An F-test for a subset of regression coefficients is often used in order to compare two nested linear models. An adaptive test is proposed that has higher power than this F-test for many non-normal distributions of error terms. The adaptive test uses a weighted least squares procedure with weights determined from the Studentized deleted residuals from a linear model. A permutation method is then used so that the resulting test maintains its size near the nominal value. Results from several simulation studies are used to compare the power of the adaptive test to the F-test. The adaptive test is recommended as a way of increasing the power of many common tests when used with models that have few parameters whenever the distribution of errors is non-normal and the number of observations exceeds 20.
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