2
$\begingroup$

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)?

$\endgroup$
  • $\begingroup$ 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
1
$\begingroup$

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.

| cite | improve this answer | |
$\endgroup$
  • 1
    $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.