# Travis: Segment 33

#### To Calculate

**1. How many distinct m by n contingency tables are there that have exactly N total events?**
I'm not sure how to simplify this expression, but I worked out the total to be

<math> \sum_{a_1 = 0}^N \sum_{a_2 = 0}^{N-a_1} \dots \sum_{a_{mn-1}}^{N-a_1 - \dots - a_{mn-2}} { N \choose a_1 } { N - a_1 \choose a_2 } \dots { N-a_1-a_2 - \dots - a_{mn-2} \choose a_{mn-1}} </math>

**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. **

#### 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?**