Statistics Tip: the F and Chi-square Tests of Variance

​Most users of statistics are familiar with the F-test for Variances. But there is also a Chi-Square Test for the Variance. What's the difference?

​The F-test compares the Variances from 2 different Populations or Processes. It basically divides one Variance by the other and uses the appropriate F Distribution to determine whether there is a Statistically Significant difference.

If you're familiar with t-tests, the F-test is analogous to the 2-Sample t-test. The F-test is a Parametric test. It requires that the data from both the 2 Samples each be roughly Normal.

The following  compare-and-contrast table may help clarify these concepts:

​Chi-Square (like z, t, and F) is a Test Statistic. That is, it has an associated family of Probability Distributions.
 
The Chi-Square Test for the Variance compares the Variance from a Single Population or Process to a Variance that we specify. That specified Variance could be a target value, a historical value, or anything else.
 
Since there is only 1 Sample of data from the single Population or Process, the Chi-Square test is analogous to the 1-Sample t-test.
 
In contrast to the the F-test, the Chi-Square test is Nonparametric. It has no restrictions on the data. 

Videos: I have published the following relevant videos on my YouTube channel, "Statistics from A to Z"

• F Distribution:  https://youtu.be/w1TvaQgoNCY 
• Chi-Square -- the Test Statistic and Its Distributions: https://youtu.be/RJMNkzuxOA4   
• t: the Test Statistic and Its Distributions: youtu.be/3GCJU_RCgoM