R: Steel's k-Treatments vs. Control Test

steelsKSampleTest {PMCMRplus} | R Documentation

## Steel's k-Treatments vs. Control Test

### Description

Performs the non-parametric Steel's test for simultaneously testing k-treatments vs. one control.

### Usage

    steelsKSampleTest(x, ...)

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

    ## S3 method for class 'formula'
    steelsKSampleTest(
      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

It tests H: F(i) = F(0), ~ i ≤ k, against A: F(i) > F(0) (greater) with at least one inequality being strict.

The function is a wrapper function that calls `Steel.test` of the package kSamples with argument `method = "asymptotic"`.

### 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

Scholz, F. and Zhu, A. (2019). kSamples: K-Sample Rank Tests and their Combinations. R package version 1.2-9. https://CRAN.R-project.org/package=kSamples

Steel, R. G. D. (1959) A Multiple Comparison Rank Sum Test: Treatments Versus Control, Biometrics 15, 560–572.

### See Also

`Steel.test`, `flignerWolfeTest`

### 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("0", "I", "II")

    ## Steel's Test
    steelsKSampleTest(x ~ g, alternative = "greater")

    ## Example from USEPA (2002):
    ## Reproduction data from a Ceriodaphnia dubia
    ## 7-day chronic test to several concentrations
    ## of effluent. Dose level 50% is excluded.
    x <- c(20, 26, 26, 23, 24, 27, 26, 23, 27, 24,
    13, 15, 14, 13, 23, 26, 0, 25, 26, 27,
    18, 22, 13, 13, 23, 22, 20, 22, 23, 22,
    14, 22, 20, 23, 20, 23, 25, 24, 25, 21,
    9, 0, 9, 7, 6, 10, 12, 14, 9, 13,
    rep(0,10))
    g <- gl(6, 10)
    levels(g) <- c("Control", "3%", "6%", "12%", "25%", "50%")

    ## NOEC at 3%, LOEC at 6%
    steelsKSampleTest(x ~ g, subset = g != "50%", alternative = "less")

[Package PMCMRplus version 1.9.0 Index]