Description Usage Arguments Details Value Author(s) References Examples
Implementation of the asymptotically distributionfree test for equivalence of two continuous distributions in terms of the MannWhitneyWilcoxon 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 lefthand limit of the hypothetical equivalence range for π_+  1/2 
eps2_ 
righthand 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 MannWhitney 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 lefthand limit of the hypothetical equivalence range for π_+  1/2 
eps2_ 
righthand limit of the hypothetical equivalence range for π_+  1/2 
W+ 
observed value of the Ustatistics 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 MannWhitney statistic. Biometrical Journal 38 (1996), 695710.
Wellek S: Testing statistical hypotheses of equivalence and noninferiority. Second edition. Boca Raton: Chapman & Hall/CRC Press, 2010, Par. 6.2.
1 2 3 
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
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.