# Segment 16. Multiple Hypotheses

## Contents

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### Problems

#### To Calculate

1. Simulate the following: You have M=50 p-values, none actually causal, so that they are drawn from a uniform distribution. Not knowing this sad fact, you apply the Benjamini-Hochberg prescription with Failed to parse (unknown error): \alpha=0.05 and possibly call some discoveries as true. By repeated simulation, estimate the probability of thus getting N wrongly-called discoveries, for N=0, 1, 2, and 3.

2. Does the distribution that you found in problem 1 depend on M? On Failed to parse (unknown error): \alpha ? Derive its form analytically for the usual case of Failed to parse (unknown error): \alpha \ll 1 ?

$i=0}^{i=M$
Show that, under the null hypothesis, S is distributed as $Chisquare$ and describe how you would obtain a combined p-value for this statistic.