Sample size for proportions in repeated measures I'm trying to help a scientist design a study for the occurrence of salmonella microbes.  He would like to compare an experimental antimicrobial formulation against a chlorine (bleach) at poultry farms.  Because background rates of salmonella differ over time, he plans to measure % poultry w/salmonella before treatment, and after treatment. So the measurement will be the difference of before/after % salmonella for the experimental vs. chlorine formulas.  
Can anyone advise on how to estimate the sample sizes necessary?  Let's say the background rate is 50%; after bleach it's 20%; and we want to detect whether the experimental formulation changes the rate by +/- 10%.  thank you
EDIT:
What I'm struggling with is how to incorporate the background rates. Let's call them p3 and p4, the "before" salmonella rates for bleach and experimental samples, respectively. So the statistic to be estimated is the difference of differences: Experimental(After-Before) - Bleach(After-Before) = (p0-p2) - (p3-p1). To fully account for the sampling variation of "before" rates p2 and p3 in the sample-size calculation --- is it as simple as using p0(1-p0)+p1(1-p1)+p2(1-p2)+p3(1-p3) wherever there's a variation term in the sample-size equation? Let all samples sizes be equal, n1 = n2 = n.
 A: Let's take a stab at a first-order approximation assuming simple random sampling and a constant proportion of infection for any treatment.  Assume the sample size is large enough that a normal approximation can be used in a hypothesis test on proportions so we can calculate a z statistic like so
$z = \frac{p_t - p_0}{\sqrt{p_0(1-p_0)(\frac{1}{n_1}+\frac{1}{n_2})}}$
This is the sample statistic for a two-sample test, new formula vs. bleach, since we expect the effect of bleach to be random as well as the effect of the new formula.
Then let $n = n_1 = n_2$, since balanced experiments have the greatest power, and use your specifications that $|p_t - p_0| \geq 0.1$, $p_0 = 0.2$.  To attain a test statistic $|z| \geq 2$ (Type I error of about 5%), this works out to $n \approx 128$.  This is a reasonable sample size for the normal approximation to work, but it's definitely a lower bound.
I'd recommend doing a similar calculation based on the desired power for the test to control Type II error, since an underpowered design has a high probability of missing an actual effect.
Once you've done all this basic spadework, start looking at the stuff whuber addresses.  In particular, it's not clear from your problem statement whether the samples of poultry measured are different groups of subjects, or the same groups of subjects.  If they're the same, you're into paired t test or repeated measures territory, and you need someone smarter than me to help out!
