srktie_d {EQUIVNONINF} | R Documentation |
Implementation of a generalized version of the signed-rank test for equivalence allowing for arbitrary patterns of ties between the within-subject differences. For details see Wellek S (2010) Testing statistical hypotheses of equivalence and noninferiority. Second edition, Par. 5.5.
srktie_d(n,alpha,eps1,eps2,d)
n |
sample size |
alpha |
significance level |
eps1 |
absolute value of the left-hand limit of the hypothetical equivalence range for q_+/(1-q_0) - 1/2 |
eps2 |
right-hand limit of the hypothetical equivalence range for q_+/(1-q_0) - 1/2 |
d |
row vector with the intraindividual differences for all n pairs as components |
Notation: q_+ and q_0 stands for the functional defined by q_+ = P[D_i+D_j>0] and q_0 = P[D_i+D_j=0], respectively, with D_i and D_j as the intraindividual differences observed in two individuals independently selected from the underlying bivariate population.
n |
sample size |
alpha |
significance level |
eps1 |
absolute value of the left-hand limit of the hypothetical equivalence range for q_+/(1-q_0) - 1/2 |
eps2 |
right-hand limit of the hypothetical equivalence range for q_+/(1-q_0) - 1/2 |
U_pl |
observed value of the U-statistics estimator of q_+ |
U_0 |
observed value of the U-statistics estimator of q_0 |
UAS_PL |
observed value of U_+/(1-U_0) |
TAUHAS |
square root of the estimated asymtotic variance of √{n}U_+/(1-U_0) |
CRIT |
upper critical bound to √{n}|U_+/(1-U_0) - 1/2 - (\varepsilon_2-\varepsilon_1)/2|/\hat{τ} |
REJ |
indicator of a positive [=1] vs negative [=0] rejection decision to be taken with the data under analysis |
The function srktie_d can be viewed as the paired-data analogue of mwtie_xy
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. 5.5.
d <- c(0.8,0.2,0.0,-0.1,-0.3,0.3,-0.1,0.4,0.6,0.2,0.0,-0.2,-0.3,0.0,0.1,0.3,-0.3, 0.1,-0.2,-0.5,0.2,-0.1,0.2,-0.1) srktie_d(24,0.05,0.2602,0.2602,d)