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Wilcoxon Signed-Rank Test using SPSS

Introduction

The Wilcoxon signed-rank test is the nonparametric test equivalent to the dependent t-test. As the Wilcoxon signed-rank test does not assume normality in the data, it can be used when this assumption has been violated and the use of the dependent t-test is inappropriate. It is used to compare two sets of scores that come from the same participants. This can occur when we wish to investigate any change in scores from one time point to another, or when individuals are subjected to more than one condition.

For example, you could use a Wilcoxon signed-rank test to understand whether there was a difference in smokers' daily cigarette consumption before and after a 6 week hypnotherapy programme (i.e., your dependent variable would be "daily cigarette consumption", and your two related groups would be the cigarette consumption values "before" and "after" the hypnotherapy programme). You could also use a Wilcoxon signed-rank test to understand whether there was a difference in reaction times under two different lighting conditions (i.e., your dependent variable would be "reaction time", measured in milliseconds, and your two related groups would be reaction times in a room using "blue light" versus "red light").

This "quick start" guide shows you how to carry out a Wilcoxon signed-rank test using SPSS, as well as interpret and report the results from this test. However, before we introduce you to this procedure, you need to understand the different assumptions that your data must meet in order for a Wilcoxon signed-rank test to give you a valid result. We discuss these assumptions next.

SPSS

Assumptions

When you choose to analyse your data using a Wilcoxon signed-rank test, part of the process involves checking to make sure that the data you want to analyse can actually be analysed using a Wilcoxon signed-rank test. You need to do this because it is only appropriate to use a Wilcoxon signed-rank test if your data "passes" three assumptions that are required for a Wilcoxon signed-rank test to give you a valid result. The first two assumptions relate to your study design and the types of variables you measured. The third assumption reflects the nature of your data and is the one assumption you test using SPSS. These three assumptions as briefly explained below:

In the section, Test Procedure in SPSS, we illustrate the SPSS procedure to perform a Wilcoxon signed-rank test. First, we introduce the example that is used in this "quick start" guide.

SPSS

Example

A pain researcher is interested in finding methods to reduce lower back pain in individuals without having to use drugs. The researcher thinks that having acupuncture in the lower back might reduce back pain. To investigate this, the researcher recruits 25 participants to their study. At the beginning of the study, the researcher asks the participants to rate their back pain on a scale of 1 to 10, with 10 indicating the greatest level of pain. After 4 weeks of twice weekly acupuncture, the participants are asked again to indicate their level of back pain on a scale of 1 to 10, with 10 indicating the greatest level of pain. The researcher wishes to understand whether the participants' pain levels changed after they had undergone the acupuncture, so a Wilcoxon signed-rank test is run.

In our enhanced Wilcoxon signed-rank test guide, we show you how to correctly enter data in SPSS to run a Wilcoxon signed-rank test. You can learn about our enhanced data setup content here. Alternately, we have a generic, "quick start" guide to show you how to enter data into SPSS, available here. In our enhanced Wilcoxon signed-rank test guide, we also explain how to deal with missing values in your data set (e.g., if a participant completed a pre-test, but failed to turn up to the post-test). In the next section, we take you through the Wilcoxon signed-rank test procedure using SPSS.

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SPSS

Test Procedure in SPSS

The six steps below show you how to analyse your data using a Wilcoxon signed-rank test in SPSS. At the end of these six steps, we show you how to interpret the results from this test.

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SPSS

SPSS Output of the Wilcoxon Signed-Rank Test

SPSS generates a number of tables in the Output Viewer under the title NPar Tests. In this section, we focus on these three tables to help you understand the results you may obtain when running a Wilcoxon signed-rank test on your data.

Descriptives Table

The Descriptive Statistics table is where SPSS has generated descriptive and quartile statistics for your variables if you selected these options. If you did not select these options, this table will not appear in your results. You can use the results from this table to describe the Pain Score scores before and after the acupuncture treatment. As you have used a nonparametric test it is most likely that you should use the quartiles information to describe both your groups.

The Wilcoxon Signed-Rank Test Dialog Box

Published with written permission from SPSS Inc., an IBM Company.


Ranks Table

The Ranks table provides some interesting data on the comparison of participants' Before (Pre) and After (Post) Pain Score. We can see from the table's legend that 11 participants had a higher pre-acupuncture treatment Pain Score than after their treatment. However, 4 participants had a higher Pain Score after treatment and 10 participants saw no change in their Pain Score.

The Wilcoxon Signed-Rank Test Dialog Box

Published with written permission from SPSS Inc., an IBM Company.


Test Statistics Table

By examining the final Test Statistics table, we can discover whether these changes, due to acupuncture treatment, led overall to a statistically significant difference in Pain Scores. We are looking for the "Asymp. Sig. (2-tailed)" value, which in this case is 0.071. This is the p-value for the test. We report the Wilcoxon signed-ranks test using the Z statistic.

The Wilcoxon Signed-Rank Test Dialog Box

Published with written permission from SPSS Inc., an IBM Company.


Reporting the Output from the Wilcoxon Sign-Rank Test

Based on the results above, we could report the results of the study as follows:

A Wilcoxon signed-rank test showed that a 4 week, twice weekly acupuncture treatment course did not elicit a statistically significant change in lower back pain in individuals with existing lower back pain (Z = -1.807, p = 0.071). Indeed, median Pain Score rating was 5.0 both pre- and post-treatment.

In our enhanced Wilcoxon signed-rank test guide, we: (a) show you how to interpret and write up the results of the Wilcoxon signed-rank test irrespective of whether you ran the legacy procedure (as illustrated in this guide) or the newer procedure in SPSS; (b) provide a more detailed explanation of how to interpret median values and paired differences, as well as negative ranks, positive ranks and ties, and finally, asymptotic p-values; and (c) illustrate how to write up the results from your Wilcoxon signed-rank test procedure if you need to report this in a dissertation/thesis, assignment or research report. We do this using the Harvard and APA styles. You can access our enhanced Wilcoxon signed-rank test guide, as well as all of our SPSS content, by subscribing to the site here, or learn more about our enhanced content in general here.

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