The Overall t-test Investigating a Conflict between the Individual t-test and the Overall F-test in Regression Analysis

Abstract

Researchers may confront conflicting conclusions on the effects of predictors by the individual t-test and the overall F-test in regression analysis. For example, the overall effect may be significant by the overall F-test whereas none of the individual effects are significant by the individual t-test. This paper shows that the conflict may result from different views on the recovered effects of predictors. It proposes an overall t-test assessing the overall effect, and recommends one to use the overall t-test to investigate the conflict between the individual t-test and the overall F-test. The overall F-test assesses the overall effect under the assumption that the true effects of predictors are exactly captured by the recovered effects of predictors. In contrast, the overall t-test assesses the overall effect under the assumption that the true effects are captured by the means and variance-covariances of the recovered effects. This paper ends with practical guidelines for interpreting the effects of predictors when there exists a conflict between the individual t-test and the overall F-test.