sgnrk {EQUIVNONINF}

Signed rank test for equivalence of an arbitrary continuous distribution of the intraindividual differences in terms of the probability of a positive sign of a Walsh average: test statistic and critical upper bound

Description

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,\S 5.4.

Usage

sgnrk(alpha,n,qpl1,qpl2,d) 

Arguments

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

Details

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 \pi_+ = P[X>Y].

Value

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{\sigma}

REJ

indicator of a positive [=1] vs negative [=0] rejection decision to be taken with the data under analysis

Author(s)

Stefan Wellek <[e-mail]>
Peter Ziegler <[e-mail]>

References

Wellek S: Testing statistical hypotheses of equivalence and noninferiority. Second edition. Boca Raton: Chapman & Hall/CRC Press, 2010, \S 5.4.

Examples

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)