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Local size of Woolf's asymptotic test

Source: R/local_size_asymptotic.R
local_size_asymptotic.Rd

Computes the unconditional rejection probability (local size) of Woolf's asymptotic Wald test for \(H_0\): OR = \(\theta_0\) at nuisance parameter \(p_0\), where \(p_1 = p_0 / (p_0 + \theta_0 (1 - p_0))\). Rejects \(H_0\) when \(|\log \hat{\theta} - \log \theta_0| / SE(\log \hat{\theta}) > z_{\alpha/2}\), where \(\hat{\theta} = u(n-v) / ((m-u)v)\). Uses the Haldane correction (replacing zero cells with 0.5) to handle tables where one or more cells are zero, matching the SAS macro.

Usage

local_size_asymptotic(nuisance, .odds_ratio, .m, .n, .alpha)

Arguments

nuisance

The nuisance parameter \(p_0\): success probability in group 1 under \(H_0\). Must be in \([0, 1]\).

.odds_ratio

The null hypothesis odds ratio \(\theta_0\). No default.

.m

Number of trials in group 1.

.n

Number of trials in group 2.

.alpha

Nominal significance level \(\alpha\). No default.

Value

A single numeric value: the local size of Woolf's asymptotic test at the given nuisance parameter, in \([0, 1]\).

See also

Other size: local_size_modified(), local_size_probability(), local_size_randomised(), size_modified()

Examples

local_size_asymptotic(nuisance = 0.5, .odds_ratio = 1, .m = 6, .n = 4,
                 .alpha = 0.05)
#> [1] 0.01367188