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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.

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