I have read a lot about when to use a (paired) t-test or a Wilcoxon Signed Rank Test as the non-parametric alternative but I need your help:
I have gathered some paired data and want to perform some hypothesis tests on them. Then I've calculated the differences between both groups and made a density-plot which looks like this:
As this looks kind of normally distributed, I have also performed a Shapiro-Wilk and Anderson-Darling normality test. Both deliver p-values greater than .05 (p = .1101 and p = .0955).
Although the p-values are just a bit above the significance level and the graph is rather skewed and has no "nice" bell-shape, can I assume that the data is normally distributed based on this output? So should I perform a paired t-test or should I use the Wilcoxon Signed Rank test instead?
Thank you very much!