F-test: A test for determining equality of population variances

Statistical tests, a nightmare of every research scholar, is a process that can either make your research or break it. With several statistical tests ruling the research process, there are few other tests which are least considered but are highly significant; F-test is considered to be one such test.


F-test named after Sir Ronald Fisher, is a test that assesses the equality of variances of two populations. A F-test makes use of F-distribution and is normally used when the sample size is smaller than 30. The F-test is a flexible test and can be used to evaluate multiple model terms allowing them to compare the fits of various linear models. However, there are several assumptions that must be taken into account before conducting this test. They are:

  1. Populations from which the sample is drawn should be normal.

  2. The larger of the sample variance needs to be placed in the numerator of the test statistic.


More often F-test is used to calculate the overall significance. Although it is easy to conduct the test, it is quite difficult to interpret its significance. To do this, one has to compare the p-value for the F-test to the significance level. If the p-value is less than the significance level, then the sample data provide sufficient evidence to conclude that the model under consideration fits the data better than the model with no independent variables. But if none of the independent variables are significant then the overall test is not statistically significant. 


So when should one opt for F-test?


F-test which is least considered by the scholars comes to an aid under the following circumstances.

  • You want to perform a two sample t-test in order to check the equality of the variances of the two samples.

  • You want to compare the variability of a new measurement with an old method.

The best feature of this test is that it is not limited to one purpose. I.e. F-test can be used for different purposes including:


  • Testing equality of variance - This test can be used to examine the hypothesis of the equality of two population variances. 

  • Testing equality of several means - The test for equality is carried out by the ANOVA technique.

  • Testing the significance of regression -  This test can also be used to determine the significance of the regression model. 

To learn more about F-test visit https://www.statisticshowto.datasciencecentral.com/probability-and-statistics/hypothesis-testing/f-test/.

Category : Statistical tests
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