Statistics for People Who (Think They) Hate Statistics

by Neil J. Salkind

To determine exactly how much of the variance in one variable can be accounted for by the variance in another variable, the coefficient of determination is computed by squaring the correlation coefficient. For example, if the correlation between GPA and number of hours of study time is .70 (or r GPA.time = .70), then the coefficient of determination, represented by , is .702, or .49. This means that 49% of the variance in GPA “can be explained by” or “is shared by” the variance in studying time. And the stronger the correlation, the more variance can be explained (which only makes good sense). The more two variables share in common (such as good study habits, knowledge of what’s expected in class, and lack of fatigue), the more information about performance on one score can be explained by the other score. However, if 49% of the variance can be explained, this means that 51% cannot—so even for a very strong correlation of .70, many of the reasons why scores on these variables tend to be different from one another go unexplained. This amount of unexplained variance is called the coefficient of alienation (also called the coefficient of nondetermination).