tost.stat {equivalence}

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)

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

Details

This test requires the assumption of normality of the population.

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 [e-mail]

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)))