# sgnrk: Signed rank test for equivalence of an arbitrary continuous... In EQUIVNONINF: Testing for Equivalence and Noninferiority

## 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,Par. 5.4.

## Usage

 1 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 π_+ = 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{σ} REJ indicator of a positive [=1] vs negative [=0] rejection decision to be taken with the data under analysis

## Author(s)

Stefan Wellek <[email protected]>
Peter Ziegler <[email protected]>

## References

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

## Examples

 1 2 3 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) 

### Example output

Loading required package: BiasedUrn
alpha = 0.05   n = 20   qpl1_ = 0.2398   qpl2_ = 0.7602   U+ = 0.5526316   SIGMAH = 0.1207119   CRIT = 0.5435075   REJ = 1


EQUIVNONINF documentation built on Sept. 19, 2017, 5:06 p.m.