Understanding Statistics in the Behavioral Sciences by Bakeman Roger. Robinson Byron F. & Byron F. Robinson

Author:Bakeman, Roger.,Robinson, Byron F. & Byron F. Robinson [Roger Bakeman]
Language: eng
Format: epub
ISBN: 9781135613105
Publisher: Taylor & Francis (CAM)

Occasionally, the optimally weighted sum of two predictors will produce a higher R2 than the sum of the r2s for the two predictors separately. This pattern occurs when the relation between two predictor variables hides or suppresses their real relation with the criterion variable, as can happen when the correlation between two predictor variables is negative but both correlate positively with the criterion. In the presence of such a suppressor effect the overlap between the two predictor variables is negative, which makes drawing a figure like Fig. 11.3 untenable. For further discussion of suppression see Cohen and Cohen (1983).

Even in the (relatively rare) presence of suppression, determining the unique contribution of a particular variable—the additional proportion of variance accounted for when that variable is added to the equation—is straightforward. The variable is added to the regression equation and a new R2 is computed. Its contribution is the difference between the new R2 and the R2 for the previous equation, the one that did not include the new variable. If we call the new equation the larger model and the previous equation the smaller model, then the change in R2 due to the new variable added is

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