An experiment was run 10 times in configuration a and there were A failures, 10 times in configuration b giving B failures, 10 times ... (in all 9 different configurations). I have a list of 9 numbers giving the number of failures for each configuration (out of 10).
4 4 4 3 3 2 0 2 10
I suspect the configuration makes no difference and that the failure counts might have a binomial distribution (it is tempting to classify that 10 as an outlier and remove it).
Feeding the above list of values into R's prop.test function, along with the probabilities for a binomial distribution with p=0.3556 (the mean of failure count/10) generates a warning that the Chi-squared approximation may be incorrect; not surprising giving the small sample size.
A qq-plot would also suffer from the same sample size issues.
Is there a "Fisher's exact test" equivalent for testing whether a sequence of values might be drawn from a binomial distribution?
A related but different experiment produced a failure count sequence of (no outliers here :-):
10 8 7 10 9 9 10 8 7