2

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)?

Frozen
  • 23
  • 3
  • Why do you want to do an F test for a group with identical values? Also what do you want to test? http://stats.stackexchange.com/questions/30388/can-i-do-a-t-test-if-i-have-little-to-no-variance-in-one-group – Konstantinos May 30 '15 at 00:44
  • I wanted to compare two groups with t test and check if variance is the same. – Frozen May 30 '15 at 07:24

1 Answers1

1

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.

Konstantinos
  • 216
  • 2
  • 11
  • 1
    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. – A. Donda May 30 '15 at 16:42
  • 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 $1$. – Konstantinos May 30 '15 at 18:04
  • Ok, I assumed a continuous distribution. – A. Donda May 30 '15 at 18:23