Computes the unconditional power of Woolf's asymptotic Wald test for \(H_0\): OR = 1, at response rates \((\pi_1, \pi_2)\). Rejects \(H_0\) when \(|\log \hat{\theta}| / SE(\log \hat{\theta}) > z_{\alpha/2}\), where \(\hat{\theta} = u(n-v) / ((m-u)v)\). Uses the Haldane correction (replacing zero cells with 0.5) for tables where one or more cells are zero.
Arguments
- p
Length-2 numeric vector \((\pi_1, \pi_2)\): success probability in group 1 (\(\pi_1\)) and group 2 (\(\pi_2\)) at which power is evaluated.
- .m
Number of trials in group 1.
- .n
Number of trials in group 2.
- .alpha
Nominal significance level \(\alpha\). No default.
- .superiority
Logical. If
TRUE, power is computed only over tables where the observed rate in group 2 exceeds that in group 1. Defaults toFALSE.
Value
A single numeric value: the power of Woolf's asymptotic test at the response rates \((\pi_1, \pi_2)\), in \([0, 1]\).
See also
Other power:
power_conservative(),
power_modified(),
power_probability(),
power_randomised()
Examples
power_asymptotic(p = c(0.2, 0.6), .m = 6, .n = 4, .alpha = 0.05)
#> [1] 0.08497562