I have two groups that I wish to assess for statistically significant differences (n1=1520 / n2=115). I'm actually using T-Test for independent samples.

As far as I know, there isn't a problem here because thanks to the Levene test it can assume unequal variances. The thing is, I need the 'scientific' justification for this or to know if I'm wrong (and if so, what test should I use). If anyone could help me on this matter I'd be very grateful.

## Best Answer

If you are concerned about unequal samples, the regular unpaired t-test can handle that situation just fine. If you are also concerned abount unequal variance (or standard deviation), than you should use a slightly modified version of the unpaired t-test called the Welch test. Some may also call it unpaired t-test for unequal variance. After calculating the variance (or standard deviation) of your two separate samples, you may observe there is a difference between the two (there usually is). Based on that, you may decide to test your samples both ways with regular unpaired t test and the Welch test. Pretty often the two tests come out very close leading you to the exact same conclusion regarding whether those two samples are different or not. If for some reason they diverge, look closely at the divergence between the samples' variances. If the latter are different enough, it warrants relying on the Welch test results. If they do not diverge by much, the regular unpaired t test will do just fine.