PMCMRplus: johnsonTest – R documentation

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johnsonTest

Testing against Ordered Alternatives (Johnson-Mehrotra Test)

Description

Performs the Johnson-Mehrotra test for testing against ordered alternatives in a balanced one-factorial sampling design.

Usage

johnsonTest(x, ...)

## Default S3 method:
johnsonTest(x, g, alternative = c("two.sided", "greater", "less"), ...)

## S3 method for class 'formula'
johnsonTest(
  formula,
  data,
  subset,
  na.action,
  alternative = c("two.sided", "greater", "less"),
  ...
)

Arguments

`x`	a numeric vector of data values, or a list of numeric data vectors.
`...`	further arguments to be passed to or from methods.
`g`	a vector or factor object giving the group for the corresponding elements of `"x"`. Ignored with a warning if `"x"` is a list.
`alternative`	the alternative hypothesis. Defaults to `"two.sided"`.
`formula`	a formula of the form `response ~ group` where `response` gives the data values and `group` a vector or factor of the corresponding groups.
`data`	an optional matrix or data frame (or similar: see `model.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 `NA`s. Defaults to `getOption("na.action")`.

Details

The null hypothesis, H_0: θ_1 = θ_2 = … = θ_k is tested against a simple order hypothesis, H_\mathrm{A}: θ_1 ≤ θ_2 ≤ … ≤ θ_k,~θ_1 < θ_k.

The p-values are estimated from the standard normal distribution.

Value

A list with class "htest" containing the following components:

method: a character string indicating what type of test was performed.
data.name: a character string giving the name(s) of the data.
statistic: the estimated quantile of the test statistic.
p.value: the p-value for the test.
parameter: the parameters of the test statistic, if any.
alternative: a character string describing the alternative hypothesis.
estimates: the estimates, if any.
null.value: the estimate under the null hypothesis, if any.

References

Bortz, J. (1993). Statistik für Sozialwissenschaftler (4th ed.). Berlin: Springer.

Johnson, R. A., Mehrotra, K. G. (1972) Some c-sample nonparametric tests for ordered alternatives. Journal of the Indian Statistical Association 9, 8–23.

Examples

## Example from Sachs (1997, p. 402)
x <- c(106, 114, 116, 127, 145,
       110, 125, 143, 148, 151,
       136, 139, 149, 160, 174)
g <- gl(3,5)
levels(g) <- c("A", "B", "C")

## Chacko's test
chackoTest(x, g)

## Cuzick's test
cuzickTest(x, g)

## Johnson-Mehrotra test
johnsonTest(x, g)

## Jonckheere-Terpstra test
jonckheereTest(x, g)

## Le's test
leTest(x, g)

## Spearman type test
spearmanTest(x, g)

## Murakami's BWS trend test
bwsTrendTest(x, g)

## Fligner-Wolfe test
flignerWolfeTest(x, g)

## Shan-Young-Kang test
shanTest(x, g)

PMCMRplus

Calculate Pairwise Multiple Comparisons of Mean Rank Sums Extended

v1.9.0

GPL (>= 3)

Authors

Thorsten Pohlert [aut, cre] (<https://orcid.org/0000-0003-3855-3025>)

Initial release

2021-01-12