mawi: Mann-Whitney test for equivalence of two continuous...
In EQUIVNONINF: Testing for Equivalence and Noninferiority

Description Usage Arguments Details Value Author(s) References Examples

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, Par. 6.2.

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

`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_+ - 1/2
`eps2_`	right-hand limit of the hypothetical equivalence range for π_+ - 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

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

`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_+ - 1/2
`eps2_`	right-hand limit of the hypothetical equivalence range for π_+ - 1/2
`W+`	observed value of the U-statistics estimator of π_+
`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{σ}
`REJ`	indicator of a positive [=1] vs negative [=0] rejection decision to be taken with the data under analysis

Stefan Wellek <[email protected]>
Peter Ziegler <[email protected]>

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, Par. 6.2.

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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)

Loading required package: BiasedUrn
 alpha = 0.05   m = 12   n = 12   eps1_ = 0.1382   eps2_ = 0.2602 
 W+ = 0.4166667   SIGMAH = 0.1113279   CRIT = 0.3007752   REJ = 0