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 δ/σ_D ≤ θ_1 or δ/σ_D ≥ θ_2 versus θ_1 < δ/σ_D < θ_2, with (θ_1,θ_2) as a fixed nondegenerate interval on the real line. In addition, tt1st outputs the power against the null alternative δ = 0.

### Usage

```tt1st(n,alpha,theta1,theta2,tol,itmax)
```

### Arguments

 `n` sample size `alpha` significance level `theta1` lower equivalence limit to δ/σ_D `theta2` upper equivalence limit to δ/σ_D `tol` tolerable deviation from α of the rejection probability at either boundary of the hypothetical equivalence interval `itmax` maximum number of iteration steps

### Value

 `n` sample size `alpha` significance level `theta1` lower equivalence limit to δ/σ_D `theta2` upper equivalence limit to δ/σ_D `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 t-statistic `C2` right-hand limit of the critical interval for the one-sample t-statistic `ERR1` deviation of the rejection probability from α under δ/σ_D = θ_1 `ERR2` deviation of the rejection probability from α under δ/σ_D = θ_2 `POW0` power of the UMPI test against the alternative δ = 0

### 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. 5.3.

### Examples

```tt1st(36,0.05, -0.4716,0.3853,1e-10,50)
```

[Package EQUIVNONINF version 1.0.2 Index]