Bayes Rule for haploid identification
Two genotypes: haploid and diploid.
Over a series of 9 days, root lengths on various plants are measured. The goal is, for a new sample, determine whether the sample comes from a haploid or a diploid based on its root length.
Advice
Use Bayes Rule. Let H be haploid and L>k be the event the root length is greater than a cutoff of k. Bayes Rule says
P(H  L>k) =  
P(L>k  H)P(H)/(P(L>k  H)P(H) + P(L>k  D)P(D)) = 
1/[P(L>k  D)/P(L>k  H) x P(D)/P(H)] 
where
 P(H) is the prevalence of haploids, P(D) = 1P(H)

P(L>k H), [P(L>k D)] is the probability a haploid [diploid] has root length greater than k
The prevalence needs to be determined from external data, but the probability the root length is greater than k can be determined from the data at hand. Uncertainty could be incorporated in these probabilities by assuming a prior.
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