fstretch {EQUIVNONINF} | R Documentation |
The function computes the critical constants defining the optimal test for the problem σ^2/τ^2 ≤ \varrho_1 or σ^2/τ^2 ≥ \varrho_2 versus \varrho_1 < σ^2/τ^2 < \varrho_2, with (\varrho_1,\varrho_2) as a fixed nonempty interval around unity.
fstretch(alpha,tol,itmax,ny1,ny2,rho1,rho2)
alpha |
significance level |
tol |
tolerable deviation from α of the rejection probability at either boundary of the hypothetical equivalence interval |
itmax |
maximum number of iteration steps |
ny1 |
number of degrees of freedom of the estimator of σ^2 |
ny2 |
number of degrees of freedom of the estimator of τ^2 |
rho1 |
lower equivalence limit to σ^2/τ^2 |
rho2 |
upper equivalence limit to σ^2/τ^2 |
alpha |
significance level |
tol |
tolerable deviation from α of the rejection probability at either boundary of the hypothetical equivalence interval |
itmax |
maximum number of iteration steps |
ny1 |
number of degrees of freedom of the estimator of σ^2 |
ny2 |
number of degrees of freedom of the estimator of τ^2 |
rho1 |
lower equivalence limit to σ^2/τ^2 |
rho2 |
upper equivalence limit to σ^2/τ^2 |
IT |
number of iteration steps performed until reaching the stopping criterion corresponding to TOL |
C1 |
left-hand limit of the critical interval for T = \frac{n-1}{m-1} ∑_{i=1}^m (X_i-\overline{X})^2 / ∑_{j=1}^{n-1} (Y_j-\overline{Y})^2 |
C2 |
right-hand limit of the critical interval for T = \frac{n-1}{m-1} ∑_{i=1}^m (X_i-\overline{X})^2 / ∑_{j=1}^{n-1} (Y_j-\overline{Y})^2 |
ERR |
deviation of the rejection probability from α under σ^2/τ^2 = \varrho_1 |
POW0 |
power of the UMPI test against the alternative σ^2/τ^2 = 1 |
If the two independent samples under analysis are from exponential rather than Gaussian distributions, the critical constants computed by means of fstretch with ν_1 = 2m, ν_2 = 2n, can be used for testing for equivalence with respect to the ratio of hazard rates. The only difference is that the ratio of sample means rather than variances has to be used as the test statistic then.
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. 6.5.
fstretch(0.05, 1.0e-10, 50,40,45,0.5625,1.7689)