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__
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## AuthorAndrew A. (Andy) Jawlik is the author of the book, Statistics from A to Z -- Confusing Concepts Clarified, published by Wiley. ## Archives
March 2021
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