Derivations are given of the size and power of a test of a hypothesis for an incompletely specified fixed linear model. Such a testing procedure involves a test of a hypothesis of main interest subsequent to a preliminary test to determine the inclusion or not of a term in the tentatively specified complete fixed linear model. An evaluation of the formulas of the size and power was made over a wide range of values of the parameters involved, and recommendations concerning the choice of a proper significance level are given. One important objective of this study for the fixed model was to parallel as nearly as feasible the study given by Bozivich, H., Bancroft, T. A. and Hartley, H. O. (1956), Ann. Math. Statist. 27 1017-1043 for the random model, and to compare the two. It should be noted that the results and recomendations for the fixed model are quite different from those given in the 1956 paper for the random model.