# Fisher’s Exact Test

When to use it

Use Fisher’s exact test when you’d like to do a Chi-squared test  on 2 variables but your sample size is too small.

i.e. you have 2 or more variables and you’re testing for independence between them. You have a contingency table of frequencies and some of the expected values are less than 5 (ideally you want expected frequencies no less then 10)

e.g. suppose we want to test for an association between whether you live in Oslo or Mumbai and your eye colour. We look at 100 people in Mumbai and 50 in Oslo. The first instinct would be to use a Chi-Squared test for independence.

 Observed Blue Eyes Brown Eyes Total Mumbai 2 23 25 Oslo 10 5 15 Total 12 28 40

However, there is a low expected frequency, particularly for Blue eyes in Oslo

 Expected Blue Eyes Brown Eyes Total Mumbai 7.5 17.5 25 Oslo 4.5 9.5 15 Total 12 28 40

Fisher’s exact test is an alternative. If done by hand, you can only sensibly do it for 2×2 or 2×3 tables. Some computers can cope with larger tables. However, unless you have the exact test module SPSS will only do it for 2×2 tables.

Assumptions

You have 2 variables, both of which are categorical.

Observations are independent of each other.

Observations are frequencies not proportions

What to do if you don’t meet the assumptions

If your observations are related  ans you have 2 categories in your IV consider McNemar’s test

If your observations are related and you have more than 2 categories in your IV consider Cochran’s Q test

If your expected values are large consider the Chi-Squared test of independence

If your observations are proportions, use the sample size to convert them to frequencies.

SPSS will only do this for 2×2 tables unless you have the exact test module. You don’t explicitly perform Fisher’s exact test. Go to

Analyze->Crosstabs and ask for Chi-Squared in the statistics dialogue box. If it’s available and appropriate, SPSS will automatically do Fisher’s exact test instead.