# Difference between revisions of "Segment 16. Multiple Hypotheses"

John Hawkins (talk | contribs) (Added a solution write-up to the p-value examples.) |
Bill Press (talk | contribs) |
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The direct YouTube link is [http://youtu.be/w6AjduOEN2k http://youtu.be/w6AjduOEN2k] | The direct YouTube link is [http://youtu.be/w6AjduOEN2k http://youtu.be/w6AjduOEN2k] | ||

− | Links to the slides: [http:// | + | Links to the slides: [http://wpressutexas.net/coursefiles/16.MultipleHypotheses.pdf PDF file] or [http://wpressutexas.net/coursefiles/16.MultipleHypotheses.ppt PowerPoint file] |

===Problems=== | ===Problems=== | ||

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===Class Activity=== | ===Class Activity=== | ||

− | [http:// | + | [http://wpressutexas.net/coursefiles/p_value_follow_ups.pdf P-value follow-ups] |

*[[Team 1 - Feb 21 Activity]] | *[[Team 1 - Feb 21 Activity]] | ||

− | *[[http:// | + | *[[http://wpressutexas.net/coursewiki/index.php/Segment_16...Multiple_Hypotheses Team Girls + Sanmit - Feb 21 Activity]] |

*[[Team3-021714part2]] | *[[Team3-021714part2]] | ||

*[[Feb20-Team4-P-value follow up]] | *[[Feb20-Team4-P-value follow up]] | ||

− | Here is John's written up solution: [http:// | + | Here is John's written up solution: [http://wpressutexas.net/coursewiki/images/f/fd/Pvalue_examples.pdf Pvalue Examples Solutions]. |

## Latest revision as of 14:32, 22 April 2016

#### Watch this segment

(Don't worry, what you see statically below is not the beginning of the segment. Press the play button to start at the beginning.)

{{#widget:Iframe |url=http://www.youtube.com/v/w6AjduOEN2k&hd=1 |width=800 |height=625 |border=0 }}

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 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 ? Derive its form analytically for the usual case of ?

#### 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

Show that, under the null hypothesis, S is distributed as 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.