Hypothesis Testing – How to Perform a Binomial Test When Having Replicates? Detailed Procedure

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Let's assume a cell based assay, in which some cells have an irregular shape. We can calculate the proportion of irregularly shaped cells as #irregular/#all_cells.

2 experimental treatments are assayed independently with 3 replicates each. Each replicate is an independently cultured petry-dish, in which cells are counted as described after some time.

Because of the binary outcome per cell, it seems reasonable to assume a bernoulli-distributed random process.

How would I compare such proportion data? A 2-sample binomial test comes to mind, but it's unclear how to include the replicated measurements.

And related to the comparison, I'd like to plot the mean of my proportions and a confidence interval. How would I calculate the CI?

There's a related question for count data in How to calculate confidence interval for count data in R? but I suspect that proportions should be dealt with differently.

Best Answer

Try fitting a binomial Generalized Linear Model - in R , if you have a dataframe called DF with numbers of successes (called "irregular") and failures ("regular") , and a column for treatment/group called Treat, with one Petri dish in each row, you can then do 

Mod <- glm(data = DF, cbind(irregular,regular) ~ Treat, family = "binomial") 
summary(Mod)      #This prints the results, p.values and statistics. 
exp(confint(Mod)) #This gives you the CIs for the different terms in the model
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