exact.reject.region: Rejection Region for 2x2 Tables with Independent Samples

In Exact: Unconditional Exact Test

Rejection Region for 2x2 Tables with Independent Samples

Description

Determines the rejection region for comparing two independent proportions.

Usage

exact.reject.region(n1, n2, alternative = c("two.sided", "less", "greater"),
    alpha = 0.05, npNumbers = 100, np.interval = FALSE, beta = 0.001,
    method = c("z-pooled", "z-unpooled", "boschloo", "santner and snell",
               "csm", "fisher", "pearson chisq", "yates chisq"),
    tsmethod = c("square", "central"), delta = 0, convexity = TRUE,
    useStoredCSM = TRUE)

Arguments

n1	The sample size in first group
n2	The sample size in second group
alternative	Indicates the alternative hypothesis: must be either "two.sided", "less", or "greater"
alpha	Significance level
npNumbers	Number: The number of nuisance parameters considered
np.interval	Logical: Indicates if a confidence interval on the nuisance parameter should be computed
beta	Number: Confidence level for constructing the interval of nuisance parameters considered. Only used if np.interval=TRUE
method	Indicates the method for finding the more extreme tables: must be either "Z-pooled", "Z-unpooled", "Santner and Snell", "Boschloo", "CSM", "Fisher", "Pearson Chisq", or "Yates Chisq"
tsmethod	Indicates two-sided method: must be either "square" or "central"
delta	Number: null hypothesis of the difference in proportion
convexity	Logical: assumes convexity for interval approach. Only used if np.interval=TRUE
useStoredCSM	Logical: uses stored CSM ordering matrix. Only used if method="csm"

Details

The rejection region is calculated for binomial models with independent samples. The design must know the fixed sample sizes in advance. Rejection region can be determined for any unconditional exact test in exact.test, Fisher's exact test, or chi-square test (Yates' or Pearson's; note: these are not exact tests). In very rare cases, using the nuisance parameter interval approach does not attain the convexity property, so it is possible using convexity=TRUE could yield an inaccurate power calculation with this method. This is extremely unlikely though, so default is to assume convexity and speed up computation time. For details regarding parameters, see exact.test.

Value

A matrix of the rejection region. The columns represent the number of successes in first group, rows represent the number of successess in second group, and cells represent whether the test is rejected (1) or failed to be rejected (0). This matrix represents all possible 2x2 tables.

Note

Pearson's and Yates' chi-square tests are not exact tests, so the function name may be a misnomer. These tests may have inflated type 1 error rates. These options were added to compute the rejection region efficiently when using asymptotic tests.

Author(s)

Peter Calhoun

References

Barnard, G.A. (1947) Significance tests for 2x2 tables. Biometrika, 34, 123-138

Chan, I. (2003), Proving non-inferiority or equivalence of two treatments with dichotomous endpoints using exact methods, Statistical Methods in Medical Research, 12, 37–58

See Also

power.exact.test

Examples

## Not run: 
# Ensure that the ExactData R package is available before running the CSM test.
if (requireNamespace("ExactData", quietly = TRUE)) {
exact.reject.region(n1=10, n2=20, alternative="two.sided", method="CSM")
}

## End(Not run)

exact.reject.region(n1=10, n2=20, alternative="less", method="Z-pooled", delta=0.10)

Exact documentation built on Sept. 11, 2024, 6:17 p.m.