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## Maximum likelihood estimation and factor analysis

### Psychometrika (1941-02-01) 6: 49-53 , February 01, 1941

Fisher's method of maximum likelihood is applied to the problem of estimation in factor analysis, as initiated by Lawley, and found to lead to a generalization of the Eckart matrix approximation problem. The solution of this in a special case is applied to show how test fallability enters into factor determination, it being noted that the method of communalities underestimates the number of factors.

## A note on multidimensional psychophysical analysis

### Psychometrika (1941-10-01) 6: 331-333 , October 01, 1941

On viewing Thurstone's psychophysical scale from the point of view of the mathematical theory of one-parameter continuous groups, it is seen that a variety of different psychological or statistical assumptions can all be made to lead to a scale possessing similar properties, though requiring different computational techniques for their determination. The natural extension to multi-dimensional scaling is indicated.

## The analysis of variance and covariance techniques in relation to the conventional formulas for the standard error of a difference

### Psychometrika (1941-08-01) 6: 221-233 , August 01, 1941

In this paper it is demonstrated that the analysis of variance techniques yield results equivalent to the calculation of*t* by means of expressions based on the short or the long formula. It is also shown that the covariance technique gives results equivalent to those obtained by means of the formula for*t* which should be used with matched groups. The conditions necessary for equivalent results are such that the conventional formulas for*t* would normally be used rather than the variance or covariance techniques. However, a knowledge of the relationships described in this paper should contribute to one's understanding of the variance and covariance techniques.

## Item synonymization: A method for determining the total meaning of pencil-paper reactions

### Psychometrika (1941-04-01) 6: 131-139 , April 01, 1941

Items have been studied heretofore for their value as elements of particular tests to the neglect of more fundamental research into the multiple potentiality of items. This article proposes a method of grouping items into “synonymies” comprising all of the items which correlate with a given key item. These synonymies can be used for interpretation of the total meaning of the key item: (1) by inspection of the constituent items and (2) by correlational study of obtained single scores of individual persons. The method is illustrated by four items with inter- and intra-correlations, and characteristics of an ideal background reservoir of items are pointed out.

## A simple scoring weight for test items and its reliability

### Psychometrika (1941-12-01) 6: 367-374 , December 01, 1941

It is pointed out that the scoring weights for test items should be approximations to regression-equation weights. For this reason any estimate of reliability of the weight should not be permitted to influence the size of the weight but should be used in determining the limit of acceptability of an item. A simple approximation weight is recommended for general use, and an*abac* is provided for the estimation of it when the correlation between item and criterion is the phi coefficient. A formula for the standard error of this weight is derived and tables of significant and very significant weights are presented in terms of deviations from the median weight.

## A note on the discovery of ag factor by means of Thurstone's centroid method of analysis

### Psychometrika (1941-06-01) 6: 205-208 , June 01, 1941

A fictitious factor matrix including 16 tests and 3 factors, one of which was a*g* factor, was prescribed. From it two typical factor problems, including errors of sampling, were derived. Students in training, without awareness of the factor patterns, arrived at essentially correct solutions by the use of Thurstone's centroid method with rotation of axes. Errors in the calculated factor matrix were very close in size to the sampling errors in the correlation coefficients. It is concluded that a*g* factor need not escape detection by Thurstone's procedures if the criteria of complete simple structure are not demanded.

## Zur Einführung

### Gedanken über die Seele (1941-01-01): 1-48 , January 01, 1941

### Zusammenfassung

Kann es eine Psychologie als Wissenschaft geben? Lassen sich über das Seelische Behauptungen aufstellen, die nicht nur für ihren Urheber gelten, oder anders ausgedrückt: läßt sich auch auf diesem Gebiete etwas beweisen?

## Music ability

### Psychometrika (1941-02-01) 6: 61-65 , February 01, 1941

Two batteries of music tests were factored by the centroid method. From each battery three oblique factors were extracted and in each case were tentatively identified as tonal sensitivity, retentivity (memory for elements), and memory for form. The correlations of the music tests of one battery with subtests of Cattell's intelligence test and with tests of a literary nature are also reported.

## Körper und Geist

### Gedanken über die Seele (1941-01-01): 222-277 , January 01, 1941

### Zusammenfassung

Wir haben festgestellt, daß, soweit unsere Erfahrung reicht, seelisches Leben nur in Verbindung mit körperlichen Geschehnissen beobachtet wird. Die philosophischen Fragen, vor die uns diese Erfahrung stellt, wollen wir hier nicht mehr erörtern; dem Vorwurf, das Seelenleben materialistisch erklären oder, wie Schopenhauer es ausdrückt, das unmittelbar Gegebene (das Psychische) aus dem mittelbar Gegebenen (der Materie) ableiten zu wollen, glauben wir im ersten und im dritten Abschnitt dieses Buches hinreichend entgegengetreten zu sein. W i e Körper und Seele zusammenhängen, wissen wir nicht; wohl aber müssen wir einsehen, daß es diesen Zusammenhang gibt.

## TheL-method

### Psychometrika (1941-08-01) 6: 249-266 , August 01, 1941

It is shown that the*L*-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 of*L*'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.