XLSTAT: One Sample Wilcoxon Signed Rank Test in Excel

 

Background

The one sample Wilcoxon signed-rank test is a nonparametric statistical test used to determine whether the median of a single sample differs significantly from a specified value. It is an alternative to the one sample t-test when the assumption of normality is not met.

 

Dataset for Example

The attached data represent the liking scores for a new crisp brand rated from 1 to 10 by 30 consumers. The median liking score of the strongest brand in the market is known to be 7.

Our goal is to determine whether the median liking score of the new brand is higher than 7. For this purpose, we will perform a one-sample Wilcoxon signed rank test. This test allows the comparison of an observed median to a known standard value without assuming normality. It is a non-parametric alternative to the one-sample t-test.

The results of this test can indicate us whether consumers are globally more satisfied with the new product.

 

Setting Up

• Open XLSTAT.

• Click on the Nonparametric tests menu and select the One sample Wilcoxon Signed Rank test feature:

  

• Once you have clicked on the function, the next dialog box appears.

In the General tab:

• Select the liking scores from column A in the Samples field.

In the Options tab:

• Choose Median1 > Theoretical median as the alternative hypothesis.

• Set the Theoretical median value to 7. This defines an upper-tailed (right-tailed) test.

• Select the option to compute the p-value using the asymptotic approximation of the distribution of the V statistic.

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet.

 

Interpreting the Results

The following table presents the results of the upper-tailed Wilcoxon signed-rank test.

The computed p-value is lower than the significance level = 0.05 thus we can reject Ho and accept that the median of our sample is higher than 7. Another way to draw this conclusion is using the Z statistic. Here, Z = 4.197 is higher than the critical value at a 5% level of significance (1.645) so we can reject Ho. This can be easily observed in the following graph.