R in a Nutshell, 2nd Edition

Proportion Test Design

If you are designing an experiment where you will be measuring a proportion (using prop.test), you can use the power.prop.test function:

power.prop.test(n = NULL, p1 = NULL, p2 = NULL, sig.level = 0.05,
                power = NULL,
                alternative = c("two.sided", "one.sided"),
                strict = FALSE)

For this function, n specifies the number of observations (per group), p1 is the probability of success in one group, p2 is the probability of success in the other group, sig.level is the significance level (Type I error probability), power is the power of the test (1 − Type II error probability), alternative specifies whether the test is one or two sided, and strict specifies whether to use a strict interpretation in the two-sided case. This function will calculate either n, p1, p2, sig.level, or power, depending on the input. You must specify at least four of these parameters: n, p1, p2, sig.level, power. The remaining argument must be null; this is the value that the function calculates.

As an example of power.prop.test, let’s consider situational statistics in baseball. Starting in the 2009 season, when ESPN broadcast baseball games, it displayed statistics showing how the batter performed in similar situations. More often than not, the statistics were derived from a very small number of situations. For example, ESPN might show that the hitter had 3 hits in 10 tries when hitting with 2 men on base and 2 outs. These statistics sound really interesting, but do they have any meaning? We ...