Due to limitations in experimental setup, I only have small data sets with n=3. Despite the low df the difference between treated and control is large enough to generate a significant p-value.
The problem is that with small sample sizes doing a t-test becomes more sensitive to the assumption that the data are drawn from a population of a normal distribution. In my case however, multiple independent experiments consistently yield a similar result.
I cannot group the data of the experiments because of small differences in the data. For example the increase between treated and control in one experiment is slightly bigger than in another experiment, which is likely caused by small variances in experimental conditions (it would get technical to explain this further). Despite this the same increase is consistently observed and each time the 3 data points have a small standard deviation for both groups.
So my question is whether it is defensible to make the normality assumption based on the data of multiple independent experiments with a small sample size? If not am I right that it would not be appropriate to use any statistics in this case?