I have two samples A and B, both of size 72, drawn from two different populations. I do not know anything about the population, only that they are non normal at all.
I want to know the probability that sample B is drawn from a population whose variance $Var_B$ is smaller than $Var_A$, the variance of the population of sample A, i.e. I need to estimate $P(Var_A>Var_B)$
Data are under the form of percentages, hence from 0 to 1. The means $\mu$ of the two samples are 0.16 and and 0.10
I have performed nonparametric boostrapping, finding out that $P(Var_A>Var_B)=0.95$. So far so good. However, the samples have different means. Do you think I should use some sort of normalized variance, like $Var' =\frac{Var}{\mu(1-\mu)}$?
If I use bootstrapping on this quantity, I find that t $P(Var'_B<Var'_A)= 0.72$. It does not look conclusive.
Can you suggest another approach? Do you think I should worry about the samples not having the same means? Do you think that Levene's and Fligner-Killen test can help in any way (I know they only test the hypothesis that variances are equal)?