mwtie_xy {EQUIVNONINF} R Documentation

## Distribution-free two-sample equivalence test for tied data: test statistic and critical upper bound

### 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 <stefan.wellek@zi-mannheim.de>
Peter Ziegler <peter.ziegler@zi-mannheim.de>

### 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)


[Package EQUIVNONINF version 1.0.2 Index]