My question might sound strange but this is the situation I'm dealing with! I have a dataset, consisting of 4 data series, each a measurement of a parameter of a biological sample. We have 31 samples. So we have a matrix of 4x31. I need to compare each series with the other one statistically and find the correlations and dependency of the series. So I ran Shapiro-Wilk and d'Agostino-Pearson tests to see if the data are normally distributed. The result of both tests on each of 4 series was positive and my data are normal. I also checked for outliers using Box and Whisker plots and the tests described here It turned out that there is an outlier in the 1st series (out of 4) in my dataset. Now my question is that if I am allowed to run t-test (knowing it's sensitivity to outliers) with my current data considering that the normal distribution of the data is confirmed through those 2 test? Or I have to reconsider usage (in this case, remove) the outlier and run my ANOVA and T-Test with series without outliers?
Thank you in advance