ptte.stat {equivalence}

Computes a paired t-test for equivalence from the mean and standard deviation of a sample from a normally-distributed population

Description

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 the mean and standard deviation of a sample of paired differences from a normally-distributed population.

Usage

ptte.stat(mean, std, n, alpha = 0.05, Epsilon = 0.25)

Arguments

mean

the sample mean

std

the sample standard deviation

n

sample size

alpha

test size

Epsilon

magnitude of region of similarity

Details

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). This version of the test can be applied post-hoc to any testing situation in which you have the mean, standard deviation, and sample size, and are confident that the sample is drawn from a normally-distributed population.

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.

Value

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

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

Note

The exposition in Robinson and Froese (2004) mistakenly omits the square root of the F-quantile.

Author(s)

Andrew Robinson [e-mail]

References

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.

See Also

ptte.data, tost.stat

Examples

data(ufc)
ptte.stat(mean(ufc$Height.m.p - ufc$Height.m, na.rm=TRUE),
  sd(ufc$Height.m.p - ufc$Height.m, na.rm=TRUE),
  sum(!is.na(ufc$Height.m.p - ufc$Height.m)))