ptte.data: Computes a paired t-test for equivalence from a single sample...
In equivalence: Provides Tests and Graphics for Assessing Tests of Equivalence

Description Usage Arguments Details Value Note Author(s) References See Also Examples

This function computes the test and key test quantities for the paired t-test for equivalence, as documented in Wellek (2003, pp 77-80). This function computes the test from a sample of a normally-distributed population.

1	ptte.data(x, alpha = 0.05, Epsilon = 0.25)

`x`	paired differences
`alpha`	test size
`Epsilon`	magnitude of region of similarity

This test requires the assumption of normality of the population. Under that assumption the test is the uniformly most powerful invariant test (Wellek, 2003, pp. 78-79).

The function as documented by Wellek (2003) uses units relative to the standard deviation, noting (p. 12) that 0.25 corresponds to a strict test and 0.5 to a liberal test.

A list with the following components

`Dissimilarity`	the outcome of the test of the null hypothesis of dissimilarity
`Mean`	the mean of the sample
`StdDev`	the standard deviation of the sample
`n`	the sample size
`alpha`	the size of the test
`missing`	the number of observations missing
`Epsilon`	the magnitude of the region of similarity
`cutoff`	the critical value
`Tstat`	the test statistic; if Tstat < cutoff then the null hypothesis is rejected.
`Power`	the power of the test evaluated at the observed value

This test requires the assumption of normality of the population. Under that assumption the test is the uniformly most powerful invariant test (Wellek, 2003, pp. 78-79). The exposition in Robinson and Froese (2004) mistakenly omits the square root of the F-quantile.

Andrew RobinsonA.Robinson@ms.unimelb.edu.au

Robinson, A.P., and R.E. Froese. 2004. Model validation using equivalence tests. Ecological Modelling 176, 349–358.

Wellek, S. 2003. Testing statistical hypotheses of equivalence. Chapman and Hall/CRC. 284 pp.

ptte.stat, tost.data