R: Steel's Many-to-One Rank Test

steelTest {PMCMRplus} | R Documentation

## Steel's Many-to-One Rank Test

### Description

Performs Steel's non-parametric many-to-one comparison test for Wilcox-type ranked data.

### Usage

    steelTest(x, ...)

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

    ## S3 method for class 'formula'
    steelTest(
      formula,
      data,
      subset,
      na.action,
      alternative = c("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 `greater`
`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

For many-to-one comparisons (pairwise comparisons with one control) in an one-factorial balanced layout with non-normally distributed residuals Steels's non-parametric single-step test can be performed. Let there be k treatment levels (excluding the control), then k pairwise comparisons can be performed between the i-th treatment level and the control. H_i: θ_0 = θ_i is tested in the one-tailed case (less) against A_i: θ_0 > θ_i, ~~ (1 ≤ i ≤ k).

For each control - treatment level the data are ranked in increasing order. The ranksum R_i for the i-th treatment level is compared to a critical R value and is significantly(p = 0.05) less, if R_i ≤ R. For the `alternative = "greater"` the sign is changed.

The function does not return p-values. Instead the critical R-values as given in the tables of USEPA (2002) for α = 0.05 (one-sided, less) are looked up according to the balanced sample sizes (n) and the order number of the dose level (i).

### Value

A list with class `"osrt"` that contains 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 statistic(s)

crit.value

  critical values for α = 0.05.

alternative

  a character string describing the alternative hypothesis.

parameter

  the parameter(s) of the test distribution.

dist

  a string that denotes the test distribution.

There are print and summary methods available.

### Source

The critical rank sum values were taken from Table E.5 of USEPA (2002).

USEPA (2002) Short-term Methods for Estimating the Chronic Toxicity of Effluents and Receiving Waters to Freshwater Organisms, 4th edition, EPA-821-R-02-013.

### Note

Steel's Many-to-One Rank test is only applicable for balanced designs and directional hypotheses. An error message will occur, if the design is unbalanced. In the current implementation, only one-sided tests on the level of α = 0.05 can be performed.

### References

Steel, R. G. D. (1959) A multiple comparison rank sum test: treatments versus control, Biometrics 15, 560–572.

### See Also

`wilcox.test`, `pairwise.wilcox.test`, `manyOneUTest`, `flignerWolfeTest`, `shirleyWilliamsTest`, `kwManyOneDunnTest`, `kwManyOneNdwTest`, `kwManyOneConoverTest`, `print.osrt`, `summary.osrt`

### 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
    steelTest(x ~ g)

    ## 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%
    steelTest(x ~ g, subset = g != "50%", alternative = "less")

[Package PMCMRplus version 1.7.1 Index]