Error values for pooled groups?

Question

We have 9 cages of mice, 5 (genetically identical, age- and sex-matched) mice per cage. They receive 3 treatments, so 3 cages per treatment. Among the ways to evaluate treatments is to monitor weight change (i.e. repeatedly weigh the individual animals). However, individual mice are not marked in the cages, so we don't know how individual mice change, other than cage averages. For example, we might have values like this ...

Cage 1, day 1: 18.1 gm, 19.1 gm, 18.7 gm, 18.5 gm, 19.5 gm
Cage 1, day 3: 19.1 gm, 18.8 gm, 18.9 gm, 18.4 gm, 20.1 gm
...

Cage 2, day 1: 18.8 gm, 19.0 gm, 18.1 gm, 18.2 gm, 19.9 gm
Cage 2, day 3: 17.3 gm, 16.9 gm, 17.1 gm, 18.2 gm, 18.4 gm
...

and so on.

Our question is of course the significance of the weight differences between the treatment groups. Is it possible to use a repeated measures approach on this? If so, how? If not, what's the most appropriate technique? What if we only have one cage per treatment instead of three?

Answer 1

If the same 5 animals stay in each cage during the study, then I see no reason why you couldn't use the cage as a repeated measure, say on the average weight per mouse in the cage. Then you would be analyzing 3 cages for each treatment in your original statement. If you only have 1 cage per treatment, that wouldn't be a good way to proceed as there is no way to estimate variability among cages within a single treatment, which is what you need to know to determine if the treatments have different effects.

In practice you might be better off in this case by ignoring the fact that the same individuals are involved and treat them as independent. That's not a very satisfying solution and can lead to problems of its own. The question is somewhat analogous to the issue of when to prefer paired versus unpaired t-tests. Paired comparisons are typically more powerful, but not always.

As always, the best advice is to consult a statistician before running the experiment. Notching the ears of mice is one humane way to identify individual mice within a cage.