T-Test: How large is large?

I'm doing some research, I collected data from two different groups, 80 samples in each group. The data is borderline for normality. I've read on many statistics websites that the t-test can still be used in this case if the sample size is sufficiently large. The problem I'm having is, none of the websites tell me how big sufficiently large is.

I was wondering if anyone knew of a research paper that discussed the topic or gave some actual numerical results in terms of n = ? for it to be a large sample.


TS Contributor
your question is intriguing.

The problem of sample size is related to the precision in estimating various population's parameters starting from just a sample drawn from it.

If you think about, e.g., the estimate of population mean and the standard error value (which is equal to standard deviation divided by the square root of the sample size), you will understand that as long as the sample size increases, the standard error decreases. This leads to narrow down the Confidence Interval in which the "true" mean lies.

To go back to your question, I believe that you can find some hints at the following pages



I believe, moreover, that a sample size of 80 (as in your case) is big enough to be considered "large".

By the way, when you perform hypothesis tests SigmaPlot gives you the statistical power of the test (that is the probability that the test will detect a difference if there really is a difference).

May be that other members of the Forum can give you deeper statistical insight into the issue.

I hope this helps,