# Calculate odds ratio and fisher's exact text

1. Aug 6, 2010

### hoffmann

basic statistics question:

i have two variables, M1 and M2. i want to calculate how similar these two variables are using the odds ratio. M1 and M2 are lists of things, with some elements present in both lists. i also have a background list containing the things in M1 and M2, plus more. is this how i calculate the odds ratio? (in a 2x2 table from left to right and top to bottom):

1) a = # of common elements in M1 and background / # elements in background
2) b = 1 - a
3) c = # of common elements in M2 and background / # elements in background
4) d = 1 - c

odds ratio = a*d / b*c, where a is the upper left element of the 2x2 matrix and d is the bottom right.

does this look correct? how would i go about creating a 2x2 table for the fisher exact test? just use the number of common elements without doing the division by the background in the cells?

2. Aug 6, 2010

### SW VandeCarr

That's the correct calculation the odds ratio (OR) for a 2x2 table. The 2x2 table (constrained by the marginal totals) has a hypergeometric distribution. The exact calculation is only necessary if the data are sparse (a zero in any cell for certain).

$$P=\frac{(a+b)!(c+d)!(a+d)!(b+d)!}{a!b!c!d!n!}$$

This is the probability of the data under the null hypothesis. There are calculators for this on line, but you'll have to find them yourself.

EDIT: For the variance of the odds ratio, use the delta method (Woolf) Var ln(OR)=(1/a+1/b+1/c+1/d).

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1270683/

Last edited: Aug 6, 2010
3. Aug 7, 2010

### SW VandeCarr

Last edited: Aug 8, 2010