Rejoinder to Harville (2022) and Christensen (2022) Comments on “On the Power of the F-test for Hypotheses in a Linear Model,” by Griffiths and Hill (2022)

The authors would like to thank Professors Christensen and Harville for their comments. These two authors take differ-ent approaches to generalizing and improving the proof of the theorem in Griffiths and Hill (2022). Professor Christensen’s geometric approach, and Professor Harville’s meticulous matrix algebra approach, are suitable for graduate courses in linear models for statisticians in various fields. We believe that there is pedagogic value in discussing the tradeoff between the non-CONTACT centrality parameter and the numerator degrees of freedom in the F -test, and how this affects the power of the F -test. However, just to be clear, we are not advocating adding true hypotheses as a strategy. Professor Christensen’s first sentence may be taken by some to imply that. The main points in our article are also easily demonstrated via simulation, as shown in the supplemen-tary materials, making the ideas accessible to undergraduate students.