tt1st {EQUIVNONINF} | R Documentation |
Critical constants and power against the null alternative of the one-sample t-test for equivalence with an arbitrary, maybe nonsymmetric choice of the limits of the equivalence range
Description
The function computes the critical constants defining the uniformly most powerful
invariant test for the problem
\delta/\sigma_D \le \theta_1
or \delta/\sigma_D \ge \theta_2
versus \theta_1 < \delta/\sigma_D < \theta_2
, with (\theta_1,\theta_2)
as a
fixed nondegenerate interval on the real line.
In addition, tt1st outputs the power against the null alternative \delta = 0
.
Usage
tt1st(n,alpha,theta1,theta2,tol,itmax)
Arguments
n |
sample size |
alpha |
significance level |
theta1 |
lower equivalence limit to |
theta2 |
upper equivalence limit to |
tol |
tolerable deviation from |
itmax |
maximum number of iteration steps |
Value
n |
sample size |
alpha |
significance level |
theta1 |
lower equivalence limit to |
theta2 |
upper equivalence limit to |
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 |
C2 |
right-hand limit of the critical interval for the one-sample |
ERR1 |
deviation of the rejection probability from |
ERR2 |
deviation of the rejection probability from |
POW0 |
power of the UMPI test against the alternative |
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 \alpha
is smaller than the smallest
real number representable in R.
Author(s)
Stefan Wellek <stefan.wellek@zi-mannheim.de>
Peter Ziegler <peter.ziegler@zi-mannheim.de>
References
Wellek S: Testing statistical hypotheses of equivalence and noninferiority. Second edition.
Boca Raton: Chapman & Hall/CRC Press, 2010, \S
5.3.
Examples
tt1st(36,0.05, -0.4716,0.3853,1e-10,50)