# Is this a valid experimental design?

An experiment to test 2 new treatments was performed in the following setup:
Animals were divided into 2 groups: young (A) and old (B). Animals were present for 3 periods. Each group consisted of 81 animals during the first period; 80 during the second period; and 66 during the third period.
The measurements in the consecutive periods were made on the same animals, only the number of animals changed as some of them got sick or died from reasons not related to the experiment. The highest total number of unique animals in the trial at any point in time was 2*81=162, present at the start.
The set up was the following:


Period
1               2             3
A    Standard        Treatment       Treatment
Treatment            X               Y
Group
B   Treatment        Treatment        Standard
Y               X            Treatment


The response variable ranges from zero to 100,000 with most of the values being zero i.e. Poisson distribution.

My questions are:
1) If this is a correct experimental design, what is its name?
2) How to analyze such an experiment? Looking at the distributions of variables that were measured (bacterial count), some kind of non-parametric tests will be needed.

EDIT: I am thinking of analyzes using generalized mixed model approach, but I am worried if the experiment was designed in a proper way so that the obtained results are trustworthy.

• Total number of animals is 81 * 2 = 162 or (2*81 + 80 + 66)? The largest bacterial count could be what? 3, or 300,... – user158565 Nov 8 '18 at 3:17
• Thank you for the comment. I have edited my question to answer your comment. – mapis Nov 8 '18 at 7:26
• It's a crossover design, which can be analyzed using repeated-measures procedures. If you've randomly assigned animals to groups, it's a randomized crossover design. I've edited your post; I hope I've preserved your intended meaning. – rolando2 Nov 8 '18 at 20:35
• Curious readers will want to know whether you've tested the fit of your bacterial count variable to a Poisson distribution. – rolando2 Nov 8 '18 at 20:40
• Thank you @rolando2 for your edits and for your answer. The assignment to the groups was not random. It was based on the age (young vs. old). I have not tested the distributions yet. I will provide an update on that. – mapis Nov 12 '18 at 9:10