I took before/after measurements of selected tree stems. The distribution looked normal so I used the paired t-Test. The results:

test statistic = 1.46

critical value = 1.69 (from table)

The instructions say if the test statistic < critical value there is no significant difference among the means (alpha = 0.05), and accept the null hypothesis.

I tried the same data on the Wilcoxon Signed Rank test which is to be used for non-parametric data, and the results:

test statistic = 189

critical value = 208 (alpha 0.05)

Only in this case the instructions say if the test statistic < critical value REJECT the null hypothesis.

Could you shed some light on this. Am I venturing into prohibited territory by using the wrong test i.e. Wilcoxon on parametric data? Also I've noted that critical values differ among different Wilcoxon tables found online. WT_? Is there a "certified" authentic table somewhere?