# ANOVA for difference between three percentage differences

This question is deliberately similar to a previous question: test for difference between two differences (proportions) because although the answer by StevenP was very useful, it only answered part of the question.

I have data for an analyte measured in the same people at two different times, and a fixed effect factor (genotype) which separates the subjects into 3 groups. We suspect that the percentage change (between times 1 and 2) between the 3 groups differs (note that the absolute change is not thought to be so important).

StevenP's answer was to use ANOVA with repeated measures and to check assumptions (presumably the sphericity assumption is not necessary as there are only 2 times). However, the interaction between group x time will give an indication of whether the absolute changes over time are significantly different between the 3 groups, not the percentage changes.

My question is, therefore, how to proceed with a legitimate ANOVA assessment of percentage changes ?

I suppose this question is really about how the variance is assessed and included in the analysis when the outcome is a combination of several variables. In the case of the absolute differences, for the combination outcome "measurement at time 2 minus mesaurement at time 1", a repeated measures ANOVA nicely takes into account the variance at time 2 and the variance at time 1.

However, what happens when the combination outcome is "measurement at time 2 minus measurement at time 1, divided by measurement at time 1" ?? My own feeling is that the variance at time 1 is already included in the percentage along with the variance at time 2, when the proportion or percentage was created (for each subject), and therefore a simple one-way ANOVA is needed for the percentage data only - is this correct ?