# Segment 33: Contingency Table Protocols and Exact Fisher Test - 4/19/2013

### Problem 1

**How many distinct m by n contingency tables are there that have exactly N total events?**

This is the same as trying to put N indistinguishable balls into K distinguishable bins. Thus, we have a combinatoric function to calculate this, which is C(N+K-1, K-1) to give us our total. So our answer is: C(N+mn - 1, mn-1)

### Problem 2

**For every distinct 2 by 2 contingency table containing exactly 14 elements, compute its chi-square statistic, and also its Wald statistic. Display your results as a scatter plot of one statistic versus the other.**

Here is my codehere

Currently I'm running into a problem of how to handle zeroes. The graph looks ok if I allow at least one person per bin, but I'm not sure how to go about handling zeroes.

[edit]To Think About 1. Suppose you want to find out of living under power lines causes cancer. Describe in detail how you would do this (1) as a case/control study, (2) as a longitudinal study, (3) as a snapshot study. Can you think of a way to do it as a study with all the marginals fixed (protocol 4)? 2. For an m by n contingency table, can you think of a systematic way to code "the loop over all possible contingency tables with the same marginals" in slide 8?