# Paired t-test vs Wilcoxon signed rank

I conducted a pilot study (n=14) which was evaluated retrospectively. I have four parameters with a pre-intervention and post-intervention score that I want to compare. I am wondering whether I can do hypothesis testing on this dataset. I would be interested in comparing the pre- and post-value of each parameter. As I consider them to be dependent variables, I concluded that I should use either the paired t test or the Wilcoxon signed rank test.

Here is a histogram of my data (left column = pre-intervention, right column = post-intervention):

Quote from Biostatshandbook.com:

The paired t-test is very sensitive to deviations from normality, so unless the deviation from normality is really obvious, you shouldn't worry about it.

Now, looking at the histograms I guess I should not go for a normal distribution, so I used IPython and scipy to calculate the Wilcoxon signed ranks test:

Skills before workshop : WilcoxonResult(statistic=0.0, pvalue=0.00063629914124020508)
Programming before workshop : WilcoxonResult(statistic=0.0, pvalue=0.00078911298901562993)
Importance before workshop : WilcoxonResult(statistic=0.0, pvalue=0.0040165146600327469)
Development without support : WilcoxonResult(statistic=0.0, pvalue=0.002136306416781164)


All zeros... trying paired t-test:

Skills before workshop : Ttest_relResult(statistic=10.212193147844831, pvalue=1.409449881428046e-07)
Programming before workshop : Ttest_relResult(statistic=7.3202025828291477, pvalue=5.8299747757734459e-06)
Importance before workshop : Ttest_relResult(statistic=nan, pvalue=nan)
Development without support : Ttest_relResult(statistic=5.5075705472861021, pvalue=0.00010084267272620214)


Now I am confused in interpretation. Why are there all 0's for the Wilcoxon? Am I doing something wrong or is there no correlation? Or should I go for the paired t-test despite the distribution not being (a little) skewed.

The IPython notebook is available on GitHub for anyone interested.