EQUIVNONINF (version 1.0.2)

srktie_m: Analogue of srktie_d for settings where the distribution of intraindividual differences is concentrated on a finite lattice

Description

Analogue of the function srktie_d tailored for settings where the distribution of the within-subject differences is concentrated on a finite lattice. For details see Wellek S (2010) Testing statistical hypotheses of equivalence and noninferiority. Second edition, pp.112-3.

Usage

srktie_m(n,alpha,eps1,eps2,w,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 \(q_+/(1-q_0) - 1/2\)

w

span of the lattice in which the intraindividual differences take their values

d

row vector with the intraindividual differences for all \(n\) pairs as components

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 \(q_+/(1-q_0) - 1/2\)

w

span of the lattice in which the intraindividual differences take their values

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

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.

References

Wellek S: Testing statistical hypotheses of equivalence and noninferiority. Second edition. Boca Raton: Chapman & Hall/CRC Press, 2010, pp. 112-114.

Examples

# NOT RUN {
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_m(24,0.05,0.2602,0.2602,0.1,d)
# }