R: Cochran Test

cochranTest {PMCMRplus} | R Documentation

## Cochran Test

### Description

Performs Cochran's test for testing an outlying (or inlying) variance.

### Usage

    cochranTest(x, ...)

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

    ## S3 method for class 'formula'
    cochranTest(
      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 normally distributed data the null hypothesis, H_0: σ_1^2 = σ_2^2 = … = σ_k^2 is tested against the alternative (greater) H_{\mathrm{A}}: σ_p > σ_i ~~ (i ≤ k, i \ne p) with at least one inequality being strict.

The p-value is computed with the function `pcochran`.

### 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

Cochran, W.G. (1941) The distribution of the largest of a set of estimated variances as a fraction of their total. Ann. Eugen. 11, 47–52.

Wilrich, P.-T. (2011) Critical values of Mandel's h and k, Grubbs and the Cochran test statistic. Adv. Stat. Anal.. http://dx.doi.org/10.1007/s10182-011-0185-y.

### See Also

`bartlett.test`, `fligner.test`.

### Examples

    data(Pentosan)
    cochranTest(value ~ lab, data = Pentosan, subset = (material == "A"))

[Package PMCMRplus version 1.6.0 Index]