# Questions about number of groups and group size in planned comparisons in ANCOVA

I have three questions.

1. I want to conduct a planned comparison in ANCOVA which compares three groups (n=2, n=7 and n=5) with two groups (n=11 and n=25). Is it ok to include the group with n=2 if I am only conducting a planned comparison as described above?

2. Is it ok to conduct an ANCOVA when I am only comparing two groups? E.g. if I wanted to compare left and right hemisphere groups, controlling for another variable.

3. If the DV in an ANCOVA has been transformed (because it was non-normal) does the covariate have to undergo the same transformation? E.g. If the DV is (log transformed) heart rate during an experimental condition, and the covariate is heart rate measured at baseline (which is normally distributed), does the baseline HR need to be transformed as well?

## 1 Answer

First off, with such small N, I think anything that comes close to statistical significance is going to pass the inter-ocular trauma test - it will hit you between the eyes.

I am not sure what you mean by compare 3 groups with 2 groups. Do you mean you want to combine the three groups into one, and the 2 groups into another and then compare? Whether this is reasonable or not depends on whether it makes substantive sense to combine these groups. But then the group sizes are a bit larger, which is good.

ANCOVA is fine with only 2 groups.

No, what you do to the DV does NOT have to be done to the IVs. The topic of transformations is a complex one, but this is an easy question to answer. Of course, whether it is right to transform your DV in this way is a different matter.

• To Peter's good comments, I'll add that it's hard to imagine any audience/consumer of this research who is going to give it any credibility with these sample sizes. Can you say something about the context and purpose of the research? Mar 17 '11 at 11:53
• @rolando2 "credibility" is usually associated with statistical significance, which is only indirectly related to sample size, as @Peter suggests in the first sentence. If the effect size is expected to be large, why use a large sample?
– whuber
Mar 17 '11 at 19:48
• @rolando2 the research is investigating the effect of brain surgery on different psychophysiological measures, including heart rate. The groups are defined according to areas of the brain that have been lesioned. For most DVs the smallest group is n=4 and I am using nonparametric tests, but for HR I wanted to covary the effect of baseline HR out so I used ANCOVA. However due to medications some patients had to be excluded, resulting in smaller ns, so I used planned comparisons with SPSS syntax to compare three theoretically related smaller groups together with the two larger control groups. Apr 24 '11 at 3:58