Let's say I have 100 different types of seeds - Apple, Banana, Celery, ... and I am looking at some data for germination rate. Each individual test is binomial - the seed either germinates or it does not - and so I calculate germination rate by dividing germinated samples by total samples. Unfortunately, I don't have the same number of tests for each seed - For some seeds I may have tested 1000, for others maybe only 10, for some I only tested 1.
When all is said and done, I want to know, which type(s) of seed most likely have the best (or worst) germination rate? I can't simply rank them by germination rate, since I don't have much confidence that a 100% germination rate on a test of 1 seed, is real. I can create a confidence interval - for example using the Wilson interval, which seems to be applicable here - but then I'm still not sure what to look at - the type with the highest number at the low end of the confidence interval? For example if my intervals for 3 types of seeds were:
A: 91% +/- 2% B: 80% +/- 19% C: 93% +/- 5%
Can I say 'A' most likely has the best rate, since the lower end of its confidence interval (89%) is the highest of the 3?
Is there some statistically valid way to rank the results, to find the types most likely to have the best/worst results?
