Presentation on theme: "Chapter 16: Association and Fisher’s Exact Test"— Presentation transcript:
1Chapter 16: Association and Fisher’s Exact Test Example: Pet ownership depends on gender? Is there an association between gender and pet ownership?Pet OwnerNot a Pet OwnerMale19Female113
2Chapter 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?
3Chapter 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.
4Chapter 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.
5Chapter 16: Association and Fisher’s Exact Test Thus we compute:Prob(1 male pet owner among 24 people if there are 12 pet owners) =There is chance that men and women own pets in about the same proportion.Therefore there is evidence that gender and pet ownership are not independent.
6Fisher’s Exact TestFisher’s Exact Test is a test for independence in a 2 X 2 table.Most useful for small sample sizeIs based on the hypergeomteric distribution.EPI809/Spring 2008
7Chapter 16: Association and Fisher’s Exact Test Do intramuscular magnesium injections help treatment of chronic fatigue syndrome?MagnesiumPlaceboFelt better123Did not feel better14The data come from an RCT comparing intramuscular magnesium injections withplacebo for the treatment of chronic fatigue syndrome.3 Of the 15 patientswho 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 TESTJenny V Freeman and Michael J Campbell (Scope /2007),
8Chapter 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 givenmagnesium injections are randomly selected outof the 32 (M = 15) and use hypergeometric distrProb (among the 15 magnesium takers, what is the chance that 12 felt better) =