I am exploring a tree structured as follows:
A/ parent node = parent population, size N, with a proportion of success for an experiment (eg. p = nb success / N)
B/ child nodes = sub populations for a give parent node. Ex.: level one child sizes are n1, n2, ... nn, where n1 + n2 + ... + nn = N. Success proportions are also computed (p1 = nb1 success / n1, ..., pn = nbn success / nn)
This could be summarized by the enclosed picture. What I am trying to do is cut the nodes where the proportions of success are not statistically significant. In other words, how can I trust the proportion of success for a given node, according to its population size?
The context of this question is pretty specific: p, p1, ... are always very low (between 0 and 0.0002, and node size can vary a lot, from 10 to several thousands of observations.
So how can I compute the minimum node size, so that I can consider a node proportion of success as statistically significant? Moreover, do I have to do a computation for each of the tree node, do I have to take the dependencies between the nodes into account, or is a global approximation for all the nodes acceptable?
I'm working with R. My first insight was use the prop.test function for all node and check the p-value, but I realize this completely wrong.
As anyone an idea to deal with this tricky problem?