Bonferroni Adjustments in Tests for Regression Coefficients

Abstract

A common application of multiple linear regression is to build a model that contains only those predictors that are significantly related to the response. In so doing, tests regarding the unique contribution of individual predictors to the model are often performed. It is not uncommon for practitioners to conduct each of these tests at the nominal α = 0.05 level, without regard to the effect that this practice may have on the overall Type I error rate. This research investigated the utility of making a Bonferroni adjustment when conducting these tests of the partial regression coefficients. Simulated multivariate normal populations with various correlational structures, different numbers of predictors in the model, and differing numbers of “significant” predictors in the model were generated. Ten thousand samples, 5000 each of sizes 50 and 300, were drawn from each population condition and a multiple regression analysis was performed on each sample. In every case, the observed significance levels for the Bonferroni-adjusted tests were controlled below the nominal 0.05 level as expected, and in most cases substantially lower than the observed significance levels for the unadjusted tests.