sgnrk {EQUIVNONINF} | R Documentation |
Implementation of the paired-data analogue of the Mann-Whitney-Wilcoxon test for equivalence of continuous distributions. The continuity assumption relates to the intraindividual differences D_i. For details see Wellek S (2010) Testing statistical hypotheses of equivalence and noninferiority. Second edition,Par. 5.4.
sgnrk(alpha,n,qpl1,qpl2,d)
alpha |
significance level |
n |
sample size |
qpl1 |
lower equivalence limit q_+^{\prime} to the target functional q_+ |
qpl2 |
upper equivalence limit q_+^{\prime\prime} to the target functional q_+ |
d |
row vector with the intraindividual differences for all n pairs as components |
q_+ is the probability of getting a positive sign of the so-called Walsh-average of a pair of within-subject differences and can be viewed as a natural paired-observations analogue of the Mann-Whitney functional π_+ = P[X>Y].
alpha |
significance level |
n |
sample size |
qpl1 |
lower equivalence limit q_+^{\prime} to the target functional q_+ |
qpl2 |
upper equivalence limit q_+^{\prime\prime} to the target functional q_+ |
U_pl |
observed value of the U-statistics estimator of q_+ |
SIGMAH |
square root of the estimated asymtotic variance of U_+ |
CRIT |
upper critical bound to \big|U_+-\big(q_+^{\prime}+q_+^{\prime\prime}\big)/2\big|/\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: Testing statistical hypotheses of equivalence and noninferiority. Second edition. Boca Raton: Chapman & Hall/CRC Press, 2010, Par. 5.4.
d <- c(-0.5,0.333,0.667,1.333,1.5,-2.0,-1.0,-0.167,1.667,0.833,-2.167,-1.833, 4.5,-7.5,2.667,3.333,-4.167,5.667,2.333,-2.5) sgnrk(0.05,20,0.2398,0.7602,d)