I've tried to implement the Fishers exact test on a 2x2 table as described in the Wikipedia entry but not sure of my numbers because it gives a different answer than R according to another question on this board.
Wondering if somebody can check. By way of example, I consider a hypotehtical 2x2 as follows:
Are you in favor or opposed to the death penalty?
Favor 30 30
Opposed 70 70
According to my calculations, the exact probability of this arrangement is given by row1! * row2! * col1! * col2! / cell1! & cell2! * cell3! * cell4! * (sum of cells)!
My method gives a result of 12.253%. But the question I want to answer is not this exact probability but whether political view "matter" to the peope's opinion about the death penalty. There example above indicates there clearly is not, so I guess this 12% probability represents only the likelihood of getting an exactly equal result from a random selection of s sets of 100 people
According to Wikipedia, it seems like I'm meant to figure this out by picking an arbitrary "more extreme" result and calculating its fishers exact and adding the two together.
So I tried the following which maintains row and column totals:
Favor 31 29
Opposed 69 71
hich gives a total of 11.69%
Adding the two I get 23.95% which I gather is the one tailed result, multiplying by 2 gives me 47.89% which is pretty close to what I expected, that in this case the results suggest that there is a 50% chance that observed results are same as those I would have gotten from random selection of people, both liberal and conservative.
My question is: a) do the numbers seem correctly calculated, and b) is my interpretation correct?