There are helpful questions and answers for how to calculate the required sample size (or carry out a power analysis) for MANOVA, but not for MANCOVA using the freely-available G Power software.
Is there a way to do so for MANCOVA using G*Power?
The specific MANCOVA has:
- three continuous response variables
- a categorical predictor variable with six groups
- three other continuous predictor variables
We're interested in carrying out a power analysis for the main effects of the categorical predictor variable, the main effects of the three other continuous variables, and, potentially, the interaction between the categorical predictor variable and one of the three continuous predictor variables.
I'm open to other software, especially if it is open-source or freely available.
Best Answer
Specifying a power analysis for a manova (or mancova, same thing really) is hard because there are so many things to think about, and some of these don't get reported in the output. E.g. power of manova is affected by the consistency of the effects across predictors and the [1] correlations between the outcome variables - and the correlations between the outcomes isn't something that's often thought about. You also need to consider the correlations between the predictors, and you have 8 predictors (5 dummy coded, three continuous) so there are 36 correlations (or covariances, plus 8 variances) that you need to specify.
You need to consider that you will be looking at univariate tests and multivariate tests, and for the multivariate tests you need to worry about the sphericity assumption, if that will be violated, if you will use a correction, or if you will use the lower bound estimates.
I know of three approaches to getting the power - first, you can use the SPSS MANOVA function (if you have SPSS) [2]. SPSS has a power option in manova, which is a bit weird and useless (because it's a transformation of the p-value. This could be written in any program, but I've never seen it implemented anywhere else.
Second, you can use a structural equation modeling (SEM) approach [3]. SEMs make specifying the model and estimating the power much easier, and you can use a free package like Lavaan (which is part of R).
Finally, you can run a simulation, and you can do that in any software you like.
My approach would be to make a whole lot of simplifying assumptions, and make them on the conservative side (so your power is underestimated, rather than overestimated), and then run a simulation.
[1] https://psycnet.apa.org/buy/1994-32083-001
[2] https://link.springer.com/article/10.3758/BF03195405
[3] https://bmcmedresmethodol.biomedcentral.com/articles/10.1186/1471-2288-3-27