srktie_d {EQUIVNONINF}

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, \S 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 \sqrt{n}U_+/(1-U_0)

CRIT

upper critical bound to \sqrt{n}|U_+/(1-U_0) - 1/2 - (\varepsilon_2-\varepsilon_1)/2|/\hat{\tau}

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 <[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 5.5.

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)