power.t.test {stats} R Documentation

## Power calculations for one and two sample t tests

### Description

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

### Usage

```power.t.test(n = NULL, delta = NULL, sd = 1, sig.level = 0.05,
power = NULL,
type = c("two.sample", "one.sample", "paired"),
alternative = c("two.sided", "one.sided"),
strict = FALSE, tol = .Machine\$double.eps^0.25)
```

### Arguments

 `n` number of observations (per group) `delta` true difference in means `sd` standard deviation `sig.level` significance level (Type I error probability) `power` power of test (1 minus Type II error probability) `type` string specifying the type of t test. Can be abbreviated. `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.

### Details

Exactly one of the parameters `n`, `delta`, `power`, `sd`, and `sig.level` must be passed as `NULL`, and that parameter is determined from the others. Notice that the last two have non-NULL defaults, so NULL must be explicitly passed if you want to compute them.

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.

### Value

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

### Note

`uniroot` is used to solve the power equation for unknowns, so you may see errors from it, notably about inability to bracket the root when invalid arguments are given.

### Author(s)

Peter Dalgaard. Based on previous work by Claus Ekstrøm

`t.test`, `uniroot`
``` power.t.test(n = 20, delta = 1)