ptte.stat: 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)

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

Arguments

mean: the sample mean
std: the sample standard deviation
n: sample size
alpha: test size
Epsilon: magnitude of region of similarity

Author

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

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.

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.

Examples

Run this code

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)))

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