PMCMRplus (version 1.9.6)

power.williams.test: Power calculations for minimum detectable difference of the Williams' test

Description

Compute the power of a Williams' test, or determine parameters to obtain a target power.

Usage

power.williams.test(n = NULL, k, delta, sd = 1, power = NULL, ...)

Value

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

Arguments

n

number of observations (per group).

k

number of treatment groups.

delta

clinically meaningful minimal difference (between a treatment group and control).

sd

common standard deviation.

power

power of test (1 minus Type II error probability).

...

further arguments, currently ignored.

Details

Exactly one of the parameters n or power must be passed as NULL, and that parameter is determined from the others.

The function has implemented the following Eq. in order to estimate power (Chow et al. 2008):

$$1-\beta =1-\mathrm{\Phi }(T_{K\alpha v}-|\mathrm{\Delta }|/\sigma \sqrt{2/n})$$

with $|\mathrm{\Delta }|$ the clinically meaningful minimal difference, $T_{K\alpha v}$ the critical Williams' t-statistic for $\alpha =0.05$, $v=\mathrm{\infty }$ degree of freedom and $\mathrm{\Phi }$ the probability function of the standard normal function.

The required sample size (balanced design) is estimated numerically (see optimise). The optimal sample size is searched within the interval of $3\le n\le 120$ in order to minimise the squared difference between nominal power and estimated power.

References

Chow, S.-C., Shao, J., Wan, H., 2008, Sample Size Calculations in Clinical Research, 2nd ed, Chapman & Hall/CRC: Boca Raton, FL.

See Also

optimise williamsTest

Examples

## Chow et al. 2008, p. 288 depicts 53 (rounded),
## better use ceiling for rounding
power.williams.test(power = 0.8, k = 3, delta = 11, sd = 22)
power.williams.test(n = 54, k = 3, delta = 11, sd = 22)

## PASS manual example:
## up-rounded n values are:
## 116, 52, 29, 14, 8 and 5
## according to PASS manual, p. 595-5
D <- c(10, 15, 20, 30, 40, 50)
y <- sapply(D, function(delta) {
 power.williams.test(power = 0.9, k = 4, delta = delta, sd = 25)$n
 })
ceiling(y)

if (FALSE) {
 ## compare with power.t.test
 ## and bonferroni correction
 power.t.test(power = 0.9, delta = 50, sd = 25,
 sig.level = 0.05 / 4, alternative = "one.sided")
}