On the Power of the F-test for Hypotheses in a Linear Model

William E. Griffiths and Carter Hill

The American Statistician, 2022, vol. 76, issue 1, 78-84

Abstract: We improve students’ understanding of the F-test for linear hypotheses in a linear model by explaining elements that affect the power of the test. Including true restrictions in a joint null hypothesis affects test power in a way that is not generally known. Asking a student whether including the true restrictions in the null hypothesis will increase or decrease power, the student is likely to say: “I don’t know.” The student’s answer is not bad because the power depends on the noncentrality parameter and the degrees of freedom. We show that adding true restrictions to a linear hypothesis cannot decrease the noncentrality parameter of the F-statistic, a result many will find counterintuitive. Adding true restrictions can increase or decrease F-test power depending on the offsetting negative effect of reducing the numerator degrees of freedom. We provide illustrative examples of these results and prove them for the general case.

Date: 2022
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DOI: 10.1080/00031305.2021.1979652

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