tt2st: Critical constants and power against the null alternative of...

Description Usage Arguments Value Note Author(s) References Examples

View source: R/tt2st.R

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 <[email protected]>
Peter Ziegler <[email protected]>

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)

EQUIVNONINF documentation built on Sept. 19, 2017, 5:06 p.m.