srktie_d {EQUIVNONINF} R Documentation

## Generalized signed rank test for equivalence for tied data: test statistic and critical upper bound

### Description

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.

### Usage

srktie_d(n,alpha,eps1,eps2,d)


### Arguments

 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

### Details

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.

### Value

 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

### Note

The function srktie_d can be viewed as the paired-data analogue of mwtie_xy

### Author(s)

Stefan Wellek <stefan.wellek@zi-mannheim.de>
Peter Ziegler <peter.ziegler@zi-mannheim.de>

### References

Wellek S: Testing statistical hypotheses of equivalence and noninferiority. Second edition. Boca Raton: Chapman & Hall/CRC Press, 2010, Par. 5.5.

### Examples

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)


[Package EQUIVNONINF version 1.0.2 Index]