Cautions in Interpreting Variance Explained (2 of 3)

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Rosenthal (1990) showed that although aspirin cut the risk of a heart attack approximately in half, it explained only 0.0011 of the variance (0.11%). Similarly, Abelson (1985) found that batting average accounted for a trivial proportion of the variance in baseball game outcomes. Therefore, measures of proportion of variance explained do not always communicate the importance of an effect accurately.

A third problem, closely related to the second, is that the importance of an effect cannot be determined apart from the context in which the importance is to be assessed: a variable that may not be a major determinant of another variable may still be important in certain contexts. For example, Martell, Lane, and Willis (1996) demonstrated how a sex bias that accounts for only 1% of the variance in promotions could cause large differences between the proportion of males and females that reach the higher levels of management in a company. A further problem with measures of variance explained is that they measure the size of an effect relative to the variability of subjects rather than by some absolute standard.