I'm trying to understand the statistical analysis I saw in a clinical study. They measured performance of 3 groups of subjects with a series of performance measures (A, B, C, ..., N). The objective was to find out if there was a difference between the performance of the 3 groups, and if yes, then in which ways they differed.
Their analysis consisted of doing a MANOVA like this:
set.seed(100) group <- rep(c(0,1), each=40) A <- rnorm(80, 5, .5) + .1 * group B <- rnorm(80, 9, .3) + .2 * group + .5 * A C <- rnorm(80, 12, .3) + .2 * group + .7 * B d.1 <- data.frame(A = A, B = B, C = C, group = group) fit.manova <- manova(cbind(A, B, C) ~ group, d.1) summary(fit.manova, test="Pillai") Df Pillai approx F num Df den Df Pr(>F) group 1 0.19669 6.2027 3 76 0.0007949 *** Residuals 78
When they showed they see significant differences, they continued to perform a series of ANOVA tests for each DV, i.e.:
summary(lm(A ~ group, d.1)) summary(lm(B ~ group, d.1)) summary(lm(C ~ group, d.1))
to find out which performance measures where different between the groups.
What I'd like to know is:
- Is this approach (MANOVA followed by series of ANOVA) justified? Are there strict assumptions before we could take this path?
- If yes, should there be some kind of correction for the second step, i.e. series of ANOVAs for individual DVs (multiple-comparisons)? What kid of correction?
- What is the recommended approach for problems like this with multiple DVs?
EDIT 1: changed the text to include an example code.
EDIT 2: updated the example. DVs are now correlated.
EDIT 3: this is actually a very common situation in studies involving objective measures. Devices typically just spit out an array of measures, even if you don't specifically ask for them. For example, you have two groups, a control and patient group, and do a laboratory gait analysis. The gait analysis systems gives you 50 different gait measures. Your research question might be: do the two groups have similar gait? If not, in which ways do they differ?