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.     

A factor analysis of mechanical ability tests

The intercorrelations of thirty-seven variables, including the Minnesota battery of mechanical ability tests, the seven MacQuarrie tests of mechanical ability, O'Connor's Wiggly blocks, and the Stenquist picture-matching test, were analyzed by Thurstone's centroid method. Five factors, Perceptual, Verbal, Youth, Manual Agility, and Spatial, were taken out. Factors prominent in so-called mechanical ability tests are the Spatial and Perceptual ones with Mac-Quarrie's dotting test significantly high in the Manual Agility factor. Each of the factors can be measured with group pencil-and-paper tests.Acknowledgment is gratefully made to the State Engineering Experiment Station at the Georgia School of Technology for sponsoring and financially supporting the studies; to the Graduate Research Committee of the University of Illinois for providing funds for the purchase of tests and the tabulation of data; and to Dr. E. L. Welker of the University of Illinois Mathematics Department for assistance with statistical problems.     

О правилах исчисления предложе ий

, .     

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).     

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.     

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 simplified method for approximating multiple regression coefficients

A method of exhaustion has been described for calculating regression coefficients. This method dispenses with the solution of simultaneous equations but utilizes a process of successive extraction in obtaining's, where each successive is maximized. This procedure permits the worker to discard as he goes along those weights which are deemed unsatisfactory for purposes of prediction. The coefficients and theR in a problem involving a criterion and six independent variables were calculated in sixty minutes. TheR's obtained by this method are smaller than those yielded by the Doolittle technique, but in problems which have been considered this discrepancy has not exceeded .05.     

In de Schaduwen van Gisteren

Ohne ZusammenfassungNoot van de Red.:Prof. Huizinga, wien wij het hier volgende artikel van Prof. Mannoury ter inzage zonden, deelt ons mede, dat hij van de aangeboden gelegenheid, op dit hem in meer dan één opzicht sympathieke artikel te repliceeren, geen gebruik zal maken.     

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.     

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.     

Over de Zedelijke Beoordeeling van Oorlog

Fragment uit het hoofdstukOorlog en Vrede van het boek Neen en Ja, in Mei verschijnend bij H. J. Paris, Amsterdam.     

“Parallel proportional profiles” and other principles for determining the choice of factors by rotation

The choosing of a set of factors likely to correspond to the real psychological unitary traits in a situation usually reduces to finding a satisfactory rotation in a Thurstone centroid analysis. Seven principles, three of which are new, are described whereby rotation may be determined and/or judged. It is argued that the most fundamental is the principle of parallel proportional profiles or simultaneous simple structure. A mathematical proof of the uniqueness of determination by this means is attempted and equations are suggested for discovering the unique position.     

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.     

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.     

Note on the relationship between internal consistency and test-retest estimates of the reliability of a test

A comparison of the test-retest and internal consistency estimates of reliability coefficients is given, and it is shown that the two methods give different results. Application of the analysis of variance and covariance method reveals that there is not just one but a number of reliability coefficients involved, and that an estimate of each of these may be obtained. The analysis shows that in using the test-retest method the error or remainder effects are not independent on the two trials, possibly because the individuals remember the items and their responses to them on the previous trial.     

Alternative views on correlations between persons

The article discusses the general principles involved in factorizing correlations between persons, and compares the special techniques put forward by Burt and Stephenson respectively. The chief points of agreement and disagreement are summarized. In statistical procedure the two writers prove to be largely in accord; but they differ over the psychological and the methodological implications, the chief source of divergence being the so-called reciprocity principle.     

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.     

Studies in measurement of the relations among sovereign states

This article describes the application of three psychometric methods to the problem of measurement of the friendly or hostile relations among states of the world today. To secure judgments, schedules were sent to students of international affairs at several times during the last five years. The method of equal-appearing intervals was used to determine the relative probability of war for 88 pairs of states in January, 1937; the method of triadic combinations to determine relative friendliness among the Great Powers in November, 1938; and the method of multidimensional or group rank order to measure the attitudes of important states toward the Great Powers in March and April, 1939; June, 1940; and June, 1941. A chart of scale values for the pairs of Great Powers shows the changing trends since 1937. The last two methods were used to depict the Great Powers in multidimensional space according to their mutual friendliness, thus permitting the application of a type of factor analysis. The reliability of the methods employed was high, and various types of evidence support the general validity of the results.The writer is indebted to Professors Quincy Wright, and L. L. Thurstone and Dr. M. W. Richardson, for advice at various stages in these studies.     

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.     

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.