Non-parametric Analysis of Relationship

Understanding the Fisher’s Exact test

The Fisher Exact test is a significance test that is employed in a 2 by two contingency/ crosstabulation tables instead of the chi square test, especially when there are very small sample size that Ch-square tests cannot be accurate with. In Fisher's Exact Test, researchers are investigating the association or link between two dichotomous categorical variables, comparable to the chi-square test. The main distinction is that Fisher's Exact Test is only employed when one of the cells in a 2 by 2 contingency table has less than five observations.

Fisher's Exact Test is frequently employed in research with small sample sizes (n= 20) and when a study has encountered unusual results. Fisher's Exact Test does not interpret the p-value. Instead, the unadjusted odds ratio with a 95% confidence interval are used. Because one of the four cells in the 2 by 2 contingency tables has a small number of observations, the 95 percent confidence interval will be quite large. On the other hand, when a 2 by 2 table has a cell with an expected count of frequencies which is less than 5, the Fisher Exact test is computed in addition to the chi square test in SPSS.

Key highlights of the Fisher’s exact test

• The Fisher Exact test examines the likelihood of obtaining a table that is as strong as possible due to sampling chance. The fraction of cases that are diagonal with the most cases is defined as the word "strong."
• In one-tailed tests, the Fisher Exact test is commonly utilized. It can, however, also be employed as a two-tailed test.
• It's also known as the Fisher Irwin test. It was given this name because Fisher, Irwin, and Yates created it in the 1930’s.

Assumptions

When you decide that you are going to conduct a Fisher’s exact test, the first step to determine whether the data being used for the analysis can actually be used to the test. This involves checking for various assumptions that are required to get valid and accurate results, these assumptions are;

1. It is assumed that the sample selected from the population was obtained through a random sampling technique.
2. A directional hypothesis is assumed in the Fisher Exact test. The directed hypothesis is similar to the one assumed in a one-tailed test hypothesis. In simpler words, the directional hypothesis suggested is that there is either a positive or negative association but not both, hence the directional phrase.
3. This test assumes independence of observation. As such, it assumes that a given observation is not affected by the observations of the next groups and so on. If the data is pooled or combined (not independent), the Fisher Exact test's assumption is violated.
4. Mutual exclusivity of each observations is assumed in the Fisher Exact test. To put it another way, each and every observation can only fit into one cell in the table but not in any other cell after that.
5. It is expected that the variables are measured at a categorical level with two or more groups.

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