How to Use the Wilcoxon Test: A Step-by-Step Guide in R and SPSS

What is the Wilcoxon test?

The Wilcoxon test is a useful statistical tool that you can use when you want to compare two groups of data. Unlike some other tests, such as the t-test, the Wilcoxon test does not make strict assumptions about the distribution of the data. It is particularly helpful when the data are not normally distributed or when you have small sample sizes.

Imagine that you have two data sets and want to know whether they differ significantly. The Wilcoxon test compares the median values of the two groups. It ranks the values from low to high, assigns ranks, and then calculates the differences between the ranks. Finally, a test statistic is calculated, allowing you to decide whether the differences are statistically significant or not.

How is the Wilcoxon test conducted?

Implementation in R with an example

Now let’s get practical! Here is a simple example of how you can perform the Wilcoxon test in R:

# Fiktiver Datensatz
gruppe1 <- c(5, 7, 9, 6, 8)
gruppe2 <- c(10, 11, 12, 9, 10)

# Wilcoxon-Test durchführen
test <- wilcox.test(gruppe1, gruppe2)

# Ergebnis anzeigen
print(test)

In this case, you are comparing two groups that may differ in their values. R will do all the work for you and present the result of the test.

Implementation in SPSS

If you use SPSS, the Wilcoxon test is just as easy to conduct. Here are the steps:

  1. Load Data: Load the data into SPSS.
  2. Select Test: Select “Analyze” > “Nonparametric Tests” > “2 Related Samples”.
  3. Select Variables: Select the variables you want to compare.
  4. Select the Wilcoxon test: Choose the “Wilcoxon test” and click “OK”.
  5. Interpret the results: The results will be displayed in the results view. Pay attention to the W value and the p-value to interpret the test as described above.

SPSS will then perform the analysis and present the results to you, just as in R!

Implementation in JASP

JASP is another popular tool for statistical analyses, and it is also possible to perform the Wilcoxon test in this program. Here are the steps for performing the Wilcoxon test for two dependent samples in JASP:

  1. Load the data: Open JASP and load your data. This can be an Excel, CSV, or other supported file.
  2. Select the variables: After loading your data, you need to identify the variables you want to compare.
  3. Select the test: Click on “Frequentist” in the menu bar at the top, and then select “T-Tests” > “Paired Samples T-Test”. (The Wilcoxon test is the non-parametric counterpart to the paired t-test and can be found in the same menu.)
  4. Assign the variables: Drag the variables you want to compare into the fields for “Paired Variables”.
  5. Select the Wilcoxon test: Check the box next to “Wilcoxon” to use the Wilcoxon test instead of the t-test.
  6. Interpret the results: The results will be displayed in the results view. Pay attention to the W value and the p-value to interpret the test as described above.
  7. Export the results: If you wish, you can export the results by going to “File” > “Export” > “Results” and selecting the desired format.

JASP makes it quite easy to perform the Wilcoxon test, and the user interface is intuitively designed, so even beginners can quickly obtain results.

Implementation in PSPP

PSPP is a free software program for the statistical analysis of samples and provides a free alternative to SPSS. You can perform the Wilcoxon test for two related samples in PSPP by following these steps:

  1. Import or Enter Data: Open PSPP and load your data either by importing a file (for example, a CSV file) or by manually entering the data in the data window.
  2. Select Variables: Identify the two variables (columns) you want to compare. Make sure they are defined as numeric variables.
  3. Select the Test: In the main menu, click “Analyze,” then “Nonparametric Tests,” and finally “2 Related Samples.”
  4. Specify the Test Type: A dialog box will open. Select the two variables you want to compare and move them to the “Test Pairs” field. Make sure that the checkbox for the Wilcoxon test is selected.
  5. Configure Options: If necessary, you can configure additional options for the test, such as the confidence level.
  6. Run the Test: Click “OK” to run the test. The results will be displayed in the output window.
  7. Interpret the Results: The output contains the Wilcoxon W statistic and the corresponding p-value. Interpret these values to determine whether the difference between the groups is statistically significant.
  8. Saving or Exporting Results: You can transfer the results to another document by copying and pasting them, or save them as a file by selecting “File” > “Export”.

By following these steps, you can successfully perform and interpret the Wilcoxon test in PSPP. The menus and options may vary slightly depending on the version of PSPP, but the general steps remain the same.

How is the Wilcoxon test interpreted and reported?

  1. The p-value: This value indicates whether the difference between the two groups is statistically significant. If the p-value is less than 0.05, there is generally a significant difference.
  2. The test statistic (W): This is the value calculated from the differences in ranks. It is often used to describe the size of the effect.

Example

Suppose you performed the Wilcoxon test in R and obtained the following output:

Wilcoxon rank sum test

data:  gruppe1 and gruppe2
W = 0, p-value = 0.043
alternative hypothesis: true location shift is not equal to 0

Interpretation

  • Value of W: W = 0, indicating that all ranks in one of the groups were higher than those in the other.
  • p-value: p = 0.043, which is less than 0.05 and therefore indicates that the difference between the groups is statistically significant.

Reporting the Wilcoxon Test

If you want to present your results in a scientific report or article according to APA guidelines, you should report the test, the W value, and the p-value. In this case, the correct wording would be:

“A Wilcoxon rank-sum test indicated a significant difference between the groups, W = 0, p = 0.043.”

This wording provides the reader with a clear and concise summary of the analysis conducted and its results, in accordance with APA standards.

Conclusion

The Wilcoxon test is a robust and versatile tool that you should have in your statistical toolbox. Whether you use R or SPSS, the test helps you identify differences between two groups, even when the data do not meet the strict requirements of other tests. This gives you another method for answering scientific questions or making business decisions.

I hope this blog post helps you better understand the Wilcoxon test and apply it yourself!