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

1 2 3 4 |

`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. |

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

1 | ```
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 EkstrĂ¸m

`prop.test`

, `uniroot`

1 2 3 4 5 6 7 8 9 10 11 12 | ```
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
``` |

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