rtost {equivalence} | R Documentation |
Computes a robust TOST for equivalence from paired or unpaired data
Description
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)].
Usage
rtost(x, y = NULL, alpha = 0.05, epsilon = 0.31, tr = 0.2, ...)
Arguments
x |
the first (or only) sample |
y |
the second sample |
alpha |
test size |
tr |
the proportion (percent/100) of the data set to be trimmed |
epsilon |
magnitude of region of similarity |
... |
arguments to be passed to yuen.t.test |
Details
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.
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 is the tost for equivalence (tost equivalence) wrapped around the robust, trimmed mean, winsorized variance yuen.t.test (yuen PairedData).
Author(s)
Gregory Belenky belenky@wsu.edu
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.
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.
See Also
Examples
data(ufc)
rtost(ufc$Height.m.p, ufc$Height.m, epsilon = 1, tr = 0.2)