rtost: Computes a robust TOST for equivalence from paired or...

In equivalence: Provides Tests and Graphics for Assessing Tests of Equivalence

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 [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.

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

tost, yuen.t.test

Examples

data(ufc)
rtost(ufc$Height.m.p, ufc$Height.m, epsilon = 1, tr = 0.2)

Example output

Loading required package: lattice
Loading required package: boot

Attaching package: 'boot'

The following object is masked from 'package:lattice':

    melanoma

Loading required package: PairedData
Loading required package: MASS
Loading required package: gld
Loading required package: mvtnorm
Loading required package: ggplot2

Attaching package: 'PairedData'

The following object is masked from 'package:base':

    summary

$mean.diff
[1] 0.7978774

$se.diff
[1] 0.4923998

$alpha
[1] 0.05

$ci.diff
[1] -0.01370916  1.60946406
attr(,"conf.level")
[1] 0.9

$df
      df 
452.6509 

$epsilon
[1] 1

$result
[1] "not rejected"

$p.value
[1] 0.3408224

$check.me
[1] 0.5957549 1.0000000
attr(,"conf.level")
[1] 0.3183553

equivalence documentation built on May 1, 2019, 9:15 p.m.