A device for facilitating the computation of the first four moments about the mean

A mechanical device is described which materially reduces the time, labor, and probability of errors which are involved in the computation of certain moments about the mean. The use of the device is illustrated with the computation of the mean, standard deviation,g ₁ as a measure of skewness, andg ₂ as a measure of kurtosis of data from a given study.Grateful acknowledgment is made to the Holter Research Foundation of Helena, Montana for the grant-in-aid which made possible the development of this device.     

Linear dependence in multiple correlation work

The problem in multiple correlation work of nonsense results attributable to linear dependence of variables, which has been discussed by Ragnar Frisch in relation to economic data, is presented from the standpoint of its significance in psychological research. It is shown that a symmetric correlation determinant with unity in the diagonal cells can vanish only when there is a first-order or partial correlation of unity between one pair of the variables. On the basis of this result, it is argued that the problem should be expected to cause less difficulty in the field of psychology than in economics and that psychologists should be able to avoid the pitfall by bringing to bear their knowledge of the variables with which they are working.     

The relation between results obtainable with raw and corrected correlation coefficients in multiple factor analysis

This paper presents three theorems concerning the relation between results with obtained and corrected correlation coefficients in the Thurstone method of multiple factor analysis. (1) The rank of the correlational matrix, and thus the number of factors involved, is unaffected by correcting the obtained coefficients for attenuation. (2) The communality of a variable when the obtained coefficients have been corrected for attenuation is equal to the communality with obtained coefficients divided by the reliability coefficient of the variable. (3) The relationship is shown between the factorial matrix of a correlational matrix of raw correlation coefficients and the factorial matrix of a correlational matrix of corrected correlation coefficients, and a method of obtaining either of these factorial matrices from the other is indicated.     

Sampling theory in item analysis

Since item values obtained by item analysis procedures are not always stable from one situation to another, it follows that selection of items for validity or difficulty is sometimes useless. An application of Chi Square to testing homogeneity of item values is made, in the case of theUL method, and illustrative data are presented. A method of applying sampling theory to Horst's maximizing function is outlined, as illustrative of author's observation that the results of item analysis by any of various methods may be similarly tested.