# Repeated measures anova or ancova ... or other!

I'm working on a trial and would really like some suggestions on how to analyse my data.

The study is a randomised crossover trial. I am interested in glucose response to three different lengths of an exercise. Each invididual will undergo one of three different lengths of exercise per lab day (0, 30 and 60 minutes). There are 6 measurement periods: pre exposure, post exposure time 1, 2, 3, 4 & 5.

Data is assumed to be normal

Dependent continuous: glucose

Independent categorical: exercise length (0, 30 and 60 minutes)

I have a two questions: #1 Would repeated measures (within subjects) anova be appropriate in this case? Or is linear mixed model more appropriate?

#2 However, I also plan analysing by age (older and younger adults) as I want to know if the age of participants effects the outcome. Would this case mean that I could use age as a covariate and therefore use ANCOVA? Or maybe something else?

Question 1. Chapter 7 of Frank Harrell's course notes and book discuss different ways to handle longitudinal data. For a simple situation like this, his suggestion to try generalized least squares would seem to be a good choice. That allows for a wider range of correlation structures than simple repeated-measures models to handle the correlations within individuals, and it doesn't require measurements at the same times for all individuals (and thus can handle missing data). Generalized least squares doesn't impose a Gaussian distribution of random effects, as a mixed model would. It's implemented, for example, by the gls() function in the R nlme package; Harrell provides a useful wrapper for gls() in the Gls() function of his rms package.