I have minimal statistics knowledge (biologist, I know its not a good excuse) and was hoping to get some help with this analysis. I am measuring the area of muscle fibers in mice, where one muscle is damaged (D) and the other is undamaged (U); this is done to control mice as well as a group treated with a drug. I hope to evaluate whether the drug affects muscle regeneration, using fiber size as a proxy of how well they have healed. Each muscle has about 100 fibers but the numbers are unequal, each mouse has one D and one U muscle, and each treatment has 3 mice.
Initially I was simply pooling all the fiber diameters and using ANOVA (like, control-D, control-U, drug-D, and drug-U) but I've noticed that the values vary considerably between mice regardless of whether they had the drug or not. I am hoping instead then to take the ratio of the mean D vs mean U muscle for each mouse, and compare the populations with a t-test; this sounds like it would better represent the question. I have no idea however to perform the test - I have the standard deviations from finding the means for each muscle, but what happens when I take the ratio of damaged to undamaged? How can I determine if the drug had a significant effect on these ratios?
If anyone can point me to more information, or recommend a better way of approaching this question, that would be fantastic!
What you should be using is an odd's ratio test. You need to construct a table that looks like this. This is a standard Odd's Ratio:
-------------------------------------------------
Trial Drug (+) | Control (-)
Exposed (+) a | b
---------------------------------|---------------
Not Exposed (-) c | d
---------------------------------|---------------
So I think your Odd's ratio would look something like this:
|---------------------------------------------------------|
| Trial Drug (+) | Control/Placebo (-) |
| # Damaged Muscles (+) a | b |
| --------------------------------|-----------------------|
| # Non-Damaged Muscles (-) c | d |
| --------------------------------|-----------------------|
Odds Ratio = (a / c) / (b / d)
= (a * d) / (b * c)
I think what an Odd's Ratio (OR) means is that if OR > 1, then your drug has a positive (+) effect on muscle repair. If OR = 1, then your drug has statistically no difference than using your control drug or placebo. So it doesn't matter. If OR < 1, then your drug has a worse effect on the muscle repair than your control/placebo, so it's damaging your mice.
a,b,c, & d probably would represent the sum of mice in each condition.
For more detailed information about how to do an Odd's Ratio and OD's Ratio confidence Intervals you should read up on this from the National Institute's of Health.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2938757/
Since you are dealing with Factor's you might want to use a Pearson's Chi-Squared Test on your 2 by 2 table when you make it a matrix, and that's how you can get your p-value. This can be computed in R, as you can see ...
Good luck!