fisher_boschloo_midN {MIDN}

Nearly exact sample size calculation for the Fisher-Boschloo test for differences between independent binomial proportions

Description

The function computes the exact sample sizes required in the randomized UMPU test and its conservative nonrandomized version for attaining prespecified power. In a final step, the mean of both quantities is output as an nearly exact value required in the Fisher-Boschloo test, a powerful nonrandomized version of the exact Fisher-type test.

Usage

fisher_boschloo_midN(alpha, SW, p1, p2, POWO, mton_a, mton_b)

Arguments

alpha

target significance level

SW

step width for increasing p2 in the search for the size of a given critical region in the sample space of (X,Y)

p1

true value of the responder rate for Population 1

p2

true value of the responder rate for Population 2

POWO

power to be obtained against the alternative (p1,p2)

mton_a

desired ratio of sample sizes: numerator

mton_b

desired ratio of sample sizes: denominator

Value

mstart

initial value of 1st sample size

nstart

initial value of 2nd sample size

Mex

size of Sample 1 for randomized UMPU test

Nex

size of Sample 2 for randomized UMPU test

POWEX

power of randomized UMPU test attained with m=Mex,n=Nex

Mnr

size of Sample 1 for conservative nonrandomized Fisher-type test

Nnr

size of Sample 2 for conservative nonrandomized Fisher-type test

POWNR

power of conservative nonrandomized Fisher-type test attained with m=Mnr,n=Nnr

midN_m

nearly exact size of Sample 1 for Boschloo-Fisher test

midN_n

nearly exact size of Sample 1 for Boschloo-Fisher test

Author(s)

Stefan Wellek <[e-mail]>
Peter Ziegler <[e-mail]>

References

Wellek S: Nearly exact sample size calculation for powerful nonrandomized tests for differences between binomial proportions. Statistica Neerlandica 69 (2015), 358-373.

Examples

result1 <- fisher_boschloo_midN(0.025,0.0001,0.95,0.8,0.8,2,1)
POWEX <- result1[5]
result1  # shows values of vector result1
POWEX    # shows value of POWEX