P-value from the SAS Proc FREQ exact test

Computes the two-sided Fisher exact p-value for \(H_0\): OR = odds_ratio by summing all probabilities in the conditional distribution of \(U\) given \(T = t\) that are no greater than the observed probability \(P_{\theta_0}(U = s \mid T = t)\). The conditional distribution is the Fisher non-central hypergeometric with the specified odds ratio, computed via BiasedUrn::dFNCHypergeo(). When odds_ratio = 1 this reduces to the standard central hypergeometric, matching the p-value reported by SAS Proc FREQ for \(H_0\): OR = 1.

Usage

pvalue_probability(s, t, m, n, odds_ratio = 1)

Arguments

s

Number of successes observed in group 1. No default.

t

Total number of successes across both groups (\(t = s + \) successes in group 2); the conditioning variable in the hypergeometric distribution. No default.

m

Number of trials in group 1. No default.

n

Number of trials in group 2. No default.

odds_ratio

Null hypothesis odds ratio \(\theta_0\). Defaults to 1.

Value

A single numeric value: the two-sided conditional exact p-value, in \([0, 1]\).

See also

local_size_probability() for the local size of the SAS Proc FREQ exact test; power_probability() for the power of the SAS Proc FREQ exact test; modified_fisher_exact_test() for the main user-facing function.

Examples

# Two-sided exact p-value for 5/12 vs 7/11 under H0: OR = 1
# (here t = u + v = 5 + 7 = 12):
pvalue_probability(s = 5, t = 12, m = 12, n = 11, odds_ratio = 1)
#> [1] 0.4136492