P-value and conclusion 2 points possible {graded} Continue with the likelihood ratio test for the HIP experiment. 1. What is the p-value of the likelihood ratio test based on the observed data? {Please enter the value with a precision of 3 decimal points} 2. Do we reject the null hypothesis with significance level 0.05? O Reject 0 Do not reject 3. How does Holm-Bonferroni achieve this? First, we run through an example of the Holm-Bonferroni correction. Consider four null hypotheses H1, . . ., H4, with unadjusted p-values p1 = 0.01, p2 = 0.04, ps = 0.03, p4 = 0.005, to be tested at significance level or = 0.05. What is the result of Holm-Bonferroni? O Reject H1, H2 O Reject H3, HA O Reject H1, HA O Reject H16. Bonferroni correction and Holm-Bonferroni correction Bookmark this page Exercises due Sep 8, 2021 06:59 CDT We can control the size of FWER by choosing significance levels of the individual tests to vary with the size of the series of tests. In practice, this translates to correcting p-values before comparing with a fixed significance level e.g. o = 0.05. Update (Feb 21): The following notes have been newly added. Bonferroni Correction In a series of m tests, if the significance level of each test is set to o/m, or equivalently if the null hypothesis ; of each test i is rejected when the corresponding p-value is bounded by: then FWER 1) = P(Vien {V; = 1}) [P( Ti =1) = = m - La. where V is number of tests reported to be significant among all tests with true null hypotheses. I'; is test i, so that I; = 1 corresponds to H; rejected To = {i = 1... m|H; true} is the set of all indices i such that test i has a true null hypothesis Ho mo is the size of To HideHoIm-Bonferroni Correction The Holm-Bonferroni method makes adaptive adjustments to the rejection criterion of each test. The procedure is as follows. Suppose we are testing for m. hypotheses. - Sort the m p-values in increasing orderpm g pm 5 . . . 5 pm