tt1st: Critical constants and power against the null alternative of...

In EQUIVNONINF: Testing for Equivalence and Noninferiority

Description

The function computes the critical constants defining the uniformly most powerful invariant test for the problem δ/σ_D ≤ θ_1 or δ/σ_D ≥ θ_2 versus θ_1 < δ/σ_D < θ_2, with (θ_1,θ_2) as a fixed nondegenerate interval on the real line. In addition, tt1st outputs the power against the null alternative δ = 0.

Usage

tt1st(n,alpha,theta1,theta2,tol,itmax) 

Arguments

n	sample size
alpha	significance level
theta1	lower equivalence limit to δ/σ_D
theta2	upper equivalence limit to δ/σ_D
tol	tolerable deviation from α of the rejection probability at either boundary of the hypothetical equivalence interval
itmax	maximum number of iteration steps

Value

n	sample size
alpha	significance level
theta1	lower equivalence limit to δ/σ_D
theta2	upper equivalence limit to δ/σ_D
IT	number of iteration steps performed until reaching the stopping criterion corresponding to TOL
C1	left-hand limit of the critical interval for the one-sample t-statistic
C2	right-hand limit of the critical interval for the one-sample t-statistic
ERR1	deviation of the rejection probability from α under δ/σ_D = θ_1
ERR2	deviation of the rejection probability from α under δ/σ_D = θ_2
POW0	power of the UMPI test against the alternative δ = 0

Note

If the output value of ERR2 is NA, the deviation of the rejection probability at the right-hand boundary of the hypothetical equivalence interval from α is smaller than the smallest real number representable in R.

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, Par. 5.3.

Examples

tt1st(36,0.05, -0.4716,0.3853,1e-10,50)

EQUIVNONINF documentation built on July 12, 2021, 5:08 p.m.