3
$\begingroup$

enter image description here

We have a series of tests that we can consider such as two sample t test, wilcoxon rank sum, signed rank, paired t test, etc. But here since we don't have the actual data, this means that I am limited in what tests I could use. So for this I did not assume equal variance but the samples are large enough to assume normality. The groups are independent from one another and the observations are as well (this may work here but there could be some dependence since the flies were in the same cages). In this case would it be appropriate if I conduct a two sample t test (unequal variances)?

$\endgroup$

1 Answer 1

3
$\begingroup$

The usual F-test for equality of variances has the test statistic $8^2/2^2 = 16$ with $199$ degrees of freedom in each of the numerator and denominator, and the probability that an F-distributed random variable with those degrees of freedom would exceed $16$ is effectively $0$. This strongly points to unequal variances. I think the validity of this test may be sensitive to the assumption of normality of the two distributions, and we have no way to assess that without seeing more than summary statistics.

BEGIN QUOTE the samples are large enough to assume normality END QUOTE

I wonder if some confusion is at work here. The sampling distribution of sample means will be nearly normal for large sample sizes, but that's not at all the same thing as saying the distributions of F-statistics will still be F-distributions if the populations are not normally distributed.

$\endgroup$
3
  • $\begingroup$ I read that using a F-test to test for equality of variances is a bad idea to see if we should proceed with another test. $\endgroup$
    – user60887
    Commented Oct 10, 2015 at 22:47
  • $\begingroup$ Perhaps it's a bad idea unless one has nearly normally distributed populations, but in this case we have no way to know about that. $\endgroup$ Commented Oct 10, 2015 at 22:47
  • $\begingroup$ This was pretty much all I was given. I know that two sample t tests are quite robust with departures from normality. I guess that's pretty much the only option I know of. $\endgroup$
    – user60887
    Commented Oct 10, 2015 at 22:49

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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