The paired-samples t-test is used to determine whether the mean difference between paired observations is statistically significantly different from zero. The participants are either the same individuals tested at two time points or under two different conditions on the same dependent variable. Alternatively, you could have two groups of participants that have been matched (paired) on one or more characteristics (e.g., IQ, age, gender, etc.) and tested on one dependent variable. The paired-samples t-test is also referred to as the dependent t-test, repeated measures t-test, or simply abbreviated to the paired t-test.
For example, you could use a paired-samples t-test to understand whether there was a mean difference in dieters’ daily calorie consumption before and after a six week hypnotherapy programme (i.e., your dependent variable would be “daily calorie consumption”, and your two related groups would be calorie consumption values “before” and “after” the hypnotherapy programme). You could also use a paired-samples t-test to determine whether there was a mean 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”).
In order to run a paired-samples t-test, there are four assumptions that need to be considered. The first two relate to your choice of study design and the nature of your data, whilst the second two relate to the paired-samples t-test itself:
- Assumption #1: You have one dependent variable that is measured at the continuous (i.e., ratio or interval) level. Examples of continuous variables include revision time (measured in hours), intelligence (measured using IQ score), exam performance (measured from 0 to 100), weight (measured in kg), and so forth. If you are unfamiliar with any of the above terms, you might wish to read our Types of variables guide.
- Assumption #2: You have one independent variable that consists of two categorical, related groups or matched pairs (i.e., a dichotomous variable). “Related groups” indicates that the two groups are not independent. The primary reason for having related groups is having the same participants in each group. It is possible to have the same participants in each group when each participant has been measured on two occasions on the same dependent variable. For example, you might have measured 10 individuals’ performance in a spelling test (the dependent variable) before and after they underwent a new form of computerized teaching method to improve spelling. You would like to know if the computer training improved their spelling performance. The first related group consists of the participants at the beginning (prior to) the computerized spelling training and the second related group consists of the same participants, but now at the end of the computerized training. The paired-samples t-test can also be used to compare different participants (e.g., matched pairs), but this does not happen as often.
- Assumption #3: There should be no significant outliers in the differences between the two related groups. If there are any difference scores, difference, that are unusual, in that their value is extremely small or large compared to the other scores, these scores are called outliers (e.g., 8 participants in a group scored between 60-75 out of 100 in a difficult maths test, but one participant scored 98 out of 100). Outliers can have a large negative effect on your results because they can exert a large influence (i.e., change) on the mean and standard deviation for the difference scores, which can affect the statistical test results. Outliers are more important to consider when you have smaller sample sizes because the effect of the outlier will be greater, all other things being equal. Therefore, in this example, you need to investigate whether the difference scores between the two paired observations (i.e., the difference scores) contain any outliers.
- Assumption #4: The distribution of the differences in the dependent variable between the two related groups should be approximately normally distributed. The assumption of normality is necessary for statistical significance testing using a paired-samples t-test. However, the paired-samples t-test is considered “robust” to violations of normality. This means that violations of this assumption can be somewhat tolerated and the test will still provide valid results. Therefore, you will often hear of this test only requiring approximately normal data. Furthermore, as sample size increases, the distribution can be very non-normal, and thanks to the Central Limit Theorem, the paired-samples t-test can still provide valid results. Therefore, in this example, you need to investigate whether the difference scores between the two paired observations, difference, are normally distributed.
SPSS Statistics will have generated two tables that contain all the information you need to report the results of a paired-samples t-test. In this section, we explain how to interpret these two tables, including descriptive statistics, the differences between trials, statistical significance and the null and alternative hypotheses, as well as showing you how to calculate an effect size.
- SPSS Statistics will have generated two tables that contain all the information you require to report the results of a paired-samples t-test.
- You can start by presenting some useful descriptive statistics from the SPSS Statistics output that will help you get a “feel” for your data (and will also be used when you report your results). Next, we discuss how to evaluate the differences between the two variables (i.e., carb_proteinminus carb), as well as different measures of variability you can consider, including the standard deviation, standard error of the mean and 95% confidence intervals.
- After you have reported the magnitude (size) of the mean difference and its likely range, you can determine whether there is a statistically significant mean difference between your two related groups, including how to interpret the t-value, degrees of freedom and p-value. Based on this result, we explain how to report the null and alternative hypothesis.