Control of false track rate using multiple hypothesis confirmation

2004 ◽  
Author(s):  
S.P. Noyes
Keyword(s):  
Multiple Hypothesis

scholarly journals Distributions associated with simultaneous multiple hypothesis testing

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Chang Yu ◽  
Daniel Zelterman
Keyword(s):  
Latent Variable ◽  
Power Analysis ◽  
Marginal Distribution ◽  
Multiple Hypothesis Testing ◽  
Family Wise Error Rate ◽  
Uniform Distributions ◽  
Multiple Hypothesis ◽  
The Family ◽  
Alternative Hypotheses ◽  
Cancer Studies

Abstract We develop the distribution for the number of hypotheses found to be statistically significant using the rule from Simes (Biometrika 73: 751–754, 1986) for controlling the family-wise error rate (FWER). We find the distribution of the number of statistically significant p-values under the null hypothesis and show this follows a normal distribution under the alternative. We propose a parametric distribution ΨI(·) to model the marginal distribution of p-values sampled from a mixture of null uniform and non-uniform distributions under different alternative hypotheses. The ΨI distribution is useful when there are many different alternative hypotheses and these are not individually well understood. We fit ΨI to data from three cancer studies and use it to illustrate the distribution of the number of notable hypotheses observed in these examples. We model dependence in sampled p-values using a latent variable. These methods can be combined to illustrate a power analysis in planning a larger study on the basis of a smaller pilot experiment.

scholarly journals The Romano–Wolf multiple-hypothesis correction in Stata

2020 ◽  
Vol 20 (4) ◽  
pp. 812-843
Author(s):  
Damian Clarke ◽  
Joseph P. Romano ◽  
Michael Wolf
Keyword(s):  
Error Rate ◽  
Multiple Testing ◽  
Original Data ◽  
Dependence Structure ◽  
Familywise Error Rate ◽  
Testing Procedures ◽  
Multiple Testing Procedures ◽  
Multiple Hypothesis ◽  
Wide Range ◽  
Performance Gains

When considering multiple-hypothesis tests simultaneously, standard statistical techniques will lead to overrejection of null hypotheses unless the multiplicity of the testing framework is explicitly considered. In this article, we discuss the Romano–Wolf multiple-hypothesis correction and document its implementation in Stata. The Romano–Wolf correction (asymptotically) controls the familywise error rate, that is, the probability of rejecting at least one true null hypothesis among a family of hypotheses under test. This correction is considerably more powerful than earlier multiple-testing procedures, such as the Bonferroni and Holm corrections, given that it takes into account the dependence structure of the test statistics by resampling from the original data. We describe a command, rwolf, that implements this correction and provide several examples based on a wide range of models. We document and discuss the performance gains from using rwolf over other multiple-testing procedures that control the familywise error rate.

scholarly journals Multiple hypothesis evaluation in auditing

2002 ◽  
Vol 42 (3) ◽  
pp. 251-277 ◽  
Author(s):  
Rajendra P. Srivastava ◽  
Arnold Wright ◽  
Theodore J. Mock
Keyword(s):  
Multiple Hypothesis ◽  
Hypothesis Evaluation
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