# Is there a statistical significance in my paired sample data after performing Wilcoxon signed rank test?

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 . 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?

• Since $p\le 0.99$, you reject $H_0$ at the 1% level of confidence, not the 99% level! (But since $p$ is actually much smaller than $0.99$, and indeed very small indeed, it's safe to reject $H_0$ anyway.)
– whuber
Oct 9, 2012 at 22:00
• @whuber Thanks for the reply. Indeed I should reject $H_0$ at the 1% level confidence. I am confused though - at what level is rejecting better 99% or 1%? Oct 9, 2012 at 22:16