(II. Teil) Individuum,Gesellschaft und Staat

Ohne ZusammenfassungI. Teil: Synthese, Vo.l VII (1948–49) S. 536–549     

О геометрической интерпретации логических выражений

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Теория нормативных предлозений

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О правилах исчисления предложе ий

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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.     

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.     

O regułach rachunku zdań

Streszczenie Zmienn istotn wyraenia rachunku zda nazywam zmienn, której warto przy pewnym ukadzie wartoci innych zmiennych wpywa na warto caego wyraenia.     

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.     

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.     

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.     

II. Das „Sein”

Ohne ZusammenfassungDieser Aufsatz ist die Fortsetzung des Aufsatzes Das Ding im Jahrgang 1938.     

Why do people factor?

This is a very simple explanation of factor analysis primarily for the factorial layman. The interpretation of factors and the comparisons of various factor solutions are illustrated with a hypothetical example so designed that the reader can visualize all the relationships in a two-dimensional graph.     

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.     

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.     

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.     

Het Belang van de Taalkundige Psychologie

Uit de Rede uitgesproken bij de aanvaarding van het ambt van buitengewoon hoogleeraar in de zedekunde en de wijsbegeerte van den Godsdienst aan de Universiteit van Amsterdam, op 28 September 1939.In druk verschenen bij H. J. Paris, Amsterdam.     

A note on correcting for chance success in objective tests

The conventional scoring formula to correct for guessing is derived and is compared with a regression method for scoring which has been recently proposed by Hamilton. It is shown that the usual formula,S=R–W/(n–1), yields a close approximation (correct within one point) to the maximum-likelihood estimate of an individual's true score on the test, if we assume that the individual knows or does not know the answer to each item, that guessing at unknown items is random, and that success at guessing is governed by the binomial law. It is also shown that the usual scoring formula yields an unbiased estimate of the individual's true score, when the true score is defined as the mean score over an indefinitely large number of independent attempts at the test or at equivalent (parallel) tests.