mawi {EQUIVNONINF} | R Documentation |
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.
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 <stefan.wellek@zi-mannheim.de>
Peter Ziegler <peter.ziegler@zi-mannheim.de>
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.
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)