I have a paired data consisting of $N$ = 421 samples. I would like to find out if there is statistical significance between the paired samples. Since, I do not know the underlying data distribution I select the Wilcoxon Signed Rank test for my task. I use the SciPy stats module in Python to do the job for me [0]. This function returns the $z$ statistic (under the large-sample approximation that the signed-rank statistic is normally distributed) and $p$ value for the two-sided test. I received the following values as output
$z = 4788.5$
$p = 1.00530788183* 10^{-8}$
The Null Hypothesis $H_o$ Wilcoxon Signed Rank test [1,2,3] states that there is no difference between the paired samples. Since, the $p \leq 0.99$ , I reject $H_0$ as my null hypothesis at 1% confidence interval and conclude that the difference between the two paired samples is statistically significant.
I have two questions -
$Q1$ Is my choice of Wilcoxon Signed Rank test a correct choice. If not, what should I use?
$Q2$ Are my conclusions from the significance test correct? If not, can you please explain why they are not correct?
[0] http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.wilcoxon.html#scipy.stats.wilcoxon [1] http://blog.excelmasterseries.com/2010/10/wilcoxon-signed-rank-test-in-excel-for_13.html
[2] Please help me interpret these Wilcoxon signed-rank test results