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Consider a one-way analysis of covariance model. Suppose that the parameterof interest theta is a specified linear contrast of the expected responses, fora given value of the covariate. Also suppose that the inference of interest isa 1-alpha confidence interval for theta. The following two-stage procedure hasbeen proposed to determine the form of the model. In Stage 1, we carry out an Ftest of the null hypothesis that the slopes are all zero against thealternative hypothesis that they are not all zero. If this null hypothesis isaccepted then we assume that the slopes are all zero; otherwise we proceed toStage 2. In Stage 2, we carry out an F test of the null hypothesis that theslopes are all equal against the alternative hypothesis that they are not allequal. If this null hypothesis is accepted then we assume that the slopes areall equal; otherwise this assumption is not made. We present a generalmethodology for the examination of the effect of this two-stage model selectionprocedure on the coverage probability of a subsequently-constructed confidenceinterval for theta, with nominal coverage 1-alpha. This methodology is appliedto a numerical example for which it is shown that this confidence interval iscompletely inadequate.

The coverage probability of confidence intervals in one-way analysis of covariance after two F tests