How to Run Wilcoxon Signed Rank Test in SPSS|2025

Discover How to Run Wilcoxon Signed Rank Test in SPSS with this easy-to-follow guide, covering data setup, test execution, and result interpretation for non-parametric analysis.

The Wilcoxon Signed Rank Test is a non-parametric statistical test that is used to determine whether there is a statistically significant difference between two related variables. This test is often employed when the data do not meet the assumptions of a parametric test, such as the paired t-test, which requires normally distributed differences. The Wilcoxon Signed Rank Test compares the ranks of the differences between paired observations. It is particularly useful for data that are ordinal or when assumptions of normality are violated.

In this paper, we will explore how to run the Wilcoxon Signed Rank Test in SPSS, interpret the results, and report them according to APA standards. We will also address important considerations such as whether to use a one-tailed or two-tailed test and how to interpret the Z value.

Step-by-Step Guide to Running the Wilcoxon Signed Rank Test in SPSS

Preparing Your Data

Before running the Wilcoxon Signed Rank Test in SPSS, ensure that your data is organized in a way that is compatible with the test. The data should consist of two related groups or paired samples. For example, you may have measurements taken before and after an intervention, or data from two related conditions.

The data should be entered into two columns in SPSS, one for each of the paired groups. Ensure that each row corresponds to a single participant or observation. For example, if you are testing whether a treatment has an effect on a group of participants, one column might represent pre-treatment scores, and the other column might represent post-treatment scores.

Running the Wilcoxon Signed Rank Test

To perform the Wilcoxon Signed Rank Test in SPSS:

1. Open SPSS and load your dataset.
2. Navigate to Analyze in the top menu, select Nonparametric Tests, and then select Related Samples.
3. In the dialog box, select the two variables (paired groups) that you wish to compare.
4. Ensure that the test type is set to Wilcoxon. You may also want to select whether you wish to perform a one-tailed or two-tailed test. This is determined by your research hypothesis.
5. Click OK to run the test.

Interpreting the Output

Once the test is run, SPSS will provide output that includes the results of the Wilcoxon Signed Rank Test. The most important values to focus on are:

• Z value: This represents the test statistic for the Wilcoxon Signed Rank Test. A large absolute value of Z indicates a significant difference between the paired groups.
• Asymptotic significance (p-value): This value indicates whether the difference between the paired groups is statistically significant. A p-value of less than 0.05 typically indicates a significant difference.

Wilcoxon Signed Rank Test SPSS Interpretation

When interpreting the Wilcoxon Signed Rank Test results, you need to examine both the Z value and the p-value to make conclusions about the data:

• If the p-value is less than your chosen significance level (usually 0.05), then you reject the null hypothesis, suggesting that there is a significant difference between the paired groups.
• The Z value is used to assess the strength and direction of the difference. A negative Z value indicates that the second group (or condition) has higher values than the first, while a positive Z value indicates the opposite.

Example: Let’s assume you have a dataset where participants’ scores before and after treatment are compared. If you obtain a p-value of 0.02 and a Z value of -2.35, this suggests a significant decrease in scores after the treatment.

How to Report Wilcoxon Signed Rank Test Results in Tables

When reporting the results of the Wilcoxon Signed Rank Test, it is important to present the results clearly and in an organized manner. The results should be reported in a table with the following information:

• The name of the test.
• The Z value.
• The p-value.
• The direction of the effect (positive or negative).

An example table might look like this:

In this case, the Z value of -2.35 indicates that the post-treatment scores are significantly lower than the pre-treatment scores (assuming a two-tailed test and a significance level of 0.05).

Wilcoxon Signed Rank Test Reporting Results in APA Style

When reporting the results of a statistical test in APA format, clarity and conciseness are key. The general structure for reporting the Wilcoxon Signed Rank Test follows this format:

• Test name: Wilcoxon Signed Rank Test.
• Test statistic (Z value): The test statistic is usually reported as the Z value.
• Sample size: The number of paired observations.
• p-value: The significance level of the test.
• Direction of the effect: Whether the test shows an increase or decrease in scores (if applicable).

Here is an example of how to report the Wilcoxon Signed Rank Test in APA style:

“The Wilcoxon Signed Rank Test was used to compare participants’ scores before and after treatment. The results indicated a significant difference between the pre-treatment (M = 45.32) and post-treatment (M = 30.47) scores, Z = -2.35, p = 0.02, suggesting that the treatment led to a significant decrease in scores.”

Wilcoxon Signed Rank Test One-Tailed or Two-Tailed

The decision to use a one-tailed or two-tailed test depends on your research hypothesis:

• One-tailed test: A one-tailed test is used when you have a directional hypothesis, meaning you expect the difference between the paired groups to be in a specific direction (e.g., you expect post-treatment scores to be lower than pre-treatment scores). A one-tailed test is more powerful but only tests for differences in one direction.
• Two-tailed test: A two-tailed test is used when you do not have a directional hypothesis and are open to the possibility that the difference could be in either direction (e.g., post-treatment scores could be either higher or lower than pre-treatment scores). A two-tailed test is more common in most research situations.

In SPSS, you can select whether to run a one-tailed or two-tailed test in the test dialog box.

One Sample Wilcoxon Signed Rank Test in SPSS

A one-sample Wilcoxon Signed Rank Test can be used when you are comparing a single sample against a known value or a theoretical median. The procedure for running this test in SPSS is similar to the paired samples test. You simply enter the observed values in one column and the theoretical or expected value in another column.

The steps are as follows:

1. Enter your sample data into SPSS.
2. Navigate to Analyze → Nonparametric Tests → Related Samples.
3. Select the variable for analysis and compare it to the constant or expected value.
4. Choose the Wilcoxon test and run the analysis.

The interpretation and reporting of a one-sample Wilcoxon Signed Rank Test follow the same principles as the paired test, but in this case, the “paired” group is the theoretical value rather than another set of observations.

Wilcoxon Signed Rank Test Interpretation Z Value

The Z value in the Wilcoxon Signed Rank Test is the test statistic that reflects the number of standard deviations the observed differences are from zero (i.e., no effect). A larger absolute value of Z indicates a stronger effect or greater departure from the null hypothesis.

• If the Z value is large (either positive or negative), this indicates a larger difference between the paired samples.
• A Z value of 0 means there is no difference between the paired samples.
• The significance level (p-value) tells you whether the observed difference is statistically significant. Typically, if p < 0.05, the result is significant.

Conclusion

The Wilcoxon Signed Rank Test in SPSS is a powerful tool for analyzing paired or related data when the assumptions of normality are violated. It provides a non-parametric alternative to the paired t-test and is commonly used in fields such as psychology, medicine, and social sciences. By following the steps outlined in this paper, you can easily run the Wilcoxon Signed Rank Test, interpret the results, and report them in an APA-compliant format. Always ensure to choose the correct type of test (one-tailed or two-tailed) based on your research hypothesis and the direction of the expected effect.