# tt2st: 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 (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.

## Usage

 1 tt2st(m,n,alpha,eps1,eps2,tol,itmax) 

## Arguments

 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

## Value

 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

## 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 <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, Par. 6.1.

## Examples

 1 tt2st(12,12,0.05,0.50,1.00,1e-10,50) 

### Example output

Loading required package: BiasedUrn
m = 12   n = 12  alpha = 0.05   eps1 = 0.5   eps2 = 1   it = 25   c1 = 0.2797658   c2 = 0.9308834   ERR1 = 6.765859e-11   ERR2 = NA   POW0 = 0.2101268


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