Thank you obh, I have a question on this point (maybe due to my misunderstanding of the normality assumption).

If the assumption is the normality of population that the data is collected from, maybe another study with normal distribution of large sample should suggest the normality assumption being meat in this small sample size case. But the normality assumption is not about the normality of the population, but the sample mean of sample size n, right? Then what other knowledge can suggest the normality assumption is meat in this case of small sample size?

Thank you! (Forgive me, without systematic statistic knowledge, I just find information from different sources so contradictory.)

Hi jjx,

The normality assumption is for the differences, but if both groups' distribution is normal then the differences' distribution will also be normal.

Anyway, the t-test is robust to non-normality. (since it runs over the average, CLT...)

If the data is reasonably symmetrical then the average may be okay even for a sample size of 15.

For example, even with a sample size of 10, the average of the uniform distribution distributes normally.

Other tests may be more sensitive to the normality, for example, the F test is running over the ratio of the variances.