tt2st {EQUIVNONINF} | R Documentation |
The function computes the critical constants defining the uniformly most powerful invariant test for the problem (ξ-η)/σ ≤ -\varepsilon_1 or (ξ-η)/σ ≥ \varepsilon_2 versus -\varepsilon_1 < (ξ-η)/σ < \varepsilon_2, with ξ and η denoting the expected values of two normal distributions with common variance σ^2 from which independent samples are taken. In addition, tt2st outputs the power against the null alternative ξ = η.
tt2st(m,n,alpha,eps1,eps2,tol,itmax)
m |
size of the sample from {\cal N}(ξ,σ^2) |
n |
size of the sample from {\cal N}(η,σ^2) |
alpha |
significance level |
eps1 |
absolute value of the lower equivalence limit to (ξ-η)/σ |
eps2 |
upper equivalence limit to (ξ-η)/σ |
tol |
tolerable deviation from α of the rejection probability at either boundary of the hypothetical equivalence interval |
itmax |
maximum number of iteration steps |
m |
size of the sample from {\cal N}(ξ,σ^2) |
n |
size of the sample from {\cal N}(η,σ^2) |
alpha |
significance level |
eps1 |
absolute value of the lower equivalence limit to (ξ-η)/σ |
eps2 |
upper equivalence limit to (ξ-η)/σ |
IT |
number of iteration steps performed until reaching the stopping criterion corresponding to TOL |
C1 |
left-hand limit of the critical interval for the two-sample t-statistic |
C2 |
right-hand limit of the critical interval for the two-sample t-statistic |
ERR1 |
deviation of the rejection probability from α under (ξ-η)/σ= -\varepsilon_1 |
ERR2 |
deviation of the rejection probability from α under (ξ-η)/σ= \varepsilon_2 |
POW0 |
power of the UMPI test against the alternative ξ = η |
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. 6.1.
tt2st(12,12,0.05,0.50,1.00,1e-10,50)