Chapter 16: Association and Fisher’s Exact Test Example: Pet ownership depends on gender? Is there an association between gender and pet ownership? Pet Owner Not a Pet Owner Male 1 9 Female 11 3

Chapter 16: Association and Fisher’s Exact Test P = the person owns M = the person is male Prob(Own Pet given person is Male) = 0.1 Prob(Own Pet given person is Female) = 0.79 This suggests that there is association (dependence) between gender and pet Ownership. Can we generalize this fact for all cases?

Chapter 16: Association and Fisher’s Exact Test Is pet ownership evenly distributed among men and women? Another way to look at this: How likely is it that one gets the above table among all possible tables with the same condition? Hypergeometric distribution helps answers this question.

Chapter 16: Association and Fisher’s Exact Test Note that there are many possibilities for similar situations. To use the hypergeometric distribution, think of the problem as follows: N = 24 people, divided into 2 groups: Men = 10; Women= 14 Note: If pet ownership is evenly distributed among men and women, then we can think of the 12 pet owners to be selected randomly from the group of 24 people. M = 12.

Chapter 16: Association and Fisher’s Exact Test Thus we compute: Prob(1 male pet owner among 24 people if there are 12 pet owners) = 0.0013 There is 0.0013 chance that men and women own pets in about the same proportion. Therefore there is evidence that gender and pet ownership are not independent.

Fisher’s Exact Test Fisher’s Exact Test is a test for independence in a 2 X 2 table. Most useful for small sample size Is based on the hypergeomteric distribution. EPI809/Spring 2008

Chapter 16: Association and Fisher’s Exact Test Do intramuscular magnesium injections help treatment of chronic fatigue syndrome? Magnesium Placebo Felt better 12 3 Did not feel better 14 The data come from an RCT comparing intramuscular magnesium injections with placebo for the treatment of chronic fatigue syndrome.3 Of the 15 patients who had the intra-muscular magnesium injections 12 felt better (80 per cent) whereas, of the 17 on placebo, only three felt better (18 per cent). THE ANALYSIS OF CATEGORICAL DATA: FISHER’S EXACT TEST Jenny V Freeman and Michael J Campbell (Scope /2007), http://www.shef.ac.uk/polopoly_fs/1.43998!/file/tutorial-9-fishers.pdf

Chapter 16: Association and Fisher’s Exact Test Think of the 32 people divided into two groups, those who felt better (n = 15) and those who did not (N-n = 17). Now assume that the 15 who were given magnesium injections are randomly selected out of the 32 (M = 15) and use hypergeometric distr Prob (among the 15 magnesium takers, what is the chance that 12 felt better) = 0.000547