I have two groups with 20 elements in each. In one group variance is equal 0. I want to do f-test. Can I? And how should I interpret results (in this case)?
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Best Answer
Since one group's elements are identical values (variance zero), and the other's are not, intuition says that variance is not the same. There is no need for a test.
The F-test for variances takes the ratio of the sample variances: $$ F = frac{S_X^2}{S_Y^2}$$ So you see that if $Y$ is the one group with the identical values (low variance) it is not defined and if $X$ (zero=low variance) it is zero (test failure). So, by definition, the larger variance should be placed in the numerator. Hence, you get an F-statistic of infinity and you can claim that the variances are different.
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