# Sign Test using SPSS Statistics

## Introduction

The "paired-samples sign test", typically referred to as just the "sign test", is used to determine whether there is a median difference between paired or matched observations. The test can be considered as an alternative to the dependent t-test (also called the paired-samples t-test) or Wilcoxon signed-rank test when the distribution of differences between paired observations is neither normal nor symmetrical, respectively. Most commonly, participants are tested at two time points or under two different conditions on the same continuous dependent variable. However, two different groups of participants are possible as part of a "matched-pairs" study design.

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

This "quick start" guide shows you how to carry out a sign test using SPSS Statistics, 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 sign test to give you a valid result. We discuss these assumptions next.

## Assumptions

When you choose to analyse your data using a sign test, part of the process involves checking to make sure that the data you want to analyse can actually be analysed using a sign test. You need to do this because it is only appropriate to use a sign test if your data "passes" four assumptions that are required for a sign test to give you a valid result. You cannot test these assumptions with SPSS Statistics because they relate to your study design and choice of variables. However, you should check whether your study meets these four assumptions before moving on. If these assumptions are not met, there is likely to be a different statistical test that you can use instead. These four assumptions are explained below:

• Assumption #1: Your dependent variable should be measured on a continuous (i.e., interval or ratio) or ordinal level. Examples of continuous variables include weight (measured in kilograms), temperature (measured in °C), salary (measured in US dollars), revision time (measured in hours), intelligence (measured using IQ score), speed (measured in mph), exam performance (measured from 0 to 100), sales (measured in US dollars), and so forth. Examples of ordinal variables include Likert items (e.g., a 7-point scale from strongly agree through to strongly disagree), physical activity level (e.g., 4 groups: sedentary, low, moderate and high), customers liking a product (ranging from "Not very much", to "It is OK", to "Yes, a lot"), the pain felt by patients after hip replacement surgery (e.g., "No pain", "Mild pain", "Moderate pain", "Strong pain" and "Severe pain"), amongst other ways of ranking categories (e.g., a 5-point scale explaining how much a customer liked a product, ranging from "Not very much" to "Yes, a lot"). If you are unsure whether your dependent variable is continuous or ordinal, see our Types of Variable guide.
• Assumption #2: Your independent variable should consist of two categorical, "related groups" or "matched pairs". "Related groups" indicates that the same subjects are present in both groups. The reason that it is possible to have the same subjects in each group is because each subject has been measured on two occasions on the same dependent variable. For example, you might have measured 100 participants' salary in US dollars (i.e., the dependent variable) before and after they took an MBA to improve their employability and salary (i.e., the two "time points" where participants' salary was measured – "before" and "after" the MBA course – reflect the two "related groups" of the independent variable). Since the same participants were measured at these two time points, the groups are related. It is also common for related groups to reflect two different conditions that all participants undergo (i.e., these conditions are sometimes called interventions, treatments or trials). For example, 30 participants undergo a hypnotherapy programme (condition A) and drug programme (condition B) to determine which is more effective (if any) at treating depression.
• Assumption #3: The paired observations for each participant need to be independent. That is, one participant's values cannot influence another participant's values.
• Assumption #4: The difference scores (i.e., differences between the paired observations) are from a continuous distribution. The hazard of breaking this assumption is that there might not be a unique median.

If your study design and data meets these four assumptions, you can run the SPSS Statistics procedure for the sign test, which we illustrate in the Test Procedure in SPSS Statistics section. First, we set out the example we use to explain the sign test procedure in SPSS Statistics.

## Example

A researcher wants to test a new formula for a sports drink that improves running performance. Instead of a regular, carbohydrate-only drink, this new sports drink contains a new carbohydrate-protein mixture. The researcher would like to know whether this new carbohydrate-protein drink leads to a difference in performance compared to the carbohydrate-only sports drink. To do this, the researcher recruited 20 participants who each performed two trials in which they had to run as far as possible in two hours on a treadmill. In one of the trials they drank the carbohydrate-only drink and in the other trial they drank the carbohydrate-protein drink. The order of the trials was counterbalanced and the distance they ran in both trials was recorded.

Therefore, for a sign test, you will have two variables. In this example, these are: (1) carb, which is the distance run (in km) in two hours for the carbohydrate-only trial; and (2) carb_protein, which is the distance run (in km) in two hours for the carbohydrate-protein trial. The researcher would like to determine whether there was a difference in the distance run between the two trials, and therefore, if there is a performance difference between the two different sports drinks. In variable terms, the researcher wants to know if the median of the differences between the carb and carb_protein scores is 0 (zero).

In our enhanced sign test guide, we show you how to correctly enter data in SPSS Statistics to run a sign test. You can learn about our enhanced data setup content on our Features: Data Setup page or access the enhanced sign test guide by subscribing to Laerd Statistics. In the next section, we take you through the sign test procedure using SPSS Statistics.

## Test Procedure in SPSS Statistics

The four steps below show you how to analyse your data using a sign test in SPSS Statistics. At the end of these four steps, we show you how to interpret the results from this test.

1. Click Analyze > Nonparametric Tests > Legacy Dialogs > 2 Related Samples... on the main menu:

Note 1: The procedure that follows is identical for SPSS Statistics versions 17 to 28, as well as the subscription version of SPSS Statistics, with version 28 and the subscription version being the latest versions of SPSS Statistics. However, in version 27 and the subscription version, SPSS Statistics introduced a new look to their interface called "SPSS Light", replacing the previous look for versions 26 and earlier versions, which was called "SPSS Standard". Therefore, if you have SPSS Statistics versions 27 or 28 (or the subscription version of SPSS Statistics), the images that follow will be light grey rather than blue. However, the procedure is identical.

Note 2: We show you the Legacy Dialogs > 2 Related Samples procedure in SPSS Statistics to run the sign test below because this can be used with a wide range of versions of SPSS Statistics. However, you can also run the sign test using the Nonparametric Tests > Related Samples procedure in SPSS Statistics, which is available for versions 18 to 28 and the subscription version of SPSS Statistics. This Nonparametric Tests > Related Samples procedure provides additional statistics and more graphical options than the Legacy Dialogs > 2 Related Samples procedure. Therefore, we show you how to run the Nonparametric Tests > Related Samples procedure and interpret and report the output from it in our enhanced sign test guide. You can access the enhanced sign test guide by subscribing to Laerd Statistics.

Published with written permission from SPSS Statistics, IBM Corporation.

You will be presented with the Two-Related-Samples Tests dialogue box, as shown below:

Published with written permission from SPSS Statistics, IBM Corporation.

2. You need to transfer the variables carb and carb_protein into the Test Pairs: box by highlighting both variables (clicking on both whilst holding down the shift-key) and clicking on the button (N.B., you can also transfer each variable separately). You will end up with a screen similar to the one below:

Published with written permission from SPSS Statistics, IBM Corporation.

Explanation: The above instructs SPSS Statistics to calculate the Wilcoxon signed-rank test on carb_protein minus carb. As such, we need to change this default, which we do in the next step.

3. Deselect Wilcoxon and select Sign in the –Test Type– area. You will end up with the following screen:

Published with written permission from SPSS Statistics, IBM Corporation.

4. Click on the button to generate the output.
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## SPSS Statistics Output of the Sign Test

SPSS Statistics will generate quite a few tables of output for a sign test. In this section, we show you the three main tables required to understand your results from the sign test procedure, assuming that no assumptions have been violated. You should start by interpreting median values and paired differences.

### Median Values and Paired Differences

Before we delve into the statistical results of the sign test, it is best if we first get our bearings by examining the median values we have generated. There are median values for the two trials (i.e., the two groups of the independent variable) and for the paired differences. This information is presented in the Report table, as shown below (the procedure to produce this table is included in our enhanced sign test guide):

Published with written permission from SPSS Statistics, IBM Corporation.

You can see that the table contains the medians of the variables carb and carb_protein, as well as the median of the differences (difference) (i.e., the column names reflect the names of the variables).

### Frequencies Table: Positives, Negatives and Ties

You should evaluate the number of positive, negative and tied paired differences to understand each participant's (relative) response to the two trials. These paired differences will also give you an indication of what to expect for the result of the sign test (remembering that the test is based on the signed differences). This information is provided in the Frequencies table, as shown below:

Published with written permission from SPSS Statistics, IBM Corporation.

You can see how many participants decreased (the "Negative Differences" row), improved (the "Positive Differences" row) or witnessed no change (the "Ties" row) in their performance in the carbohydrate-protein trial (i.e., carb_protein) compared to the carbohydrate-only trial (i.e., carb).

### Test Statistics Table

We can now move on to discovering whether the median of the difference in distance ran between the trials is statistically significant using these signed differences. The result of the sign test is found in the Test Statistics table, as shown below:

Published with written permission from SPSS Statistics, IBM Corporation.

The statistical significance (i.e., p-value) of the sign test is found in the "Exact Sig. (2-tailed)" row of the table above. However, if you had more than a total of 25 positive and negative differences, an "Asymp. Sig. (2-sided test)" row will be displayed instead. We explain the differences between the two ways that the p-value is calculated in our enhanced sign test guide.

### Reporting the Output from the Sign Test

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

• General

Twenty participants were recruited to understand the performance benefits of a carbohydrate-protein versus carbohydrate-only drink on running performance as measured by the distance run in two hours on a treadmill. An exact sign test was used to compare the differences in distance run in the two trials. The carbohydrate-protein drink elicited a statistically significant median increase in distance run (0.113 km) compared to the carbohydrate-only drink, p = .004.

In our enhanced sign test guide, we: (a) show you how to interpret and write up the results of the sign test irrespective of whether you ran the Legacy Dialogs > 2 Related Samples procedure (as illustrated in this guide) or the Nonparametric Tests > Related Samples procedure in SPSS Statistics; (b) provide a more detailed explanation of how to interpret median values and paired differences, as well as positives, negatives and ties, and finally, exact and asymptotic p-values; and (c) illustrate how to write up the results from your sign 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 sign test guide, as well as all of our SPSS Statistics content, by subscribing to Laerd Statistics, or learn more about our enhanced content in general on our Features: Overview page.

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