Exact (version 3.3)

exact.reject.region: 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)

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.

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"

Author

Peter Calhoun

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.

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

if (FALSE) {
# 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")
}
}

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