I want to calculate the sample size required to detect a 50% change in the probability of an binary outcome.
The base probability is .2. A 50% increase would go from .2 to .3. A 50% decrease would go from .2 to .1.
In this example, assuming a normal distribution, it should be easier to detect an increase compared to a decrease because there will be more observations in the former. Using power.prop.test in R confirms that the former requires a smaller sample size. However, using pwr command gives only a single sample size. How is that single sample size derived?