A repeated measures<\/strong> or paired samples<\/strong> design is all about minimizing confounding variables like participant characteristics by either using the same person in multiple levels of a factor or pairing participants up in each group based on similar characteristics or relationship and then having them take part in different treatments.\u00a0Matched subjects<\/strong> is another word used to describe this kind of test and it is used specifically to refer to designs in which different people are matched up by their characteristics. Participants are often matched by age, gender, race, socioeconomic status, or other demographic features, but can also be matched up on other characteristics the researchers might consider possible confounds. Twin studies are a good example of this kind of design; one twin has to be matched up with the other – they can’t be matched to someone else’s twin.<\/span><\/p>\n To reiterate the differences between a repeated measures t-test and the other kinds of tests you may have learned up to this point, a\u00a0single sample t-test revolves around drawing conclusions about a treated population based on a sample mean and an untreated population mean (no standard deviation). An i<\/span><\/b>ndependent sample t-tests are all about comparing the means of two samples (usually a control group\/untreated group and a treated group) to draw inferences about how there might be differences between those two groups in the broader population. Different, randomly assigned participants are used in each group.\u00a0<\/span>Related samples t-tests are like independent sample t-tests except they use the same person for multiple test groups or they match people based on their characteristics or relationships to cut down on extraneous variables which may interfere with the data.<\/span><\/p>\n The <\/span>mean difference<\/b> is calculated by subtracting the two scores collected from each person (because there are two testing groups), adding all of those differences up, and then dividing that number by the number of scores. This is done because rather than just compare means between the two samples, like in an independent samples t-test, we have the opportunity to first calculate the difference between each individual to see how the treatment affected them.\u00a0<\/span><\/p>\n The <\/span>estimated standard error of the mean difference is<\/span> a measure of how much the mean difference might vary from one occasion to the next. This is different from independent measures because instead of pooling variance between two samples, you base your sum of squares on the difference between the two scores and then calculate the estimated standard error like you would a single sample t test. <\/span><\/b><\/p>\n The null and alternative hypothesis are written as follows:<\/p>\nMean Difference and Estimated Standard Error of the Mean Difference<\/h2>\n
Hypothesis Testing with Repeated Measures t-tests<\/h2>\n