# 1 control group vs. 2 treatments: one ANOVA or two t-tests?

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?

• The null hypothesis of the global F-test from ANOVA is of no importance here, so there is no reason to run an F-test first and then, depending on its "answer", dig deeper. If you want to test the two working hypotheses "First treatment is systematically different from control" and "Second treatment is systematically different from control", then the two t-tests might be the best way to go (depending on groups sizes etc.) Dec 2, 2013 at 18:33
• By "systematically" I mean "on average" here. Wasn't too clear. Dec 2, 2013 at 18:39
• You can go straight to Dunnett's test if you want to control the family-wise error rate; or, as @Michael says, do two t-tests, if you want to control the individual error rates for each. Dec 2, 2013 at 20:21
• Will you be making any inferences of the kind, "A-control was significant while B-control was not significant and therefore there is a difference between A and B"? If so, then Dunnett's or two t-test are definitely not sufficient for your analysis.
– John
Dec 2, 2013 at 20:22
• Note that the two treatments cannot be "different from each other but not from the control", although you could find a pattern 'significant' contrasts that logically necessitates there are some type I or type II errors (more here, if you're interested). Dec 2, 2013 at 22:39

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.