Question

In terms of statistical validity, how is running an independent sample t test w/ a small sample size problematic?

Answer 1

To run a independent sample t-test with a small sample size the following problems occur:

i) To use the t-test one of the assumption is the population should be normally distributed so if the sample size is low one cannot approximate it to be normally distributed because central limit theorem does not apply for small samples.

So the small sample should vaguely be normally distributed and it is quite difficult to verify this because of the small sample size, but if sample is large enough central limit theorem can be used to approximate and distribution to normal distribution.

ii) Inaccurate results

Because of the small sample size it is difficult to extract the whole information from the population and because of the less information the conclusions obtained might differ from the actual observations as only a few observations were used to conclude about the whole population.