False negative control for multiple acceptance-support hypotheses testing problem
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Hypothesis tests can be categorized as rejection-support tests or acceptance-support tests. Type I error in a rejection-support test has the same effect as type II error in an acceptance-support test. Most hypothesis testing is based on type I error control, but it increases type II error. Similar to how researchers control type I error when performing multiple rejection tests, researchers might want to control type II error in multiple acceptance-support testing. In this thesis, I discuss various methods to control decision errors in multiple testing. As an example, I conduct multiple normality tests with four different normality formulae under four different alternative hypotheses. I discuss estimation of the ratio between the null hypothesis and non-discovery rate, and also balance the trade-off between false discovery rate and non-discovery rate to find more cost-effective critical points. I apply this discussion to real data about breast cancer.