The Conditional Level of the F—Test
Abstract Suppose that in regression problems the simultaneous confidence intervals of the S-method are used only when a preliminary F-test rejects the null hypothesis that the regression parameters are zero. (Some of Scheffe's work emphasizes this usage [12, p. 87; 13, p. 66].) The probability of coverage should then be conditioned on the rejection. That for sufficiently large critical values and at least two degrees of freedom for error the conditional probability of simultaneous coverage is always smaller than the unconditional probability is established in this article. Also included are Monte Carlo studies of the discrepancy and interpretation.