Local size of the SAS Proc FREQ exact test

Computes the unconditional rejection probability (local size) of the SAS Proc FREQ exact test for \(H_0\): OR = \(\theta_0\) at nuisance parameter \(p_0\), where \(p_1 = p_0 / (p_0 + \theta_0 (1 - p_0))\). For each possible table \((i, j)\), rejection is determined by pvalue_probability(): the sum of Fisher non-central hypergeometric probabilities (given \(T = i + j\) and OR = \(\theta_0\)) that are no greater than the observed probability, compared against \(\alpha\).

Usage

local_size_probability(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 the SAS Proc FREQ exact test at the given nuisance parameter, in \([0, 1]\).

See also

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

Examples

local_size_probability(nuisance = 0.5, .odds_ratio = 1, .m = 6, .n = 4,
                    .alpha = 0.05)
#> [1] 0.02148438