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- W3094101422 abstract "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." @default.
- W3094101422 created "2020-10-29" @default.
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- W3094101422 date "2020-10-19" @default.
- W3094101422 modified "2023-10-16" @default.
- W3094101422 title "Distributions associated with simultaneous multiple hypothesis testing" @default.
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- W3094101422 doi "https://doi.org/10.1186/s40488-020-00109-6" @default.
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