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"
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Andrew A. (Andy) Jawlik is the author of the book, Statistics from A to Z -- Confusing Concepts Clarified, published by Wiley.