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# Should I use a dependent samples t-test or repeated measures ANOVA?

Posted July 13, 2020

For students learning about statistics, some ask whether they should use an dependent samples t-test (also called a paired samples t-test) or a repeated-measures ANOVA.  Let’s start at the beginning.  Both of these tests assess differences across the same observations (or pairs) on scale level variables.  For example, is there a difference in GPA at time 1 and GPA at time 2, or is there partner agreement on Extraversion, etc.

### Assumptions

Both the dependent samples t-test and the repeated measures ANOVA have the same assumptions: normality and homogeneity of variance.  The normality assumptions can be assessed with a Shapiro Wilks test or by a Q-Q scatterplot for normality.  The homogeneity of variance test is often assessed with the Levene’s test.  In the Shapiro and Levene’s test, a non-significant result is good and indicates that the assumptions of the paired sample t-test or repeated measures ANOVA are met.

So which one should I use?

For a test of difference in a scale variable measured at two time points (GPA at time 1 and time 2) or by a paired samples (partner responses), the resulting t-value and F-value are equivalent, and the probability is exactly the same.  If the probability is 0.05 or less, we conclude that the means differ across pairs (or time periods).

Caveat

If your dependent variable is measures at three or more time periods (GPA at time 1, time 2, and time 3) or if your outcome measure has three corresponding values (partner 1, partner 2, and child), then you must use the repeated measures ANOVA.  The dependent samples t-test only permits variables at only two time periods.

If you want to see for yourself, you can go to www.IntellectusStatistics.com, try it for a week for free, download an example dataset, then run both the paired samples t-test and the repeated measures ANOVA.

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