In the analysis of a two‐period crossover study Grizzle (1965) suggests that, if a preliminary test for a period by treatment interaction (residual effect, carryover effect) is significant at the 10 % level, the direct effects of the treatments should be compared by performing a t ‐test on the data from the first period only. In this note it is shown that under Grizzle's model the comparison of the direct treatment effects is equivalent to a Behrens‐Fisher problem. Depending on one's viewpoint–Bayesian, fiducial, or sampling theory–different solutions are possible. The solutions are illustrated using three well‐known data sets.
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Andrew P. Grieve (1987) studied this question.