hypothesis testing depending on the distribution of the data

[Are-Pro-Gram-In]

I have a paired dataset where the before-treatment observations are non-normally distributed (Shapiro-Wilk test p-value = 0.007) and the after-treatment observations are normally distributed (Shapiro-Wilk test p-value = 0.997). What type of test can I use to see if the before-treatment observations and after-treatment observations are statistically significantly different? The dataset size is n = 17. Would I use the Wilcoxon Signed Rank test? Suggestions for post-hoc tests?

 

[Karabiner]

Well, in a paired sample, not the distribution of the variables does matter, but the distribution of the differences.
But with a small sample like yours, Wilcoxon looks like a good choice. What do you mean by post-hoc tests?
They are only needed after global tests including more than 2 levels. Here, you only have the two levels pre-post.

With kind regards

Karabiner