# Is two-way ANOVA appropriate?

This is the description of my study. I'm experimenting with three plants: A, B, and C. These plants are supposed to reduce blood glucose for diabetic patients. I want to determine which of these three plants has a longer effect on blood glucose reduction after a single administration into mice. This is done by measuring the blood glucose from mice at 7 time points (day 1, 2, 3, 5, 7, 10, and 14). So there are 4 groups (untreated, treated with A, treated with B, and treated with C). For each group 3 mice were used (n=3). My goals are:

1. To determine if the effect of each plant treatment is significant compared to untreated.
2. To compare the effect of the among the groups for each day.
3. To determine which treated group has the longest effect after 14 days.

My solution is to use two-way ANOVA since there are more than 2 groups and I want to compare the groups in each day and finally the overall effect.

Is the this the correct method? Will I be able to rank which will be the best plant followed by the 2nd and the 3rd? Or should I use time series analysis?

• Do you have any hypothesis about the shape of the decay? You should have one. Then there's no good reason to treat days categorically.
– John
Commented Sep 22, 2013 at 8:11

Every mouse is sampled at seven different time points. These are repeated measurements, and the lack of independence between these repeated measurements violates the assumptions of the standard two-way ANOVA. In addition, there could be differences between the individual mice from the beginning, and taking these individual differences into account could be a good idea.

If all the mice are very similar in their response, and the time itself does not much affect the blood glucose level, this could potentially be analyzed with a two-way ANOVA, but I would rather prefer a repeated measures ANOVA, or more generally a mixed model regression approach.

However, most of the (good) statistical software packages offer the possibility to fit a two-way ANOVA, but not nearly all contain the functionality to fit a mixed model. You do not mention the software you have access to, but this could be a limiting factor, too.

Your sample size is small, so you may have various little issues with not meeting assumptions, but try this.....

2-way repeated measures anova with group as between-subjects IV and time as within-subjects IV. Be sure to include interaction effects. You may encounter issues with sphericity (mauchly's test)

When did the injection take place? If it was after Day 1, an option I'd prefer would be to do a 2-way repeated measures ancova by including day 1 as the covariate.

Comparing each group and time individually post-hoc is not going to be very practical. If the analysis is significant, I'd just plot the data using side-by-side boxplots and make conclusions based on what you see visually. Comparing each group regardless of time, however, should not be too hard.

In #3, you say it like you are only interested in day 14. You could get rid of all days between 1 and 14, and make the analysis much more simple. But I presume this isn't something you'd want to do