mawi {EQUIVNONINF}

Mann-Whitney test for equivalence of two continuous distributions of arbitrary shape: test statistic and critical upper bound

Description

Implementation of the asymptotically distribution-free test for equivalence of two continuous distributions in terms of the Mann-Whitney-Wilcoxon functional. For details see Wellek S (2010) Testing statistical hypotheses of equivalence and noninferiority. Second edition, \S 6.2.

Usage

mawi(alpha,m,n,eps1_,eps2_,x,y) 

Arguments

alpha

significance level

m

size of Sample 1

n

size of Sample 2

eps1_

absolute value of the left-hand limit of the hypothetical equivalence range for \pi_+ - 1/2

eps2_

right-hand limit of the hypothetical equivalence range for \pi_+ - 1/2

x

row vector with the m observations making up Sample1 as components

y

row vector with the n observations making up Sample2 as components

Details

Notation: \pi_+ stands for the Mann-Whitney functional defined by \pi_+ = P[X>Y], with X\sim F \equiv cdf of Population 1 being independent of Y\sim G \equiv cdf of Population 2.

Value

alpha

significance level

m

size of Sample 1

n

size of Sample 2

eps1_

absolute value of the left-hand limit of the hypothetical equivalence range for \pi_+ - 1/2

eps2_

right-hand limit of the hypothetical equivalence range for \pi_+ - 1/2

W+

observed value of the U-statistics estimator of \pi_+

SIGMAH

square root of the estimated asymtotic variance of W_+

CRIT

upper critical bound to |W_+ - 1/2 - (\varepsilon^\prime_2-\varepsilon^\prime_1)/2|/\hat{\sigma}

REJ

indicator of a positive [=1] vs negative [=0] rejection decision to be taken with the data under analysis

Author(s)

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

References

Wellek S: A new approach to equivalence assessment in standard comparative bioavailability trials by means of the Mann-Whitney statistic. Biometrical Journal 38 (1996), 695-710.

Wellek S: Testing statistical hypotheses of equivalence and noninferiority. Second edition. Boca Raton: Chapman & Hall/CRC Press, 2010, \S 6.2.

Examples

x <- c(10.3,11.3,2.0,-6.1,6.2,6.8,3.7,-3.3,-3.6,-3.5,13.7,12.6)
y <- c(3.3,17.7,6.7,11.1,-5.8,6.9,5.8,3.0,6.0,3.5,18.7,9.6)
mawi(0.05,12,12,0.1382,0.2602,x,y)