tost {equivalence}R Documentation

Computes a TOST for equivalence from paired or unpaired data

Description

This function computes the test and key test quantities for the two one-sided test for equivalence, as documented in Schuirmann (1981) and Westlake (1981). This function computes the test for a sample of paired differences or two samples, assumed to be from a normally-distributed population.

Usage

tost(x, y = NULL, alpha = 0.05, epsilon, ...)

Arguments

x the first (or only) sample
y the second sample
alpha test size
epsilon magnitude of region of similarity
... arguments to be passed to t.test

Details

This test requires the assumption of normality of the population, or an invocation of large-sample theory. The function wraps around the t.test function, so it provides tosts for the same range of designs, accepts the same arguments, and handles missing values the same way.

Value

A list with the following components

mean.diff the mean of the difference
se.diff the standard error of the difference
alpha the size of the test
ci.diff the 1-alpha confidence interval for the difference
df the degrees of freedom used for the confidence interval
epsilon the magnitude of the region of similarity
result the outcome of the test of the null hypothesis of dissimilarity
p.value the p-value of the significance test
check.me the confidence interval corresponding to the p-value

Note

This test requires the assumption of normality of the population. The components of the test are t-based confidence intervals, so the Central Limit Theorem and Slutsky's Theorem may be relevant to its application in large samples.

Author(s)

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

References

Schuirmann, D.L. 1981. On hypothesis testing to determine if the mean of a normal distribution is contained in a known interval. Biometrics 37 617.

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.

Westlake, W.J. 1981. Response to T.B.L. Kirkwood: bioequivalence testing - a need to rethink. Biometrics 37, 589-594.

See Also

tost.stat, ptte.data

Examples

data(ufc)
tost(ufc$Height.m.p, ufc$Height.m, epsilon = 1)

[Package equivalence version 0.5.5 Index]