Distributions associated with simultaneous multiple hypothesis testing
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 n...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2020-10-01
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| Series: | Journal of Statistical Distributions and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s40488-020-00109-6 |
| Summary: | 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 Ψ I (·) to model the marginal distribution of p-values sampled from a mixture of null uniform and non-uniform distributions under different alternative hypotheses. The Ψ I distribution is useful when there are many different alternative hypotheses and these are not individually well understood. We fit Ψ I 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. |
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| ISSN: | 2195-5832 |