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## Time scores and factor analysis

### Psychometrika (1940-03-01) 5: 67-74 , March 01, 1940

The assumption of specific operation times leads to equations similar to those which are the basis for a factor analysis but in which the time scores replace item scores. An analysis of time scores is shown to lead to results equivalent, in a first approximation, to those obtained from an analysis of item scores. It is suggested that by modifying the factor technique it may be possible to use additional information to check with the results from an analysis.

## Note on the computation of tetrachoric correlation

### Psychometrika (1940-06-01) 5: 137-140 , June 01, 1940

## Comment on Wilson and Worcester's “note on factor analysis”

### Psychometrika (1940-06-01) 5: 117-120 , June 01, 1940

## Contributions to the mathematical theory of human relations III

### Psychometrika (1940-09-01) 5: 203-210 , September 01, 1940

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.

## A matrix multiplier

### Psychometrika (1940-12-01) 5: 289-294 , December 01, 1940

A machine to expedite matrix multiplication has been developed by modifying the International Business Machines Corporation scoring machine. The principles and operation of the machine are described, and time and accuracy estimates are indicated.

## Experimental study of simple structure

### Psychometrika (1940-06-01) 5: 153-168 , June 01, 1940

A battery of thirty-six tests was given to a group of high-school seniors. The factorial analysis reveals essentially the same primary factors that were found in previous studies. The test battery reveals a simple structure.

## A synthetic approach to factor analysis

### Psychometrika (1940-12-01) 5: 235-250 , December 01, 1940

## Contributions to the mathematical theory of human relations. IV

### Psychometrika (1940-12-01) 5: 299-303 , December 01, 1940

An attempt is made to define and treat analytically the concept of individual freedom in a society. Two possible definitions are briefly discussed. One takes as a measure of freedom the ratio (*w*_{0} −*w*)*w*_{0}, where*w*_{0} is the maximum amount of work that a person can physically perform per unit time and*w* is the amount of work which he has actually to perform per unit time in a given society. The other definition takes as a measure of freedom that fraction of an individual's time during which he can indulge in any activity of his own choice without interfering with other individuals. Expressions are derived by way of illustration, giving the individual freedom in terms of other parameters which characterize the social structure.

## A factor analysis of mechanical ability tests

### Psychometrika (1940-03-01) 5: 17-33 , March 01, 1940

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.

## Multiple rectilinear prediction and the resolution into components

### Psychometrika (1940-06-01) 5: 75-99 , June 01, 1940

It is assumed that a battery of*n* tests has been resolved into components in a common factor space of*r* dimensions and a unique factor space of at most*n* dimensions, where*r* is much less than*n*. Simplified formulas for ordinary multiple and partial correlation of tests are derived directly in terms of the components. The best (in the sense of least squares) linear regression equations for predicting factor scores from test scores are derived also in terms of the components. Spearman's “single factor” prediction formulas emerge as special cases. The last part of the paper shows how the communality is an upper bound for multiple correlation. A necessary and sufficient condition is established for the square of the multiple correlation coefficient of test*j* on the remaining*n*—1 tests to approach the communality of test*j* as a limit as*n* increases indefinitely while*r* remains constant. Limits are established for partial correlation and regression coefficients and for the prediction of factor scores.