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A Brief Review of Multiple Testing Problems in Clinical Experiments
Published in Albert Vexler, Alan D. Hutson, Xiwei Chen, Statistical Testing Strategies in the Health Sciences, 2017
Albert Vexler, Alan D. Hutson, Xiwei Chen
If each of the m hypotheses is tested separately at a pre-specified significance level α, for example, α = 0.05, it can be shown that the proportion of incorrectly rejected hypotheses will not exceed a. This is known as the control of the comparison-wise error rate or per comparison error rate, where comparison-wise error rate refers to the probability of committing a Type I error on a single, pre-specified test. However, preserving the comparison-wise error rate for a single test is not the same concept as preserving the error rate for multiple tests under consideration.
Post Hoc Analysis and Adjustments for Multiple Comparisons
Published in Gueorguieva Ralitza, Statistical Methods in Psychiatry and Related Fields, 2017
Another important measure to consider is the per-comparison error rate (PCER) which is the expected proportion of all hypotheses that are falsely rejected null hypotheses, i.e., . If all comparisons in the set are performed at a 5% significance level (i.e., no correction for multiple tests is applied), then the PCER is controlled at 5%. Depending on how many of the hypotheses in the set are true null hypotheses, this leads to a potentially substantial increase in the FWER. If all hypotheses are true null hypotheses, the increase is large even with a moderate number of hypotheses in the test, which has motivated the development of classical multiple comparison procedures that control the FWER. But if only a few of the hypotheses are true null hypotheses, then the increase may not be as large and strict FWER control may be at the expense of missing important signals, which has motivated the development of procedures that control the false discovery rate (FDR).
How reliable are the multiple comparison methods for odds ratio?
Published in Journal of Applied Statistics, 2022
The measures to assess the hypotheses tested were divided in the classes of power measures and error measures. The former are the any-pair power (ANPP), all pairs power (APP), positive predictive value (PPV), true negative rate (TNR). The latter are per-comparison error rate (PCER), family-wise error rate (FWER), and false discovery rate (FDR).