Fisher’s test

By Data Tricks, 28 July 2020

What is Fisher’s test?

Fisher’s test is a good alternative to a chi-square test of independence when the expected value in any one of the cells in a contingency table is less than 5.

One of the main differences between a chi-square test of independence and a Fisher’s test is that the p-value in a chi-square test is an approximation which tends towards the exact value as the sample size goes towards infinity. In a Fisher’s test, the p-value is exact and not an approximation, which is why it is sometimes called Fisher’s exact test.

Example in R

Let’s create some nominal data:

set.seed(150)
data <- data.frame(sampleA = sample(c("Positive","Positive","Negative"), 30, replace = TRUE),
sampleB = sample(c("Positive","Positive","Negative"), 30, replace = TRUE))
frequencies <- table(data$sampleA, data$sampleB)

Look at the contingency table, we have one cell less than 5:

         Negative Positive
Negative        3        9
Positive        9        9

Perform the Fisher’s test using the fisher.test function:

test <- fisher.test(x = data$sampleA, y = data$sampleB)

Analyse the result:

> test

       Fisher's Exact Test for Count Data

data: data$sampleA and data$sampleB
p-value = 0.2599
alternative hypothesis: true odds ratio is not equal to 1
95 percent confidence interval:
 0.04497001 2.03461029
sample estimates:
odds ratio
 0.3458827

p-value

The p-value is 0.26, which is above the 5% significance level and therefore the null hypothesis cannot be rejected.

Is Fisher’s the right test?

Use our interactive tool to help you choose the right statistical test or read our article on how to choose the right statistical test.

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