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Dependent T-Test using SPSS

Introduction

The dependent t-test (called the paired-samples t-test in SPSS) compares the means between two related groups on the same continuous, dependent variable. For example, you could use a dependent t-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). If your dependent variable is dichotomous, you should instead use McNemar's test.

This "quick start" guide shows you how to carry out a dependent t-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 dependent t-test to give you a valid result. We discuss these assumptions next.

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Assumptions

When you choose to analyse your data using a dependent t-test, part of the process involves checking to make sure that the data you want to analyse can actually be analysed using a dependent t-test. You need to do this because it is only appropriate to use a dependent t-test if your data "passes" four assumptions that are required for a dependent t-test to give you a valid result. In practice, checking for these four assumptions just adds a little bit more time to your analysis, requiring you to click a few more buttons in SPSS when performing your analysis, as well as think a little bit more about your data, but it is not a difficult task.

Before we introduce you to these four assumptions, do not be surprised if, when analysing your own data using SPSS, one or more of these assumptions is violated (i.e., is not met). This is not uncommon when working with real-world data rather than textbook examples, which often only show you how to carry out a dependent t-test when everything goes well! However, don't worry. Even when your data fails certain assumptions, there is often a solution to overcome this. First, let's take a look at these four assumptions:

You can check assumptions #3 and #4 using SPSS. Before doing this, you should make sure that your data meets assumptions #1 and #2, although you don't need SPSS to do this. When moving on to assumptions #3 and #4, we suggest testing them in this order because it represents an order where, if a violation to the assumption is not correctable, you will no longer be able to use a dependent t-test (although you may be able to run another statistical test on your data instead). Just remember that if you do not run the statistical tests on these assumptions correctly, the results you get when running a dependent t-test might not be valid. This is why we dedicate a number of sections of our enhanced dependent t-test guide to help you get this right. You can find out about our enhanced content as a whole here, or more specifically, learn how we help with testing assumptions here.

In the section, Test Procedure in SPSS, we illustrate the SPSS procedure required to perform a dependent t-test assuming that no assumptions have been violated. First, we set out the example we use to explain the dependent t-test procedure in SPSS.

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Example

A group of Sports Science students (n = 20) are selected from the population to investigate whether a 12-week plyometric-training programme improves their standing long jump performance. In order to test whether this training improves performance, the students are tested for their long jump performance before they undertake a plyometric-training programme and then again at the end of the programme (i.e., the dependent variable is "standing long jump performance", and the two related groups are the standing long jump values "before" and "after" the 12-week plyometric-training programme).

SPSS

Test Procedure in SPSS

The six steps below show you how to analyse your data using a dependent t-test in SPSS when the four assumptions in the previous section, Assumptions, have not been violated. At the end of these six steps, we show you how to interpret the results from this test. If you are looking for help to make sure your data meets assumptions #3 and #4, which are required when using a dependent t-test, and can be tested using SPSS, you can learn more in our enhanced guides here. We also show you how to correctly enter your data into SPSS in order to run a dependent t-test, as well as explaining how to deal with missing values (e.g., if a participant completed a pre-test but failed to turn up to the post-test). However, in this "quick start" guide, we focus on the six steps required to run the dependent t-test procedure using SPSS.

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Output of the Dependent T-Test in SPSS

SPSS generates three tables in the Output Viewer under the title "T-Test", but you only need to look at two tables: the Paired Samples Statistics table and the Paired Samples Test table. In addition, you will need to interpret the boxplots that you created to check for outliers and the output from the Shapiro-Wilk test for normality, which you used to determine whether the distribution of the differences in the dependent variable between the two related groups were approximately normally distributed. This is explained in our enhanced guide. However, in this "quick start" guide, we focus on the two main tables you need to understand if your data has met all the necessary assumptions:

Paired Sample Statistics Table

The first table, titled Paired Samples Statistics, is where SPSS has generated descriptive statistics for your variables. You could use the results here to describe the characteristics of the first and second jumps in your write-up.

Output for the Paired T Test

Published with written permission from SPSS, IBM Corporation.


Paired Samples Test Table

The Paired Samples Test table is where the results of the dependent t-test are presented. A lot of information is presented here and it is important to remember that this information refers to the differences between the two jumps (the subtitle reads "Paired Differences"). As such, the columns of the table labelled "Mean", "Std. Deviation", "Std. Error Mean" and "95% Confidence Interval of the Difference" refer to the mean difference between the two jumps and the standard deviation, standard error and 95% confidence interval of this mean difference, respectively. The last three columns express the results of the dependent t-test, namely the t-value ("t"), the degrees of freedom ("df") and the significance level ("Sig. (2-tailed)").

Output for the Paired T Test

Published with written permission from SPSS, IBM Corporation.

You are essentially conducting a one-sample t-test on the differences between the groups.

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Reporting the Output of the Dependent T-Test

You might report the statistics in the following format: t(degrees of freedom) = t-value, p = significance level. In our case this would be: t(19) = -4.773, p < 0.0005. Due to the means of the two jumps and the direction of the t-value, we can conclude that there was a statistically significant improvement in jump distance following the plyometric-training programme from 2.48 ± 0.16 m to 2.52 ± 0.16 m (p < 0.0005); an improvement of 0.03 ± 0.03 m.

Note: SPSS can output the results to many decimal places, but you should understand your measurement scale in order to know whether it is appropriate to report your results with such precision.

In our enhanced dependent t-test guide, we show you how to write up the results from your assumptions tests and dependent t-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. It is also worth noting that in addition to reporting the results from your assumptions and dependent t-test, you are increasingly expected to report effect sizes. Whilst there are many different ways you can do this, we show you how to calculate effect sizes from your SPSS results in our enhanced dependent t-test guide. Effect sizes are important because whilst the dependent t-test tells you whether differences between group means are "real" (i.e., different in the population), it does not tell you the "size" of the difference. Providing the effect size in your results helps to overcome this limitation. You can learn more about our enhanced content here.

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