Travis: Segment 33

From Computational Statistics (CSE383M and CS395T)
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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?