The independent t-test that we learned about earlier (remember the Strohmetz et al. chocolate tipping study?) is used to compare the means of two levels of a between-subjects factor. It is “between subjects” because there are separate, independent subjects in the two levels of that factor. For example, when you randomly assign participants to an experimental or a control condition, then “condition” is a between-subjects factor: people who are in the experimental condition are not also in the control condition.
The independent t-test does not address the situation where you have the same people in two conditions. As mentioned above, an independent variable in which the same subjects are assigned to more than one level is called a “within-subjects” factor. When there are just two levels of the factor, you can think of the data as pairs of data points: each subject measured twice. Each datapoint in one level (e.g., “pre”) is linked to a particular datapoint in the other level (e.g., “post”), making them a pair. A common within-subjects factor is time, where the same subjects are measured at two or more time points.
For example, consider a study in which a group of students takes the GRE test at two time points: before they participate in a GRE prep course and after they participate in it. Our question is whether their scores after the prep course are higher than their scores before the prep course. To access a sample data set with pre-course and post-course scores on the GRE for 20 people (I made these up), download the following Excel file:
Look at the Data Window to get a feel for the data. You can see how the data are arranged in pairs: each subject has one score “pre” test prep and one score “post” test prep. Each pre-post set constitutes a pair of scores for a particular subject. That’s why this type of analysis is sometimes called a “paired samples test”: the data represent samples that are paired together in some way. In this case, they are paired together because the two measurements are coming from the same subjects, but you could have pairs of data that come from separate people. Consider scores obtained from fraternal twins. You could conduct a paired samples test examining whether the male twin in a fraternal twin pair responds differently from the female twin, and your data would be responses from both twins. The data are from separate people, but they are arranged as male-female pairs. Any time your data can be paired in this way and you are interested in differences, you would use a paired samples or dependent t-test instead of an independent t-test.