Suppressor Variables in Multiple Regression/Correlation

Since Horst (1941) first discussed and defined the suppressor variable in multiple regression/correlation, a number of more nearly precise definitions has been offered (Cohen and Cohen, 1975; Conger, 1974; Darlington, 1968; Velicer, 1978). This paper compares the different approaches to defining suppression, and illustrates the differences among them. Velicer's definition, which is based on the semi-partial correlation coefficient or usefulness and which is perhaps the least well known of the definitions, is shown to have several important practical advantages relative to the other definitions. The paper extends Velicer's usefulness definition to the general multiple predictor case and to analysis of variance (ANOVA) applications of multiple regression. A test for determining the significance of a suppressor effect is suggested, which is based on Velicer's definition of suppression.

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