tt2st {EQUIVNONINF} R Documentation

## Critical constants and power against the null alternative of the two-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 (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

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

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


[Package EQUIVNONINF version 1.0.2 Index]