Liu, Wei (1997) Control of directional errors with step-up multiple tests. Statistics & Probability Letters, 31 (3), 239-242. (doi:10.1016/S0167-7152(96)00036-3).
Abstract
It is shown in Shaffer (1980) that step-down multiple tests designed to control Type I errors at rate α actually control Type I and III errors jointly at rate α under certain distributional assumptions. In this note it is shown that step-up multiple tests have a similar property under the same distributional assumptions.
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