Über die Messung der psychischen Ermüdung mit Hilfe des Flimmertests

Ohne ZusammenfassungErklärung der Abkürzungen Add.-Lstg. Additionsleistung - AZ Arbeitszeit - B/sec Anzahl der Blitze je Sekundes - KP Kurzpause - Lstg. Leistung - M Mittelwert (arithm. Mittel) - TZ Teilzeit - Vfr. Verschmelzungsfrequenz = Flimmergrenze - VL Versuchsleiter - Vp. Versuchsperson - Vpn. Versuchspersonen - Mittlere Abweichung vom Mittelwert - M Mittlerer Fehler des Mittelwertes     

Efficiency of multiple-choice tests as a function of spread of item difficulties

The validity of a univocal multiple-choice test is determined for varying distributions of item difficulty and varying degrees of item precision. Validity is a function of _d ² + _v ² , where _d measures item unreliability and _v measures the spread of item difficulties. When this variance is very small, validity is high for one optimum cutting score, but the test gives relatively little valid information for other cutting scores. As this variance increases, eta increases up to a certain point, and then begins to decrease. Screening validity at the optimum cutting score declines as this variance increases, but the test becomes much more flexible, maintaining the same validity for a wide range of cutting scores. For items of the type ordinarily used in psychological tests, the test with uniform item difficulty gives greater over-all validity, and superior validity for most cutting scores, compared to a test with a range of item difficulties. When a multiple-choice test is intended to reject the poorestF per cent of the men tested, items should on the average be located at or above the threshold for men whose true ability is at theFth percentile.This research was performed under contract Nop 536 with the Bureau of Naval Personnel, and received additional support from the Bureau of Research and Service, College of Education, University of Illinois.     

О геометрической интерпретации логических выражений

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Теория нормативных предлозений

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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.     

О правилах исчисления предложе ий

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Remarks on the method of paired comparisons: III. A test of significance for paired comparisons when equal standard deviations and equal correlations are assumed

A test of goodness of fit is developed for Thurstone's method of paired comparisons, Case V. The test involves the computation of , wheren is the number of observations per pair, and and are the angles obtained by applying the inverse sine transformation to the fitted and the observed proportions respectively. The number of degrees of freedom is (k–1) (k–2)/2.This research was performed in the Laboratory of Social Relations under a grant made available to Harvard University by the RAND Corporation under the Department of the Air Force, Project RAND.     

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.     

The determination of the factor loadings of a given test from the known factor loadings of other tests

A technique is indicated by which approximations to the factor loadings of a new test may be obtained if factor loadings of a given group of tests and the correlations of the new test with the other tests are known. The technique is applicable to any orthogonal system and is especially adapted to cases in which a _ji a _jk = 0 wheni k. Application is also made to the simultaneous determination of the factor weights of a group of tests in which no additional common factor is present. The technique is useful in adding tests to a completed factorial solution and in using factorial solutions involving errors to give results which are approximately correct.     

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.     

An efficient punched-card method of computing epsilonX,epsilonX2, epsilonXY,and higher moments

A method of computing X, X ², XY and higher moments on IBM equipment is described. The basic method is that of successively summary punching, collating a variable number of blank cards behind these summary cards, gang-punching the data from the summary cards into the blank cards, and totalling the entries on these summary cards. The method appears to have several advantages over those previously described, especially if coded data are used.     

The selective efficiency of a test battery

In industrial acceptance sampling one frequently makes use of operating characteristic curves to describe the discriminating power of a particular sampling plan. Similarly, it is possible to demonstrate the selective efficiency of a test battery in terms of (a) the Applicant's Operating Characteristic (A.O.C.); (b) the Selector's Operating Characteristic (S.O.C.). The A.O.C. determines the chance of selection by means of a test for any given level of true ability. The S.O.C. connects functionally probability of success on the criterion with the predictor scores of a battery. For the case of a normal bivariate distribution the exact mathematical expressions of the OC curves are derived in terms of the correlation coefficient, the cut-off points and, and the predictor and criterion scoresX andY (in standard measures). The Efficiency IndexH is defined as the percentage of successful subjects gained by the use of a test battery, taking chance selection as a yardstick for comparison. Its optimum, for fixed and , is derived. The distribution law of the criterion scores of selectees is deduced and its first four moments are shown to depart little from normality for cases usually encountered in practice. A Quality-Gain diagram graphically illustrates the improvements secured. Another simple device, the Cost-Utility diagram, explains to management the full implications of selecting personnel by means of a test battery. Neither of the diagrams requires an understanding of the correlation coefficient. The confidence belt of the OC curves, the standard error of the mean criterion score of selectees and the standard error of the predicted number of successful applicants are determined. Finally, the full theory is applied in detail to a real test battery.This paper is the result of an investigation undertaken by the South African National Institute for Personnel Research, Johannesburg, and was completed at the Educational Testing Service, Princeton. The author wishes to thank these organizations for permission to publish this paper.     

An experimental study of the effects on item-analysis data of changing item placement and test time limit

Item-analysis data are usually obtained from a single test administration, with a given item sequence and time limit. Questions can be raised as to the effects upon item data resulting from changes in item-position and test-timing. In this study, two forms of a verbal test and two forms of a mathematics test were used. In each case, both forms of each test contained the same items, but items coming early in one form were placed late in the other. Each of these forms was administered once with a short time limit and once with generous timing to comparable groups of high school students. The relationships of various speed and power scores were determined, and the changes which occurred during the added time were studied. Values of the item indicesp (proportion right), (another difficulty index), and the item-test biserial correlation coefficient were obtained for both the speed and the power conditions and were systematically compared. The proportion right of those attempting the item, the index, and the biserialr were all found to have undesirable characteristics for items appearing late in a speeded test.The author gratefully acknowledges the suggestions and criticisms of Dr. Harold Gulliksen, Research Adviser at the Educational Testing Service.     

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).     

Image theory for the structure of quantitative variates

A universe of infinitely many quantitative variables is considered, from which a sample ofn variables is arbitrarily selected. Only linear least-squares regressions are considered, based on an infinitely large population of individuals or respondents. In the sample of variables, the predicted value of a variablex from the remainingn – 1 variables is called the partial image ofx, and the error of prediction is called the partial anti-image ofx. The predicted value ofx from the entire universe, or the limit of its partial images asn , is called the total image ofx, and the corresponding error is called the total anti-image. Images and anti-images can be used to explain why any two variablesx _j andx _k are correlated with each other, or to reveal the structure of the intercorrelations of the sample and of the universe. It is demonstrated that image theory is related to common-factor theory but has greater generality than common-factor theory, being able to deal with structures other than those describable in a Spearman-Thurstone factor space. A universal computing procedure is suggested, based upon the inverse of the correlation matrix.This paper introduces one of three new structural theories, each of which generalizes common-factor analysis in a different direction.Nodular theory extends common-factor analysis to qualitative data and to data with curvilinear regressions (6).Order-factor theory introduces the notions oforder among the observed variables and ofseparable factors (7). The presentimage theory is relevant also to the other two.Attention may be called to empirical results published since this paper was written: Louis Guttman, Two new approaches to factor analysis, Annual Technical Report on contract Nonr—731(00). The present research was aided by an uncommitted grant-in-aid from the Ford Foundation.     

General theory and methods for matric factoring

Methods are developed for factoring an arbitrary rectangular matrixS of rankr into the formFP, whereF hasr columns andP hasr rows. For the statistical problem of factor analysis,S may be the score matrix of a population of individuals on a battery of tests. ThenF is a matrix of factor loadings,P is a matrix of factor scores, andr is the number of factor variates. (As in current procedures, there remains a subsequent problem of rotation of axes and interpretation of factors, which is not discussed here.) Methods are also developed for factoring an arbitrary Gramian matrixG of rankr into the formFF, whereF hasr columns andF denotesF transposed. For the statistical problem of factor analysis,G may be the matrix of intercorrelations,R, of a battery of tests, with unity, communalities, or other parameters in the principal diagonal.R is proportional toSS, and it is shown thatS can be factored by factoringR. This may usually be the most economical procedure in practice; it should not be overlooked, however, thatS can be factored directly. The general methods build up anF (andP) in as many stages as desired; as many factors as may be deemed computationally practical can be extracted at a time. Perhaps it will usually be found convenient to extract not more than three factors at a time. Current procedures, like the centroid and principal axes, are special cases of a general method presented here for extracting one factor at a time.     

Time-limit tests: estimating their reliability and degree of speeding

Non-spurious methods are needed for estimating the coefficient of equivalence for speeded tests from single-trial data. Spuriousness in a split-half estimate depends on three conditions; the split-half method may be used if any of these is demonstrated to be absent. A lower-bounds formula,r _c, is developed. An empirical trial of this coefficient and other bounds proposed by Gulliksen demonstrates that, for moderately speeded tests, the coefficient of equivalence can be determined approximately from single-trial data. It is proposed that the degree to which tests are speeded be investigated explicitly, and an index is advanced to define this concept.     

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.     

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.