What is F-Test?

History and Definition

The objective of any statistical test is to determine the likelihood of a value in a sample, given that the null hypothesis is true. An F-test is a statistical test that compares the variances of two samples so as to test the hypothesis that the samples have been taken from populations with different variances. Its basic purpose is to check for differences among sample variance.

Specifically speaking, any statistical test in which the test statistic has an F distribution under null hypothesis is called an F-test. The F Distribution is named after R.A. Fisher, the famous statistician. It is also called the Fisher F Distribution or the Snedecor-Fisher F distribution.


Say, a retail chain wants to increase sales by focusing on loyal customers. It could study the purchase pattern of customers by conducting an F-test to monitor the shopping frequency of customers, their opinion on billing facilities, exchange facilities for defective goods and so on. The results would provide inputs and feedback for improvement and lead to higher repeat purchases and increased customer flow.

Practical Usage of F-test

The F-test is widely used in the field of medicine and by medical researchers to determine which among various treatments is better or whether two treatments will lead to similar results. It is used in various physical sciences to test the efficiency of different exploration methods or soil composition testing methods. F-test is also a good tool to determine if new variables should be added to or old variables removed from any kind of model. Say, we are debating whether or not to retain Literacy Rate in the model for calculating Mortality Rates of a country. We may conduct tests with and without including the variable ‘literacy rate’ and check the variances of the results to determine if one method is better than the other. This will help us resolve the problem of whether or not to retain the variable in the model.

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