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)?

  • $\begingroup$ Why do you want to do an F test for a group with identical values? Also what do you want to test? stats.stackexchange.com/questions/30388/… $\endgroup$ – Konstantinos May 30 '15 at 0:44
  • $\begingroup$ I wanted to compare two groups with t test and check if variance is the same. $\endgroup$ – Frozen May 30 '15 at 7:24

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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    $\begingroup$ It's not just intuition that says that. :-) To get a sample with zero variance if the population variance is non-zero is infinitely improbable. $\endgroup$ – A. Donda May 30 '15 at 16:42
  • $\begingroup$ I think I rushed too much to answer the question. What if the population is like: $0,1,2,1,1,1,2,1,1,2,0,1,2,1,1,0,1,1,1,0,2,1,1$ and we just get a sample of 5 observations? It's highly probable to get 5 observations of just $1$. $\endgroup$ – Konstantinos May 30 '15 at 18:04
  • $\begingroup$ Ok, I assumed a continuous distribution. $\endgroup$ – A. Donda May 30 '15 at 18:23

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