I have 3 groups, one control group and two treatment groups that have nothing to do with each other. I just want to see if any of those 2 treatment are different from the control group.
Textbooks say 3 groups or more, use ANOVA to avoid type-1 errors.
But I just don't understand why that applies here. On the one hand, it's only 2 t-tests so doesn't seem like the chance of error is greatly increased. And on the other hand, being that have no interest in differences between the treatment groups, by doing an ANOVA can it not be misleading? (if the two treatments are different from each other but not from the control).
So, should I do an ANOVA and if the means are different perform a "Dunnett's"?
Or just do the 2 t-tests?
Best Answer
You don't have to run an ANOVA first, but most people do out of habit. (Whether reviewers will give you a hard time about not having done so is a separate issue.) Note that the original Dunnett's test required that the conditions have equal $n$s. The test has since been generalized, so it is fine if you do not have equal $n$s, just be sure you are running the right test (and citing it properly). You can also run two t-tests instead of either an ANOVA or Dunnett's test, but if you want to control for type I error inflation, you will need to use the Bonferroni correction as your tests would not be independent.