A re-analysis of a test of the theory of two factors

The study of William Brown and William Stephenson, A Test of the Theory of Two Factors, is re-analyzed by means of the Thurstone multiple factor methods. No tests or correlations are left out of the original table of correlations as is done in the original analysis in an attempt to validate the two-factor theory. Space, verbal, and perceptual speed factors similar to those found by Thurstone, Wright, and Garrett are identified. A common factor of Maturation is postulated to account for the remaining communality of the tests. A fifth factor is considered to have no significance due to the small amount of variance which it contributes to the total.Master's Thesis, University of Chicago, Department of Psychology, 1939.     

Points of neutrality in social attitudes of delinquents and non-delinquents

Delinquent boys are compared with non-delinquents with respect to their attitudes towards a series of good and bad social acts, by the use of scales having rational origins of measurement. A new technique, essentially an extension of Thurstone's Method of Successive Intervals, is found to give results similar to Horst's Method of Balanced Values. Significant differences in mean attitude between the two groups are not found.The author wishes to thank Dr. M. W. Richardson for his invaluable encouragement and counsel in this study. This paper is a part of a dissertation accepted by the faculty of the Department of Psychology, The University of Chicago, for the degree of Doctor of Philosophy.     

A technique for facilitating the rotation of factor axes,based on an equivalence between persons and tests

A technique is outlined which may facilitate the rotation of factor axes to a meaningful position. It is based on certain relationships between the results of test and person factor analysis, and consists essentially of supplementing the test factor space with tests which are thetest-equivalents of persons or groups of persons. These persons may be, for instance, well-known types in the domain being investigated, or even freaks. The ways in which these persons may be selected and used to determine the final rotated position of the factor axes is discussed.     

A factor analysis of intra-task performance on two psychomotor tests

There are indications that even during the short time of administration of a single psychomotor test, the ability or abilities sampled may shift materially in importance. It then becomes important to know the stages in which these fluctuations occur, the stage at which the test is most complex, and the stage at which the test most nearly measures one ability at a time. This paper describes an application of factorial methods to this problem. Factor analysis of inter-trial correlations on two models of the Rudder Control Test revealed three factors, Steadiness-Control, Precision of Movement, and Strength. The same factor pattern was confirmed in a separate factor analysis on another sample in which the order of administration of the tests was reversed. Implications are pointed out for future psychomotor test development.Perceptual and Motor Skills Research Laboratory, Lackland Air Force Base, San Antonio, Texas. The opinions or conclusions contained in this report are those of the author. They are not to be construed as reflecting the views or indorsement of the Department of the Air Force.     

An I.B.M. technique for the computation of ΣX 2 and ΣXY

Given I.B.M. cards punched with scores (or any numbers)—but not their squares—a method is presented of tabulating them (on the No. 405 alphameric I.B.M. tabulator) so as to obtain the sum of squares. The technique is also adaptable to summation of cross-products. The principle is an extension of the Mendenhall-Warren-Hollerith technique of vertical progressive digiting, without the necessity of manual addition or summary-punching, and is designed for machines not equipped with the card cycle total transfer device or progressive total device. Use is made of counter rolling. Efficient use of machine capacity is made only when intercorrelations between no more than two variables are requiredin addition to sums of squares. A resumé of some techniques now commonly employed is included.The author is indebted to Dr. Paul Dwyer, Associate Professor of Mathematics, University of Michigan, for valuable criticism of the original draft; and to Mr. Alan Meacham, in charge of the University's Tabulating Station, for testing the method.     

General solution of the analysis of variance and covariance in the case of unequal or disproportionate numbers of observations in the subclasses

In this paper a preview of the problem is given. Then the mathematical solutions of estimating the sums of squares and products of different sources of variation under different assumptions are presented. Two kinds of populations from which our samples are supposed to be drawn are specified. One is defined as possessing approximately the same stratification as our sample; while the other is defined as having equal frequencies in the subclasses. For the first kind of population, we should use the restrictions of the weighted means. For the second kind, we should use the restrictions of the unweighted means. The assumptions of zero interactions and significant interactions are also considered. After working out the exact method, two approximate methods with appropriate statistical assumptions to be fulfilled are given.For a more complete account, see:Fei Tsao, General solution of the analysis of variance and covariance in the case of unequal or disproportionate numbers of observations in the subclasses. Ph.D. Thesis, University of Minnesota, 1945. Pp. 120.     

An analytical solution for approximating simple structure in factor analysis

It is proposed that a satisfactory criterion for an approximation to simple structure is the minimization of the sums of cross-products (across factors) ofsquares of factor loadings. This criterion is completely analytical and yields a unique solution; it requires no plotting, nor any decisions as to the clustering of variables into subgroups. The equations involved appear to be capable only of iterative solution; for more than three or four factors the computations become extremely laborious but may be feasible for high-speed electronic equipment. Either orthogonal or oblique solutions may be achieved. For illustrations, the Johnson-Reynolds study of flow and selection factors and the Thurstone box problem are reanalyzed. The presence of factorially complex tests produces a type of hyperplanar fit which the investigator may desire to adjust by graphical rotations; the smaller the number of such tests, the closer the criterion comes to approximating simple structure.     

Synthesis of variance

The distribution of a linear combination of two statistics distributed as is Chi-square is studied. The degree of approximation involved in assuming a Chi-square distribution is illustrated for several representative cases. It is concluded that the approximation is sufficiently accurate to use in many practical applications. Illustrations are given of its use in extending the Chi-square, the Student t and the Fisher z tests to a wider range of problems.     

A technique for criterion-keying and selecting test items

For multiple-choice tests where noa priori key exists, the initial selection of a key for maximum validity may be made on the basis of the number of persons choosing each alternative and their mean criterion score. The keying formula is derived. Once the initial keying has been done, further precision in keying and item selection may use, in addition, the mean total test score for persons choosing each alternative. Item-selection formulas suggested by Horst and by Gulliksen for maximizing test validity are both in the form of a ratio, an item-validity index divided by an item-reliability index. The formula derived here is shown to be equivalent to the numerators of these formulas. The expression in the denominators uses the total test score. Although a radical appears in the denominator of Horst's formula and not in the denominator of Gulliksen's formula, both of them select the same items in practice.The author gratefully acknowledges the suggestions and criticisms of Dr. Harold Gulliksen, Research Adviser at the Educational Testing Service.     

Contribution to the mathematical theory of human relations: VI. Periodic fluctuations in the behavior of social groups

A case of interaction between two groups of active and one group of passive individuals, in which the efforts of the influencing active groups decrease with increasing total success in the past, is studied. In that case the numbers of passive individuals, exhibiting respectively the two opposite behaviors, fluctuate periodically, with a positive damping.     

On the mutual influence of individuals in a social group

A previous mathematical study of a situation, in which the behavior of a larger group of individuals is controlled by a smaller group, is generalized for the case when the activity of the individuals in the group is continuously graded. The existence of two possible social configurations and of sudden transitions from one configuration to another are found in this case also.     

Der Faktor der Umstrukturierung und 2 Tests zu seiner Messung

Zusammenfassung Mit der hohen Korrelation zwischen einem visuellen und einem verbalen Test wurde die Existenz eines Faktors in der Wahrnehmung bzw. im Denken nachgewiesen, den man Verfügbarkeit von motorischen Schematen oder kurz B-Faktor nennen könnte.     

TheL-method

It is shown that theL-method is basic to test-building and to all combining of scores where the several sub-parts of a composite are weighted according to their respective standard deviations, i.e., with equal gross score weights or by adding the several sub-scores. With chiefly a listing adding machine, a few celluloid strips, and a master matrix table ofL's, one may, in a fraction of the time and with equally good or even better practical results, easily duplicate, with test-building material most of the feats obtainable by multiple regression equations.     

The reliability coefficient

The reliability coefficient is unlike other measures of correlation in that it is a quantitative statement of an act of judgment,—usually the test maker's, — that the things correlated are similar measures. Attempts to divorce it from this act of judgment are misdirected, just as would be an attempt to eliminate judgment of sameness of function of items when a test is originally drawn up. A coefficient of cohesion, entirely devoid of judgment, measuring the singleness of test function is proposed as an essential datum with reference to a test, but not as a substitute for the similar-form reliability co-efficient.     

Estimation of parameters in a truncated trivariate normal distribution

This paper gives maximum-likelihood estimators for certain parameters in a truncated trivariate normal distribution when the values of the other parameters are known. The estimators are functions of a random sample. Approximate variances and covariances of the estimators, when the sample size is large, are also given. The type of truncation considered is merely restriction of the range of one of the variates, whose true mean and variance are assumed to be known. Two cases of such restriction are treated: (a) ( x < + ); (b) (- <x '), where and ' are arbitrary cutoff points which are assumed to be known. A precise statement of the estimation problem is given in Section 1. Section 2 contains preliminary calculations. The estimators appear in Section 3. The asymptotic variances and covariances of the estimators are given in Section 4. The estimators and their asymptotic variances and covariances can be easily specialized to be suitable for the case of a certain truncated bivariate normal distribution (Sections 3 and 4).     

Contributions to the mathematical theory of human relations III

In continuation of a previous study, somewhat more complex relations are considered for the case of interaction of two classes, of which one organizes the activities of the other. By way of illustration it is shown how different assumptions concerning the attitudes of the individuals to such an interaction of classes lead to different mathematical expressions.     

Influence of chance error on simple structure: An empirical investigation of the effect of chance error and estimated communalities on simple structure in factorial analysis

Correlation coefficients derived from an hypothetical simple structure for twenty tests and four factors were loaded with chance error components. Centroid analyses and rotations to give least square determinations of the hypothetical simple structure were made for several conditions. It is concluded that the experimental situation of inaccurate coefficients and estimated communalities permits accurate determination of primary trait loadings provided that the rank of the centroid matrix is equal to or greater than that of the underlying primary trait matrix. Of several criteria for the completeness of factorization which were tested, none was wholly satisfactory.     

The act of surrender in the treatment of the alcoholic

The success of A. A. in the alleviation of alcoholism has provided psychiatrists with a rich source of clinical material for a study of the religious process. The paper which follows is a discussion of one aspect of that process, namely, the act of surrender. It was prepared for a psychiatric audience; it may have some pertinence for the pastoral group since it represents at least an effort at understanding the religious life. Fully aware of its deficiencies, I offer the paper in the hope that it may seem to contain a measure of truth and be of some value to pastors in their relationships with their parishioners.This article is reprinted from Quarterly Journal of Studies on Alcohol, June, 1949 where it appeared under the title The Act of Surrender in the Therapeutic Process, by permission of author and publisher.s     

Prototetyka St. Lesniewskiego

Streszczenie Prototetyka St. Len'ewskiego jest uogólnieniem dwuwartociowego rachunku zda. Wystpuj w niej obok terminów tego rachunku funktory (zarówno stae jak i zmienne) tych wszystkich kategorii semantycznych, jakie mog by zdefiniowane, gdy punktem wyjcia jest kategor a zda.W pracy zreferowane s trzy systemy prototetyki. Terminem pierwotnym dwu z nich jest implikacja, terminem pierwotnym systemu trzeciego jest równowano. Systemy o terminie pierwotnym implikacji róni s. reguami wnioskowania. W jednym z nich obowizuje regua weryfikacji, w drugim regua ekstensjonalnoci. Pierwsza z tych regu jest uogólnieniem nastpujcej reguy rachunku zda, wzbogaconego o terminy 0 i 1:Wyraenie jest tez systemu, gdy tezami systemu s oba wyraenia powstae z przez podstawienie za pewn jego zmienn symboli 0 i 1.W myl reguy ekstensjonalnoci tezami systemu s prawa ekstensjonalnoci, sformuowane dla funktorów dowolnych kategorii semantycznych wac-wych prototetyce.W pracy podaj dowody równowanoci trzech systemów prototetyki i dowód ich zupenoci.Znaczna cz wyników Leniewskiego, zreferowanych w pracy, nie bya dotd opublikowana. Opracowujc te wyniki opieraem si na notatkach z wykadów Leniewskiego, spisanych przez jego uczniów. Oryginalne notatki Leniewskiego ulegy zniszczeniu w czasie powstania warszawskiego.