Minimum sample size for unpaired t-test

Is there a “rule” to determine the minimum sample size required for a t-test to be valid?

For example, a comparison needs to be performed between the means of 2 populations. There are 7 data points from one population and only 2 data points from the other. Unfortunately, the experiment is very expensive and time consuming, and obtaining more data is not feasible.

Can a t-test be used? Why or why not? Please provide details (the population variances and distributions are not known). If a t-test can not be used, can a non parametric test (Mann Whitney) be used? Why or why not?

Answer

I’d recommend using the non-parametric Mann-Whitney U test rather than an unpaired t-test here.

There’s no absolute minimum sample size for the t-test, but as the sample sizes get smaller, the test becomes more sensitive to the assumption that both samples are drawn from populations with a normal distribution. With samples this small, especially with one sample of only two, you’d need to be very sure that the population distributions were normal — and that has to be based on external knowledge, as such small samples gives very little information in themselves about the normality or otherwise of their distributions. But you say that “the population variances and distributions are not known” (my italics).

The Mann-Whitney U test does not require any assumptions about the parametric form of the distributions, requiring only the assumption that the distributions of the two groups are the same under the null hypothesis.

Attribution
Source : Link , Question Author : Johnny Puzzled , Answer Author : onestop

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