Single subject anova I collected walking speed data over 2 weeks for a single subject. These different walking speed were separated into 7 different groups based on whether they were extracted during a shorter or longer walk. I would like to determine whether the mean and the variance of walking speeds from the different groups are different. I am unsure which statistical test is appropriate as I have only one subject. (also, the sample size in each group is different, going from 199 to 1093 values of walking speed...)
Thank you.
 A: You seem to have data with a nested structure: Some of the response values were obtained in the same bout. This may cause dependence between values observed within the same bout, which can be accounted for using a mixed-effect model.
I assume you are using R and have variables similar to the following in your dataset (dat): group (factor; predictor), speed (continuous; response), bout (factor; cluster identifier)
You can test for equality of means as follows:
library("nlme")
mod <- lme(speed ~ group, random = ~1|bout, data = dat)
anova(mod)
VarCorr(mod) 

The last rule is to check on the dependence within bouts. Higher values for the (Intercept) term indicate stronger dependence within bouts.
You can test for equality of variances as follows:
library("car")
leveneTest(residuals(mod) ~ dat$bout)

Perhaps unnecessary to add, but I would do a visual inspection of the data beforehand:
boxplot(speed ~ group + bout, data = dat)

or:
boxplot(speed ~ bout, data = dat) 
boxplot(speed ~ group, data = dat)

This will also help identify which groups differ, if any of the F-tests come out significant.
