# Difference between paired t-test and repeated measures ANOVA with two level of repeated measures

Would paired t-test and repeated measures ANOVA with two level of repeated measures on the same data give the same results? I ran a few tests and realized that their p values are the same. Does mean that the two methods are statistical equivalent? But I also find it strange that their assumptions for normality are slightly different, with paired t-test requiring difference in continuous variable to normal while repeated anova requiring the continuous variable to be normal for each level of within subject factor. Please advise.

yes, they are equivalent. these assumptions question has never been directly addressed, though. it is sometimes indicated, that the assumptions you cite for anova, when met, do cover the normality assumption for paired t-test. however, I still wonder, what when the variables are not normal within each subgroup, but their differences (calculated like for t-test) are normal? This should be enough, so the incongruence between these assumptions (as stated in every major statistics handbook) and in your question, are bothering to me too. ;)

• The tests are equivalent because $t^2$ for paired observations is identical to the F-test from repeated measures ANOVA. The assumption you give for the repeated measures ANOVA is not the narrowest, strictly correct one. A more accurate statement is more complex to state and probably wouldn't be helpful or informative for novices. You might want to look up sphericity and Mauchly's test for more information. Jul 3, 2017 at 14:01

As both are equivalent, "bivariate" repeated measures Anova works as well if only the differences are normally distributed. The more strict repeated measures requirements in the literature are only necessary if more complicated layouts with more factors and other hypotheses are included, in particular between subject factors and unequal sample sizes / heteroskedasticity between them.

I also find in my research that the results are sometimes different. The paired-samples t-test shows no statistical significance, while the repeated measures anova witihin subjects factor shows significance in both groups. My two groups of speakers are different in numbers (49 and 23) and from the paired samples test I find no significance for the second group, whereas repeated measures ANOVA shows significance for both groups.

• This does not provide an answer to the question. Once you have sufficient reputation you will be able to comment on any post; instead, provide answers that don't require clarification from the asker. - From Review Dec 24, 2021 at 11:55
• As a side note, most statisticians consider repeated measures ANOVA to have become obsolete 20 years ago, in favor of mixed effects models, generalized least squares, and Markov process models. Dec 24, 2021 at 13:16
• @mdewey This looks like a direct answer to the question articulated in the first sentence of the original post. It would be nice, however, to see an explanation concerning why the results differed or to have some description of these data that would help us understand the reason.
– whuber
Dec 24, 2021 at 15:26

No, they are different. I did both in SPSS and found very different results for a same dependent variable. In the paired samples t test, the change is significant (p<.01), whereas in the repeated measures ANOVA, the change is insignificant (p>.05).

• That sounds strange. Can you please include the details of how you did this in spss? Feb 27, 2021 at 16:22