# If one group has 23 participants and the second group has 117 participants in it, can we rely on the result of t-test? [duplicate]

I was evaluating a research paper in which the authors have 23 male participants and 117 female participants. They have applied t-test to calculate Gender differences and have even concluded on significance of the difference. I am not sure when the groups are so markedly difference in terms of their size, we can use it for drawing such conclusions. Please help me!!!

If one group has 23 participants and the second group has 117 participants in it, can we rely on the result of t-test?

I am not sure when the groups are so markedly difference in terms of their size, we can use it for drawing such conclusions.

A difference in sample size is not of itself a problem. If the assumptions on the t-test are close* to being satisfied, the result should be fine.

* what counts as 'close enough' depends on how much you can tolerate a significance level different from what it's supposed to be (and potential effect on power), and also the manner of failure of the assumptions as well as the extent of them.

If they did a equal-variance t-test, the large difference in sample size makes the test not robust to differences in population variance in the two groups. The significance level may either be inflated or deflated depending on which group has the larger variance.

On the other hand, if they did a Welch t-test, differences in variance shouldn't be much of an issue at all.

The assumption of normality won't necessarily be a big issue, it depends on what kind of non-normality and how far from normal it is. The t-test does quite well on short tailed-distributions but is reasonably robust to mild skewness and mild heavy-tailedness. If you're able to say more about what's being measured and what the distributions typically look like, I might be able to say more.

In short, it might well be okay, it kind of depends.

There isn't necessarily any problem here. If the assumptions of the $t$-test are met, the test should be fine. It should be noted that the power of the test to reject the null is lower with 23 and 117 than it would be with 70 and 70. In any case, a failure to reject the null does not mean the null is true. It may help you to read the following: