power.prop.test {stats}R Documentation

Power Calculations for Two-Sample Test for Proportions


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)



number of observations (per group)


probability in one group


probability in other group


significance level (Type I error probability)


power of test (1 minus Type II error probability)


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


use strict interpretation in two-sided case


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


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.


Object of class "power.htest", a list of the arguments (including the computed one) augmented with method and note elements.


uniroot is used to solve power equation for unknowns, so you may see errors from it, notably about inability to bracket the root when invalid arguments are given. If one of p1 and p2 is computed, then p1 < p2 is assumed and will hold, but if you specify both, p2 <= p1 is allowed.


Peter Dalgaard. Based on previous work by Claus Ekstrøm

See Also

prop.test, uniroot


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
 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

[Package stats version 3.6.0 Index]