Let's say we have a population of N = 10,000, and we want to find each individual with a certain trait T. This trait has a likelihood of occurrence of P = 0.01, so E(T) = 100 in our population. Assuming we can group individuals together and test them as a pool, what is the most efficient grouping structure to reduce the # of tests required?
CSV Naming
TRIALS-POPULATION-PROBABILITY-DIVISOR-GROUPRANGE.csv
Possible solution: calculate the 'expected contribution' (i.e. how many people we expect to determine as having/not having it) for each group size - the group size with the highest expected contribution should be the best.
C(x) = x * (q ^ x)A group of x people has a q^x probability of having none with the trait (where q = 1 - p and p is the likelihood of occurrence).
The derivative C'(x) shows an intercept at (99.499, 0), indicating C(x) peaks at X = 99.499. Very odd that this doesn't seem to be proportional to population size.