# Segment 16. Multiple Hypotheses

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The direct YouTube link is http://youtu.be/w6AjduOEN2k

Links to the slides: PDF file or PowerPoint file

### 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**
?

#### To Think About

1. Suppose you have M independent trials of an experiment, each of which yields an independent p-value. Fisher proposed combining them by forming the statistic

**Failed to parse (unknown error): S = -2\sum_{i=0}^{i=M}\log(p_i)**

Show that, under the null hypothesis, S is distributed as **Failed to parse (unknown error): \text{Chisquare}(2M)**
and describe how you would obtain a combined p-value for this statistic.

2. Fisher is sometimes credited, on the basis of problem 1, with having invented "meta-analysis", whereby results from multiple investigations can be combined to get an overall more significant result. Can you see any pitfalls in this?

### Class Activity

- Team 1 - Feb 21 Activity
- [Team Girls + Sanmit - Feb 21 Activity]
- Team3-021714part2
- Feb20-Team4-P-value follow up

Here is John's written up solution: Pvalue Examples Solutions.