tost.stat {equivalence}R Documentation

Computes a TOST for equivalence from sample statistics

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 from the statistics of a sample of paired differences of a normally-distributed population.

Usage

tost.stat(mean, std, n, null = 0, alpha = 0.05, Epsilon = 0.36, absolute = FALSE)

Arguments

mean sample mean
std sample standard deviation
n sample size
null the value of the parameter in the null hypothesis
alpha test size
Epsilon magnitude of region of similarity
absolute choose units: absolute (TRUE) or relative to the standard deviation (FALSE).

Details

This test requires the assumption of normality of the population. Wellek (2003, p. 12) suggests that 0.36 corresponds to a strict test and 0.72 to a liberal test when epsilon is in units of relative standard deviation. I have added the option to use an absolute interval (e.g. +/- 1 metre), which simply converts the cutoff to units of the sample standard deviation and applies the usual 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 non-missing sample size
alpha the size of the test
Epsilon the magnitude of the region of similarity
Interval the half-length of the two one-sided interval

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.

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.data, ptte.stat

Examples

data(ufc)
tost.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)))


[Package equivalence version 0.4.1 Index]