Analyzing College Effects: Correlation vs. Regression

A commonly used procedure in studying college effects involves an input-output model in which student input is controlled by using regression analysis to compute an expected output (e.g., Astin, 1963, 1964; Thistlethwaite & Wheeler, 1966). The correlation of a school environment variable with the residual output (i.e. actual minus expected output) is interpreted as a measure of the school's influence on the output. Although sometimes labeled a partial correlation, it is more accurately described as the part correlation (McNemar, 1962, p. 167) of the school with the output variable when the influence of the input variable has been removed from the output. A potentially serious interpretational problem is that part correlations may severely underestimate the magnitude of the true college effect. This possibility was noted previously by Richards (1966):