johnsonTest() R function from [PMCMRplus]

Testing against Ordered Alternatives (Johnson-Mehrotra Test)

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


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 NAs. Defaults to getOption("na.action").

Returns

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.

Details

The null hypothesis, H $_0: \theta_1 = \theta_2 = \ldots = \theta_k$

is tested against a simple order hypothesis, Hc(" $_\\mathrm{A}: \\theta_1 \\le \\theta_2 \\le \\ldots \\le\n$ ", " $\\theta_k,~\\theta_1 < \\theta_k$ ").

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

Note

Factor labels for g must be assigned in such a way, that they can be increasingly ordered from zero-dose control to the highest dose level, e.g. integers {0, 1, 2, ..., k} or letters {a, b, c, ...}. Otherwise the function may not select the correct values for intended zero-dose control.

It is safer, to i) label the factor levels as given above, and to ii) sort the data according to increasing dose-levels prior to call the function (see order, factor).

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)

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.

johnsonTest function