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.

• 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. – David Smith Jul 3 '17 at 14:01