This function computes the TOST and key TOST quantities for the two one-sided test for equivalence [Schuirmann (1981) and Westlake (1981)], using the robust t-test of Yuen [Yuen and Dixon (1973), Yuen (1974)] in place of the standard Welch t test (t.test stats). The yuen t test makes no assumption of normality. The function computes the robust TOST for a sample of paired differences or for two samples. The function performs almost as well as the Welch t test when the population distribution is normal and is more robust than the Welch t test in the face of non-normality (e.g., distributions that are long-tailed, heteroscedastic, or contaminated by outliers)[Yuen and Dixon (1973), Yuen (1974)].
rtost(x, y = NULL, alpha = 0.05, epsilon = 0.31, tr = 0.2, ...)A list with the following components
the mean of the difference
the standard error of the difference
the size of the test
the 1-alpha confidence interval for the difference
the degrees of freedom used for the confidence interval
the magnitude of the region of similarity
the outcome of the test of the null hypothesis of dissimilarity
the p-value of the significance test
the confidence interval corresponding to the p-value
the first (or only) sample
the second sample
test size
the proportion (percent/100) of the data set to be trimmed
magnitude of region of similarity
arguments to be passed to yuen.t.test
Gregory Belenky belenky@wsu.edu
The rtost function is wrapped around the yuen PairedData t test, a robust variant of the t test using trimmed means and winsorized variances. It provides tosts for the same range of designs, accepts the same arguments, and handles missing values the same way as tost equivalence. For the tost, the user must set epsilon, which is the magnitude of region similarity. Warning: with tr > 0.25 type I error control might be poor.
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.
Yuen, K.K. (1974) The two-sample trimmed t for unequal population variances. Biometrika, 61, 165-170.
Yuen, K.K., and Dixon, W.J. (1973) The approximate behavior and performance of the two-sample trimmed t. Biometrika, 60, 369-374.
tost, yuen.t.test
data(ufc)
rtost(ufc$Height.m.p, ufc$Height.m, epsilon = 1, tr = 0.2)
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