My data is count data. What I did is identifying if embryos had (yes = 1) or not (no = 0) malformations or delay in their development, within samples of 15 embryos.

In one type of experiment, I repeated this 6 times (6 independent replicates); in another type, I repeated this 9 times (9 independent replicates), so my n is quite low.

I observed a lot of features (between 6 and 12) in every embryo, every 24 hours for 5 days (24 hpf, 48 hpf, 72 hpf and 96 hpf) so I have a lot of data.

My first idea was to do a "repeated measures ANOVA", but unfortunately, my data are absolutely NOT normal distributed; because they're **"binary" counts** (with minimal value 0 and maximum value 15), and I have **lots of ties**.

I tried to use Friedman's test, but it really takes too long! (At least 30 minutes for every feature).

I tried a lot of ways to normalize the data (even one I had never heard before: using the arcsin of the percentage square root…!), but nothing works.

Then a lab mate told me that I could calculate the confidence interval for my controls, and take as "different" from that any value that is outside the CI.

I have the GraphPad Prism program, and it says that for calculating CI, you assume independent and gaussian distributed values. So I got stuck again at the beginning.

How can I calculate a non-parametric CI, using Prism?

On the other hand, I was thinking about using bootstrap, which theory I understand very basically, but I have never done it, and don't know if I can do it with this program.

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#### Best Answer

Instead of worrying about how non-Gaussian your data is, you can go with the fact that it has a nice clear binomial distribution. You need to fit a mixed effects logistic regression model. You can do this with the lme4 package in R (which is free). Use the lmer() function with family=binomial. A search term to use to get more info is "mixed effects generalized linear model".

It's not clear what confidence interval you want (ie estimate of what parameter? average number of malformations? or impact of some other variable on malformation rate?), but whatever your analysis is, the above approach will work.

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