mwtie_xy: Distribution-free two-sample equivalence test for tied data:...

In EQUIVNONINF: Testing for Equivalence and Noninferiority

Description

Implementation of the asymptotically distribution-free test for equivalence of discrete distributions in terms of the Mann-Whitney-Wilcoxon functional generalized to the case that ties between observations from different distributions may occur with positive probability. For details see Wellek S (2010) Testing statistical hypotheses of equivalence and noninferiority. Second edition, Par. 6.4.

Usage

mwtie_xy(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 π_+/(1-π_0) - 1/2
eps2_	right-hand limit of the hypothetical equivalence range for π_+/(1-π_0) - 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: π_+ and π_0 stands for the functional defined by π_+ = P[X>Y] and π_0 = P[X=Y], respectively, 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 π_+/(1-π_0) - 1/2
eps2_	right-hand limit of the hypothetical equivalence range for π_+/(1-π_0) - 1/2
WXY_TIE	observed value of the U-statistics – based estimator of π_+/(1-π_0)
SIGMAH	square root of the estimated asymtotic variance of W_+/(1-W_0)
CRIT	upper critical bound to |W_+/(1-W_0) - 1/2 - (\varepsilon^\prime_2-\varepsilon^\prime_1)/2|/\hat{σ}
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, Hampel B: A distribution-free two-sample equivalence test allowing for tied observations. Biometrical Journal 41 (1999), 171-186.

Wellek S: Testing statistical hypotheses of equivalence and noninferiority. Second edition. Boca Raton: Chapman & Hall/CRC Press, 2010, Par. 6.4.

Examples

x <- c(1,1,3,2,2,3,1,1,1,2)
y <- c(2,1,2,2,1,1,2,2,2,1,1,2)
mwtie_xy(0.05,10,12,0.10,0.10,x,y)

Example output

Loading required package: BiasedUrn
 alpha = 0.05   m = 10   n = 12   eps1_ = 0.1   eps2_ = 0.1   WXY_TIE = 0.527027   SIGMAH = 0.1806699   CRIT = 0.07308407   REJ = 0

EQUIVNONINF documentation built on July 12, 2021, 5:08 p.m.