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.

  • $\begingroup$ It seems to be a common misunderstanding that the assumption of ANOVA is normality of the data, where in fact it is normality of the residuals (en.wikipedia.org/wiki/…). I would try an ANOVA and report the results here, then compare them with nonparametric results. They hopefully agree a lot. $\endgroup$ – Henrik Feb 24 '12 at 20:41

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.

  • $\begingroup$ Hi!First of all, thanks for aswering. Then, I don't understand, you first talk about "mixed effects LOGISTIC regression model, and then about "mixed effects generalized LINEAR model". Finally, I downloaded the R program and the lme4 package... But it's simply chinese for me! :( There's no other "simpler" program to do that? :S $\endgroup$ – mdelsolk Feb 26 '12 at 17:52
  • $\begingroup$ Ah, and I wanted the confidence intervals of mean of every response (malformations). $\endgroup$ – mdelsolk Feb 26 '12 at 17:56
  • $\begingroup$ Logistic regression is a special case of the "generalized linear model", which is a model where the response has one of the exponential family of distributions (which includes both Gaussian and binomial) and can be related to a linear predictor via a link function. The link function can be non-linear - in the case of a response with a binomial distribution it is usually the logit function. $\endgroup$ – Peter Ellis Feb 26 '12 at 23:41
  • $\begingroup$ R does have a bit of a learning curve at first but it repays the effort quite quickly. There's some good resources out there - see eg the answers to stats.stackexchange.com/questions/138/resources-for-learning-r. In terms of alternatives, Stata is reasonably cheap and has mixed-effects logistic regression as an option in its menu. SAS can also do it but is much more expensive and probably not much easier to learn (if at all) than R. MlWin is another altnerative but I haven't used it for 10 years. $\endgroup$ – Peter Ellis Feb 26 '12 at 23:45

Your best bet here is probably multi-level logistic regression. See Dixon (2008) for a simplified discussion of the issues you're facing and some examples on how to do this in R.


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