.R., & Sait, E.M., Estimates of past and of future performances as measures of aspiration. Amer. J, Psychol. (19l*l) 51*: 102-108. 39. Hilgard, E.R., Sait, EMM., & Magaret, G.A., Level of aspiration as affected by relative standing i n an experimental social group. J. exp. Psychol. (191*0) 27: 1*11-1*21. I4O. Holt, R.R., Effects of ego-involvement upon levels of aspiration. Psychiatry, (191*5) 8: 299-317. 1*1. Holt, R.R., Level of aspiration: ambition or defense? J. exp. Psychol. (191*6) 36:. 398-1*16. 1*2. Irwin, F.W., & Mintzer, M.G.., Effect of differences i n instructions and motivation upon measures of the level of aspiration. Amer. J. Psychol. (191*2) 55: 1*00-1*06. 1*3. Johnson, D.M., How a person establishes a scale for evaluating his performance. J. exp. Psychol. (191*6) 36: 250-31*. 1*1*. Katz, Leo, On the matric analysis of sociometric data. Sociometry. (191*7) 10: 233-21*1. 1*5. Klugman, S.F., Emotional s t a b i l i t y and levels of aspiration. J. gen. Psychol. (191*8) 38: 101-118. . 1*6. Krech, D., & Kruchfield, R.S., Theory and problems of social psychol-ogy. New York, McGraw H i l l Book Co. Inc., 191*8. 1*7. Lewin, Kurt, Dembo, Tamara, Festinger, Leon, & Sears, Pauline S., Level of aspiration. Ch. 10, pp. 333-378. (In Hunt, J.McV., Personality and the behavior disorders, Volume I, N.Y., The Ronald Press Company, 191*1*.) 63." 1*8.' Lewin, Kurt, Frontiers i n group dynamics: concept, method and r e a l i t y i n social sciences; social equilibria and social change. Hum. Relat. (191*7) 1: 5-1*1. 1*9. Lippit, Ronald, Techniques for research i n group l i v i n g , J. soc. Issues. (191*6) 2: 55-61. 50. Lorimer, Frank, The differentiation of logical levels i n social inquiry. Amer. Sociol. Rev. (191*7) 12: 507-5H*. 51. Lurie, W.A., Estimating the level of vocational aspiration. J. soc. Psychol. (1939) 10: 1*67-1*73. 52. McGehee, W., Judgement and level of .aspiration. J. gen. Psychol. (191*0) 22: 3-15. 53. McLeod, R.B., New psychologies of yesterday andjboday. J. Can. Psychol. (191*9) 3 : 199-212. 51*. McNemar, Quinn, Psychological sta t i s t i c s , New York, John Wiley and Sons Inc., 191*9. . 55. Preston, M.G., Use of the coefficient of correlation i n the study of the D-score for the level of aspiration. (19l*2) Amer. J. Psychol. 55: 1*1*2-1*1*6. 56. Preston, M.G., On certain conditions controlling realism and irrealism of aspirations. J. exp. Psychol. (191*7) 37: 1*8-58. 57.. Preston, M.G., & Baratta, P., An experimental study of the auction-value of an uncertain outcome. Amer. J. Psychol. (19U8) 61: 183- " 193. 58. ' Preston, M.G., & Bayton, J.A., Differential effect of a social variable upon three levels of aspiration. J. exp. Psychol. (191*1) 29: 3 5 l -369. 59. ' Preston, M.G., & Bayton, J.A., Correlations between levels of appir-ation. J. Psychol. (19^*2) 13: 369-373. 60. " Rotter, J.B., Level of aspiration as a method os studying personality: I. A c r i t i c a l review of methodology. Psychological Rev. (19l*2) 1*9: 1*63-1*71*. 61. Rotter, J.B., Level of aspiration as a method of studying personality: II . Development and evaluation of a controlled method. J. exp. Psychol. (191*2) 31: 1*10-1*22. 62. Sears, P.S., Levels of aspiration i n academic-ally successful and un-successful shildren. J. abnorm soc. Psychol. (19l*0) 35: 1*98-536. 61* 63. Sears, P.S., Levels of aspiration i n relation to some variables of personality: c l i n c a l studies. J. soc. Psychol. (19U1) l U : 311-336. 61*. Seeley, John R., The net of reciprocal influence. A problem i n treat-sociometric data. Can. J. Psychol. (191*9) 3 : 23l*-2l*0. 65. Sletto, Raymond F., Next steps i n social measurement. Sociometry. (19U7) 10: 35U-361. 66. Smith, G.Milton,. A simplified guide to s t a t i s t i c s . New York, Rhinehart & Company, Inc., 19kl • 67. Snedecor, George W., S t a t i s t i c a l methods. Ames, Iowa, The Iowa State College Press, 191*6. 68. Steinzor, B., The development and evaluation of a measure of social interaction. Amer.. Psychol. (191*8} 3 : 266-267. (Abstract) 69. Sumner, F.C., & Johnson, E.E., Sex differences i n levels of aspir-ation and in self-estimates of performance i n a class-room situation. J. Psychol. (191*9) 27: 1*83-1*90. 70. Wolfenden, Hugh H., The fundamental principles of mathematical statis-i c s . Toronto, The Macmillan Co. of Canada Ltd., 191*2. Following item 12., insert: 13. Ezekiel, Mordecai, Methods of correlation analysis. New York, John Wiley and Sons, 19U7. 65 Appendix A: Index of Tables TABLE I Sample Tabulation Chart 19 TABLE II Results of Group 1 29 (a) Calculations 29 (b) R Scores and directions 31 (c) Histogram of distribution of R Scores 32 (d) Scattergram of R Scores and social status indices 32 TABLE III Results of Group 2 35 (a) Calculations 35 (b) R Scores and directions 36 (c) Histogram of distribution of R Scores 37 (d) Scattergram of R scores and social status indices 38 TABLE IV Results of Group 3 42 (a) Calculations 42 (b) R scores and directions 44 (c) Histogram of distribution of R scores 45 (d) Scattergram of R scores and social status indices 45 TABLE V Contingency Tables of Factors A, B,, & C, with Social Status: Group 3 48 TABLE VT Tables of Expansiveness & Recessiveness 50 (a) Contingency table of expansive recessive on Factors A and C 50 (b) Contingency table of expansive and recessive on Factor A, and high and low social status indices 50 (c) Contingency table of expansive and recessive on Factor C and high and low social status indices 50 66. TABLE 71 (Cont.) Tables of Expansiveness & Recessiveness (Cont.) (d) Contingency table of directions, expansive and recessive, on Factor A, and greater and lesser degrees of realism on Factor A. (e) Contingency table of directions, expansive and recessive, on Factor C, and greater and lesser degrees of realism on Factor C. TABLE 711 ^uartile Position of Incorrect Expected Choices in relation to the Q,uartile Position of the Subject making the Designation. 67. Appendix B; Derivation of the Formulae for W In a problem involving three variables, the separate determination of X-^  by X£ can be shown to be equal to (13, p. 500) /? 12.3 r 1 2 (1) This value i s a measure in decimal fraction terms (since/?.-^ 3 i s the partial regression coefficient of the variable X__ expressed i n terms of standard or Sigma scores) of the contribution of the measured function X 2 rbo the variance of the measured function X^. Similarly the separate determination of X__ by X__ i s equal to P 13.2 *13 _ . • (2) which i s a measure in decimal fraction terms of the contribution of the measured function X3 to the variance of the measured function X__. What remains,' the variance of X__ which i s determined by neither X 2 nor X3, can be expressed by the formula' 1 - (/313.2 r 1 3 + /tfl2.3 r 1 2 ) (3) By substitution of the appropriate subscripts denoting the three variables equations can be derived which express the separate determination of X 2 by X x (U), of X 2 by X3 (5), and of X 2 by X 2 (6)j /? 21.3 r 2 l (U) /?23.1 r 2 3 (5) 1 - (/3 21.3 r 2 1 +/?23.1 r 2 3 ) (6) and of X3'by X x (7), ^ by X 2 (8) , and of X 3 by X3 (9): /9. 31.2 r31 (7) ,3 32.1 r 3 2 " (8) ( ^ 3 1 . 2 r 3 1 +0 32.1 r 32) (9) 68 Appendix B; (Cont'd.) If we have a problem requiring the determination of the relative weights which should be given to each of three factors i n the expression of a score which i s a composite of the scores obtained on each of the three factors, i t may be solved i n the following way: When the formulae (3), (4), and (7) express the separate determination of factors 1, 2, and 3, respectively, by factor 1, then the formula for the separate determination of a composite of the three factors by factor 1 i s given by the formula (3) + (4) 4 (7) 3 (dividing by three to maintain the fractional expression). The value obtained by the application of this formula to a numerical example could be interpreted as the proportion of the composite measure which is deter-mined by the measure Factor 1, exclusive of the effects of factors 2 and 3. Or, in terms of the stated problem, the weight that should be given to the standard scores obtained on.factor 1, in the computation of standard scores which are composites of standard scores on factors 1, 2, and 3. Then i f % = (3) + (4) 4 (7) 3 similarly W2 = (1) 4 (6) » (8) 3 and w 3 = (2) 4 (5) + (9) .3. 69. Appendix Bt (Cont'd.) Substituting for the beta coefficients, the expression of these i n terms of coefficients of correlation: (Where ($k, p. 1U8) 12.3 = r12 - ,r131'23 l - p § 3 and ^(23) • T l 2 + Z ^ . 2 R ! 3 ) the formulae become: W1 » ( 1 - B | ( 2 3 ) ) + ^ 2 1 - J 2 3 Y 1 3 y * ^ r 3 1 - r 2 3 r 1 2 x ^ W2 - (1-R1(I 3) ) + f 1 2 - R 1 3 R 2 3 X , , \ + / R 3 2 - r 3 i ^ 2 1 x v. 23 / V 1 - r 2i •V 3 W3 = d - R 3 2 ( 1 2 ) ^ ( R 1 3 - R 1 2 ^ 3 2 \ + / ^ 2 3 - *2l*3L x \ V 1 - r§2 ' / I 1 - 4 / 


Citation Scheme:


Citations by CSL (citeproc-js)

Usage Statistics



Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            async >
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:


Related Items