One sample Wilcoxon Signed-Rank test

What is the Wilcoxon One-sample Signed-Rank test?

The Wilcoxon One Sample Signed-Rank test test is the non parametric version of the one sample t test. It is based on ranks and because of that, the location parameter is not here the mean but the median. This tool can be used in case you have doubts that the normality assumption necessary to apply the t test does not hold. This test allows to test the null hypothesis that the sample median is equal to a given value provided by the user.

If we designate m to be the assumed median of the sample, there are three possible alternative hypotheses to the null hypothesis:

For the two-tailed test, the null H0 and alternative Ha hypotheses are as follows:

• H0: Sample median = m

• Ha: Sample median m

In the left-tailed test, the following hypotheses are used:

• H0: Sample median = m

• Ha: Sample median < m

In the right-tailed test, the following hypotheses are used:

• H0: Sample median = m

• Ha: Sample median > m

Options for the One Sample Wilcoxon Signed-Rank test in Excel using the XLSTAT software

To compute the p-values corresponding to the various statistics, XLSTAT offers several alternatives:

• Asymptotic method: The p-value is obtained using the asymptotic approximation of the distribution of the statistic. The reliability of the approximation depends on the number of samples and on the number of measures per sample. Continuity correction is available.

• Exact method: The computation of the p-value is based on the exact distribution of the statistic.