R: Nemenyi-Damico-Wolfe Many-to-One Rank Comparison Test

kwManyOneNdwTest {PMCMRplus} | R Documentation

## Nemenyi-Damico-Wolfe Many-to-One Rank Comparison Test

### Description

Performs Nemenyi-Damico-Wolfe non-parametric many-to-one comparison test for Kruskal-type ranked data.

### Usage

    kwManyOneNdwTest(x, ...)

    ## Default S3 method:
    kwManyOneNdwTest(
      x,
      g,
      alternative = c("two.sided", "greater", "less"),
      p.adjust.method = c("single-step", p.adjust.methods),
      ...
    )

    ## S3 method for class 'formula'
    kwManyOneNdwTest(
      formula,
      data,
      subset,
      na.action,
      alternative = c("two.sided", "greater", "less"),
      p.adjust.method = c("single-step", p.adjust.methods),
      ...
    )

### 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`.
`p.adjust.method` | method for adjusting p values (see `p.adjust`).
`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 layout with non-normally distributed residuals the Nemenyi-Damico-Wolfe non-parametric test can be performed. Let there be k groups including the control, then the number of treatment levels is m = k - 1. Then m pairwise comparisons can be performed between the i-th treatment level and the control. H_i: θ_0 = θ_i is tested in the two-tailed case against A_i: θ_0 \ne θ_i, ~~ (1 ≤ i ≤ m).

If `p.adjust.method == "single-step"` is selected, the p-values will be computed from the multivariate normal distribution. Otherwise, the p-values are computed from the standard normal distribution using any of the p-adjustment methods as included in `p.adjust`.

### Value

A list with class `"PMCMR"` 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

  lower-triangle matrix of the estimated quantiles of the pairwise test statistics.

p.value

  lower-triangle matrix of the p-values for the pairwise tests.

alternative

  a character string describing the alternative hypothesis.

p.adjust.method

  a character string describing the method for p-value adjustment.

model

  a data frame of the input data.

dist

  a string that denotes the test distribution.

### Note

This function is essentially the same as `kwManyOneDunnTest`, but there is no tie correction included. Therefore, the implementation of Dunn's test is superior, when ties are present.

### References

Damico, J. A., Wolfe, D. A. (1989) Extended tables of the exact distribution of a rank statistic for treatments versus control multiple comparisons in one-way layout designs, Communications in Statistics - Theory and Methods 18, 3327–3353.

Nemenyi, P. (1963) Distribution-free Multiple Comparisons, Ph.D. thesis, Princeton University.

### See Also

`pmvt`, `TDist`, `kruskalTest`, `kwManyOneDunnTest`, `kwManyOneConoverTest`

### Examples

    ## Data set PlantGrowth
    ## Global test
    kruskalTest(weight ~ group, data = PlantGrowth)

    ## Conover's many-one comparison test
    ## single-step means p-value from multivariate t distribution
    ans <- kwManyOneConoverTest(weight ~ group, data = PlantGrowth,
                                 p.adjust.method = "single-step")
    summary(ans)

    ## Conover's many-one comparison test
    ans <- kwManyOneConoverTest(weight ~ group, data = PlantGrowth,
                                 p.adjust.method = "holm")
    summary(ans)

    ## Dunn's many-one comparison test
    ans <- kwManyOneDunnTest(weight ~ group, data = PlantGrowth,
                                 p.adjust.method = "holm")
    summary(ans)

    ## Nemenyi's many-one comparison test
    ans <- kwManyOneNdwTest(weight ~ group, data = PlantGrowth,
                            p.adjust.method = "holm")
    summary(ans)

[Package PMCMRplus version 1.6.0 Index]