Overview
A within-subjects factor is an independent variable in which participants are exposed to more than one level. For example, if you are conducting a taste test and the same participants drink several flavors, rating their reaction each time, then flavor is a within-subjects factor and your study is said to use a within-subjects design. If your study involves both a within-subjects factor and a between-subjects factor, it is said to be a mixed design.
Two statistical procedures that are used to analyze within-subjects designs are the paired samples test (also called the dependent t-test) and analysis of variance (ANOVA). A paired-samples test is used if you have only one independent variable and that variable only has two levels. For example, if you measure a groups performance on a test before training and again after training, you would have a two-level, within-subjects independent variable that would be suitable for analysis using a paired samples test.
Paired Samples Test (dependent t-test)
Review: Independent t-test for between-subjects factors
The independent t-test that we learned about earlier 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.
Paired (or dependent) t-test for within-subjects factors
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), type the following in the console input panel:
data(gre)
Data as pairs. Look at the Data Viewer to get a feel for the data:
You can see how the data are arranged in pairs: one score pre test prep and one score post test prep for each subject. Each pre-post set constitutes a pair of scores for a particular subject. Thats 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 both members of a married couple. In the case of heterosexual couples, you could conduct a paired samples test examining whether male partners score differently from female partners, and your data would be responses from both members of several couples. The data are from separate people, but they are arranged as husband-wife pairs. Any time your data can be paired in this way, you would use a paired samples test instead of an independent t-test.
