tt1st {EQUIVNONINF} | R Documentation |
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.
tt1st(n,alpha,theta1,theta2,tol,itmax)
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 |
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 |
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.
Stefan Wellek <stefan.wellek@zi-mannheim.de>
Peter Ziegler <peter.ziegler@zi-mannheim.de>
Wellek S: Testing statistical hypotheses of equivalence and noninferiority. Second edition. Boca Raton: Chapman & Hall/CRC Press, 2010, Par. 5.3.
tt1st(36,0.05, -0.4716,0.3853,1e-10,50)