﻿ Statistical Methods - Lecture 10 HcWjnyVHiTd8hN_8STvJ2rWaXvhPz4wXYCNGvD4qDkU

# Exact Probability TestLecture 9

## Fisher Exact Test

1. You have to use it if

1. Values in a cell are below 10

2. Or the grand total is below 100

3. Use the Fisher Exact Test

2. Note - Always arrange the columns and rows so Cell A has the smallest number

 Men Women Marginal Total Dieting a b a + b Not Dieting c d c + d Marginal Total a + c b + d a + b + c +d
1. Example

 Men Women Marginal Total Dieting 2 10 12 Not Dieting 3 5 8 Marginal Total 5 15 20
1. How many combinations can we make?

1. Men are the smallest in the study, so we have 5 combinations

2. Look at the marginal!

3. The Fisher test uses a Hypergeometric Distribution

4. Probability of a particular combination, i, is:

5. Note: 0! = 1

Combination 0

 Men Women Marginal Total Dieting 0 12 12 Not Dieting 5 3 8 Marginal Total 5 15 20

Probability of this combination occurring is

Combination 1

 Men Women Marginal Total Dieting 1 11 12 Not Dieting 4 4 8 Marginal Total 5 15 20

Probability of this combination occurring is

Combination 2

 Men Women Marginal Total Dieting 2 10 12 Not Dieting 3 5 8 Marginal Total 5 15 20

Probability of this combination occurring is

Combination 3

 Men Women Marginal Total Dieting 3 9 12 Not Dieting 2 6 8 Marginal Total 5 15 20

Probability of this combination occurring is

Combination 4

 Men Women Marginal Total Dieting 4 8 12 Not Dieting 1 7 8 Marginal Total 5 15 20

Probability of this combination occurring is

Combination 5

 Men Women Marginal Total Dieting 5 7 12 Not Dieting 0 8 8 Marginal Total 5 15 20

Probability of this combination occurring is

We manually map out the whole probability space for men on a diet

 P0 0.0036 Include in a P1 0.0542 Include in a P2 0.2384 P3 0.3973 P4 0.2554 P5 0.0511 Include in a Total 1 a = 0.1089

Is our particular combination significant? Are men different than women on a diet?

Our data is P2. If we choose an alpha of 5%, the best we can do in our case is to have an alpha of 11%. We take the probability that is in the tails. Alpha is the sum of P0, P1, and P5. Since our value is P2, we fail to reject and conclude men do not differ from women on a diet.