> power.prop.test(p1=0.1, p2=0.11, power=0.8,sig.level=0.05)
Two-sample comparison of proportions power calculation
n = 14750.79
p1 = 0.1
p2 = 0.11
sig.level = 0.05
power = 0.8
alternative = two.sided
NOTE: n is number in *each* group
Edit: so that's 30,000 samples. To do the same with a 5% change in the same area is still 1300 samples (alpha=0.8, p=0.05)
I normally consider relative minimum discernable effect. Your 5% absolute change is a 50% increase is the base rate. I also typically go for a higher power (e.g. 0.9). Under these conditions 60K samples is more typical.
You're right. That's a bit more reasonable, so back to my 10% change in base rate (1% abs.) but with a 90% power:
> power.prop.test(p1=0.1, p2=0.11, power=0.9,sig.level=0.05)
Two-sample comparison of proportions power calculation
n = 19746.62
p1 = 0.1
p2 = 0.11
sig.level = 0.05
power = 0.9
alternative = two.sided
NOTE: n is number in *each* group
Requires about 40,000 samples per test. I would strongly recommend anyone serious about doing this look in to MAB testing, as A-B testing is way too expensive for reasonable scale testing (unless you have a strong a priori hypothesis to test).