equiv.test: Equivalence and non-inferiority tests for one- and two-sample...
In thmild/equivUMP: Uniformly Most Powerful Invariant Tests of Equivalence

Description Usage Arguments Details Value Methods (by class) References Examples

Implementation of uniformly most powerful invariant equivalence tests for one- and two-sample problems (paired and unpaired). Also one-sided alternatives (non-inferiority and non-superiority tests) are supported. Basically a variant of a t-test with (relaxed) null and alternative hypotheses exchanged.

equiv.test(x, ...)

## Default S3 method:
equiv.test(x, y = NULL, alternative = c("two.sided",
  "less", "greater"), eps = 1, mu = 0, paired = FALSE, ...)

## S3 method for class 'formula'
equiv.test(formula, data, subset, na.action, ...)

`x`	a (non-empty) numeric vector of data values.
`...`	further arguments to be passed to or from methods.
`y`	an optional (non-empty) numeric vector of data values.
`alternative`	a character string specifying the alternative hypothesis, must be one of "`two.sided`" (default), "`greater`" or "`less`". You can specify just the initial letter.
`eps`	a single strictly positive number giving the equivalence limits.
`mu`	a number indicating the true value of the mean (or difference in means if you are performing a two sample test).
`paired`	a logical indicating whether you want a paired equivalence test in the two-sample case.
`formula`	a formula of the form `lhs ~ rhs` where `lhs` is a numeric variable giving the data values and `rhs` a factor with two levels giving the corresponding groups.
`data`	an optional matrix or data frame containing the variables in the formula `formula`. By default the variables are taken from `environment(formula)`.
`subset`	an optional vector specifying a subset of observations to be used.
`na.action`	a function which indicates what should happen when the data contain NAs. Defaults to `getOption("na.action")`.

equiv.test is modelled after (and borrows code from) R's t.test() and is intended to work as similarly as possible.

This functions implements uniformly most powerful invariant equivalence tests for one-sample and (paired or unpaired) two-sample problems. Also supported are one-sided versions (so-called non-inferiority or non-superiority tests).

All tests are on standardized (differences of) means theta:

theta = (mu_x - mu) / sigma

for the one-sample case,

theta = (mu_d - mu) / sigma_d

for the paired two-sample case and

theta = (mu_x - mu_y - mu) / sigma

for the unpaired test, where sigma is the standard deviation of x and y and sigma_d is the standard deviation of the differences. mu is a shift parameter that can be used to compare against a known value in the one-sample case. mu should usually be zero for two-sample problems.

The null and alternative hypotheses in equivalence tests (alternative = "two.sided") are

H_0: theta <= -eps \qquad or \qquad theta >= eps

vs

H_1: -eps < theta < eps

Currently, only symmetric equivalence intervals (-eps, eps) are supported.

In the non-inferority-case (alternative = "greater") we test

H_0: theta <= -eps

vs

H_1: theta > -eps

In the non-superiority-case (alternative = "less") we test

H_0: theta >= eps

vs

H_1: theta < eps

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).

The formula interface is only applicable for the two-sample tests.

A list with class htest containing the following components:

`statistic`	the value of the t-statistic.
`parameter`	the degrees of freedom for the t-statistic.
`p.value`	the p-value for the test.
`estimate`	the plug-in estimate of the standardized mean (or mean difference), i.e. the empirical mean (or difference of empirical means) divided by the empirical standard deviation. Note that this estimate is not unbiaded.
`null.value`	non-equivalence limits, i.e. boundaries of null hypothesis
`alternative`	a character string describing the alternative hypothesis.
`method`	a character string indicating what type of equivalence test was performed.
`data.name`	a character string giving the name(s) of the data.

default: Default S3 method:
formula: S3 method for class 'formula'

Wellek, S. (2010). Testing Statistical Hypotheses of Equivalence and Noniferiority. Second edition. Boca Raton: Chapman & Hall. (especially Chapters 5.3 and 6.1).

  # compare two feed from chickwts dataset
  data("chickwts")
  chickwts2 <- chickwts[chickwts$feed %in% c("linseed", "soybean"),]
  chickwts2$feed <- droplevels(chickwts2$feed)

  # similar but cannot be shown to be equivalent up to 0.5 sigma at 0.05 level^
  plot(weight ~ feed, data = chickwts2)
  equiv.test(weight ~ feed, data = chickwts2, eps = 0.5)