power.welch.t.test {MKpower}

Power Calculations for Two-sample Welch t Test

Description

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

Usage

power.welch.t.test(n = NULL, delta = NULL, sd1 = 1, sd2 = 1, 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)

delta

(expected) true difference in means

sd1

(expected) standard deviation of group 1

sd2

(expected) standard deviation of group 2

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.

Details

Exactly one of the parameters n, delta, power, sd1, sd2 and sig.level must be passed as NULL, and that parameter is determined from the others. Notice that the last three 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

The function and its documentation was adapted from power.t.test implemented by Peter Dalgaard and based on previous work by Claus Ekstroem.

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)

Matthias Kohl [e-mail]

References

S.L. Jan and G. Shieh (2011). Optimal sample sizes for Welch's test under various allocation and cost considerations. Behav Res Methods, 43, 4:1014-22.

See Also

power.t.test, t.test, uniroot

Examples

 ## identical results as power.t.test, since sd = sd1 = sd2 = 1
 power.welch.t.test(n = 20, delta = 1)
 power.welch.t.test(power = .90, delta = 1)
 power.welch.t.test(power = .90, delta = 1, alternative = "one.sided")

  ## sd1 = 0.5, sd2 = 1
 power.welch.t.test(delta = 2, sd1 = 0.5, sd2 = 1, power = 0.9)

 
 ## empirical check
 M <- 10000
 pvals.welch <- numeric(M)
 for(i in seq_len(M)){
   x <- rnorm(5, mean = 0, sd = 0.5)
   y <- rnorm(5, mean = 2, sd = 1.0)
   pvals.welch[i] <- t.test(x, y)$p.value
 }
 ## empirical power
 sum(pvals.welch < 0.05)/M