stats (version 3.6.2)

# power.prop.test: Power Calculations for Two-Sample Test for Proportions

## Description

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

## Usage

```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)```

## Arguments

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.

## Value

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

## Details

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.

`prop.test`, `uniroot`

## Examples

Run this code
```# 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
# }
```

Run the code above in your browser using DataCamp Workspace