tost.data {equivalence} | R Documentation |
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, assume to be from a normally-distributed population.
tost.data(x, null = 0, alpha = 0.05, Epsilon = 0.36, absolute = FALSE)
x |
the sample of paired differences |
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). |
This test requires the assumption of normality of the population. Wellek (2003) 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.
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 |
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.
Andrew Robinson A.Robinson@ms.unimelb.edu.au
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.
data(ufc) tost.data(ufc$Height.m.p - ufc$Height.m)