Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

I'm working with four populations consisting of true/false events. They each have a different mean and variance. I have samples from each, with different sample sizes. Call the percentage of observed true events to samples $p_{11}$, $p_{12}$, $p_{21}$, and $p_{22}$. What statistical test could I use to test the hypothesis that $\frac{p_{12}}{p_{11}} > \frac{p_{22}}{p_{21}}$?

share|improve this question
    
is there any distribution that would work well w/ a hypothesis test of this nature? –  Claudiu Mar 13 '10 at 22:17
add comment

1 Answer

Assume they are four independent beta random variables $X_i$, with means $\mu_i$.

Note that the density functions would depend on the observed samples.

We could then test the hypothesis that $\mu_1\mu_2>\mu_3\mu_4$ by setting up a quadruple integral of the joint density function over the set

$\{ (x_1,x_2,x_3,x_4)\mid x_1x_2>x_3x_4 \}$.

If this integral is small, we reject the hypothesis $\mu_1\mu_2>\mu_3\mu_4$.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.