Wilcoxon signed ranks test is a non-parametric test for a difference in central location (median) between two paired samples.
The requirements of the test are:
Data in existing Excel worksheets can be used and should be arranged in a List dataset layout. The dataset must contain two ordinal or continuous scale variables.
When entering new data we recommend using New Dataset to create a new 2 variables dataset ready for data entry.
To start the test:
Excel 97, 2000, 2002 & 2003:
Select any cell in the range containing the dataset to analyse, then click Analyse on the Analyse-it toolbar, click Compare Pairs then click Wilcoxon.
The report shows the number of observations analysed, and, if applicable, how many missing values were excluded. Since the test uses the ranked difference between paired observations, rank summary statistics for positive, negative and zero differences are shown.
The Wilcoxon statistic and hypothesis test are shown. The p-value is the probability of rejecting the null hypothesis, that the samples have the same median, when it is in fact true. A significant p-value implies that the two samples have different medians.
METHOD When the number of cases is ≤25 an exact p-value is calculated, based on the assumption of no ties (see ). If a few ties are present (the number of ties is shown next to the p-value) the p-value will be conservative. For > 25 cases a normal approximation, with correction for ties, is used (see ).
If both samples are continuous the median difference and confidence interval can be calculated to quantify the difference between the samples in terms that can be practically evaluated.
To calculate the median difference and confidence interval:
NOTE The Hodges-Lehman method used to calculate the confidence interval can be extremely time-consuming for large sample sizes. If a confidence interval is not required, or the sample sizes are large, leave the confidence level blank and the calculation will be skipped.
The median differences and confidence interval are shown.
METHOD The median difference and confidence interval are calculated using the Hodges-Lehman method (see ).
(click to enlarge)