Compute the power of the two-sample test for proportions, or determine parameters to obtain a target power.

```
power.prop.test(n = NULL, p1 = NULL, p2 = NULL, sig.level = 0.05,
power = NULL,
alternative = c("two.sided", "one.sided"),
strict = FALSE, tol = .Machine$double.eps^0.25)
```

n

number of observations (per group)

p1

probability in one group

p2

probability in other group

sig.level

significance level (Type I error probability)

power

power of test (1 minus Type II error probability)

alternative

one- or two-sided test. Can be abbreviated.

strict

use strict interpretation in two-sided case

tol

numerical tolerance used in root finding, the default providing (at least) four significant digits.

Object of class `"power.htest"`

, a list of the arguments
(including the computed one) augmented with `method`

and
`note`

elements.

Exactly one of the parameters `n`

, `p1`

, `p2`

,
`power`

, and `sig.level`

must be passed as NULL, and that
parameter is determined from the others. Notice that `sig.level`

has a non-NULL default so `NULL`

must be explicitly passed if you
want it computed.

If `strict = TRUE`

is used, the power will include the probability of
rejection in the opposite direction of the true effect, in the two-sided
case. Without this the power will be half the significance level if the
true difference is zero.

Note that not all conditions can be satisfied, e.g., for

power.prop.test(n=30, p1=0.90, p2=NULL, power=0.8, strict=TRUE)

there is no proportion `p2`

between `p1 = 0.9`

and 1, as
you'd need a sample size of at least \(n = 74\) to yield the
desired power for \((p1,p2) = (0.9, 1)\).

For these impossible conditions, currently a warning
(`warning`

) is signalled which may become an error
(`stop`

) in the future.

# NOT RUN { power.prop.test(n = 50, p1 = .50, p2 = .75) ## => power = 0.740 power.prop.test(p1 = .50, p2 = .75, power = .90) ## => n = 76.7 power.prop.test(n = 50, p1 = .5, power = .90) ## => p2 = 0.8026 power.prop.test(n = 50, p1 = .5, p2 = 0.9, power = .90, sig.level=NULL) ## => sig.l = 0.00131 power.prop.test(p1 = .5, p2 = 0.501, sig.level=.001, power=0.90) ## => n = 10451937 try( power.prop.test(n=30, p1=0.90, p2=NULL, power=0.8) ) # a warning (which may become an error) ## Reason: power.prop.test( p1=0.90, p2= 1.0, power=0.8) ##-> n = 73.37 # }