I have four sample groups. I want to compare group 1 to group 2 and compare group 3 to group 4, as I have have 2 hypothesis to test.
Should I use ANOVA with post hoc tests or run two separate t-tests?
I'm assuming you want to compare means between independent groups. I would recommend ANOVA with a priori defined contrasts since you have specific hypotheses regarding which groups should differ.
ANOVA provides for a more powerful test of group mean differences because the standard error of the mean difference is based on MS_within groups, which uses information from the entire design (the entire sample = all 4 groups). In contrast, the standard errors of the mean differences with 2 individual t tests would only be based on the sample sizes from 2 groups, respectively, and thus provide less statistical power to reject the null hypothesis of equal group means.
The ANOVA contrast test of the mean difference between two groups also has more degrees of freedom than does the conventional 2-group t tests.
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