tost: Computes a TOST for equivalence from paired or unpaired data

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

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). The function computes the test for a sample of paired differences or two samples, assumed to be from a normally-distributed population.

Much code in the function has been copied and adapted from R's t.test.default function.

Usage

tost(x, y = NULL, epsilon = 1, paired = FALSE, var.equal = FALSE,
              conf.level = 0.95, alpha = NULL,
    ...)

Arguments

x	the first (or only) sample
y	the second sample
epsilon	magnitude of region of similarity
paired	a logical indicating whether you want a paired tost
var.equal	a logical variable indicating whether to treat the two variances as being equal. If 'TRUE' then the pooled variance is used to estimate the variance otherwise the Welch (or Satterthwaite) approximation to the degrees of freedom is used.
conf.level	confidence level of the interval
alpha	test size (for backwards-compatibility, overrides conf.level)
...	arguments to be passed to other functions.

Details

The function inherits infrastructure from R's t.test.default, so a number of elements have been copied from the help file of that function.

This test requires the assumption of normality of the population, or an invocation of large-sample theory. The function wraps around the t.test function, so it provides tosts for the same range of designs, accepts the same arguments, and handles missing values the same way.

If 'paired' is 'TRUE' then both 'x' and 'y' must be specified and they must be the same length. Missing values are silently removed (in pairs if 'paired' is 'TRUE'). If 'var.equal' is 'TRUE' then the pooled estimate of the variance is used. By default, if 'var.equal' is 'FALSE' then the variance is estimated separately for both groups and the Welch modification to the degrees of freedom is used.

Value

A list with the following components

estimate	the mean of the difference
se.diff	the standard error of the difference
alpha	the size of the test
data.name	a character string giving the name(s) of the data
ci.diff	the 1-alpha confidence interval for the difference
parameter	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
method	a character string indicating what type of t-test was performed
null.value	the specified hypothesized value of the mean or mean difference depending on whether it was a one-sample tost or a two-sample tost.
tost.p.value	the p-value of the tost significance test
tost.interval	the two one-sided confidence interval corresponding to the test.

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.

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.

See Also

tost.stat, ptte.data

Examples

data(ufc)
tost(ufc$Height.m.p, ufc$Height.m, epsilon = 1, paired = TRUE)

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


	Paired TOST

data:  ufc$Height.m.p and ufc$Height.m
df = 376
sample estimates:
mean of the differences 
              0.6003913 

Epsilon: 1 
95 percent two one-sided confidence interval (TOST interval):
 0.1916419 1.0091407
Null hypothesis of statistical difference is: not rejected 
TOST p-value: 0.05389588 

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