# ANOVA or t-test and multiple testing

I have 7 groups, one healthy group and 6 treatment groups and 5 traits. I would like to test for each trait if there are any significant difference between each treatment group and healthy group.

Would it be more appropriate to perform a T-test for each trait or ANOVA? In case T-test is the answer, should I consider adjustment for 6x5=30 tests (i.e. 0.05/30)?

The usual approach is to perform ANOVA and, if ANOVA shows significant differences, perform group comparisons making adjustments for multiple comparisons.

The adjustment you propose would be Bonferroni correction which is widely used (because it's simple) but rather conservative. You might be interested in some alternatives.

• The only virtue of Bonferroni is it is simple. The problem is not it is conservative, but that it is ridiculously conservative. Much, much,better to use Dunnett, FDR, or some of the cool tools in the multcomp.
– Tim
Feb 21, 2017 at 4:09
• I don't see any value in doing the ANOVA. If all treatment effects are very similar then the power of ANOVA will be low. Feb 21, 2017 at 5:31

There is no need to do an ANOVA first if your method for comparing means controls the Type I error rate adequately. For the problem of comparing multiple groups with a control, I would recommend Dunnett's test. Because you have multiple traits, the Dunnett test results should be corrected for the number of traits with the Bonferroni adjustment.

• Isn't a problem with doing Bonferroni after Dunnett that the traits are likely correlated, but Bonferroni does poorly with correlated tests? Something like the false discovery rate correction would be my pick either after doing Dunnett, or, on all the p-values.
– Tim
Feb 21, 2017 at 4:12
• Bonferroni is conservative with correlated tests so does control the Type I error rate although it can have low power. FDR correction is a good alternative. Feb 21, 2017 at 5:25

Doing multiple t-tests increase the error (type I). It is better to do first an ANOVA and if there is a significant difference, then you can do a dunnett test (dedicated for comparison between a control group and other groups) or a Tukey test (multiple comparison).