The use of extreme groups to test for the presence of a relationship

Experimenters in psychology frequently investigate the relationship between two variables by selecting extreme groups on the first measure and comparing their mean scores on the second. This paper considers the efficacy of this procedure from the criterion of the power of the statistical tests. Optimal cutting points for the extreme groups are defined, and the power of the difference approach is compared to that of significance tests for the productmoment correlation coefficient.     

Geometrical representation of two methods of linear least squares multiple correlation

Geometrical properties and relationships of the Doolittle and square root methods of multiple correlation, as represented in the variable subspace of an orthogonal person space, are shown. The method of representation is also useful for depicting zero-order and partial correlations, as well as for the more general problem of the combination of variables.     

Some multiple correlation and predictor selection methods

The Doolittle, Wherry-Doolittle, and Summerfield-Lubin methods of multiple correlation are compared theoretically as well as by an application in which a set of predictors is selected. Wherry's method and the Summerfield-Lubin method are shown to be equivalent; the relationship of these methods to the Doolittle method is indicated. The Summerfield-Lubin method, because of its compactness and ease of computation, and because of the meaningfulness of the interim computational values, is recommended as a convenient least squares method of multiple correlation and predictor selection.     

Shorter articles and notes two more visual theorems

The basis of the widely held opinion that the spectral sensitivities of the mechanisms determining trichromacy must be linearly related to the spectral mixture functions is examined, and a proof from simple assumptions is stated.

It is proved also that, on the van der Velden hypothesis of independent sensitive units, a spatial or temporal summation law of the form AIⁿ = c implies a frequency-of-seeing curve of the form Q = I—e^-KIn (Q = probability of detecting a stimulus of size A and intensity I; n, c and K are constants).     

Aversive control of self-injurious behavior in a psychotic boy

Two studies are reported which indicate how quickly and effectively chronic self-injurious behavior was controlled in a 9-yr-old blind psychotic boy. In the first study, the self-injurious responses were punished by contingent withdrawal of human physical contact. In the second study, response-contingent electric shock was employed.