R: Grubbs Double Outlier Test

doubleGrubbsTest {PMCMRplus} | R Documentation

## Grubbs Double Outlier Test

### Description

Performs Grubbs double outlier test.

### Usage

    doubleGrubbsTest(x, alternative = c("two.sided", "greater", "less"), m = 10000)

### Arguments

`x` | a numeric vector of data.
`alternative` | the alternative hypothesis. Defaults to `"two.sided"`.
`m` | number of Monte-Carlo replicates.

### Details

Let X denote an identically and independently distributed continuous variate with realizations x_i ~~ (1 ≤ i ≤ k). Further, let the increasingly ordered realizations denote x_{(1)} ≤ x_{(2)} ≤ … ≤ x_{(n)}. Then the following model for testing two maximum outliers can be proposed:

x[(i)] = μ + ε[(i)] for i = 1, ..., n - 2 and x[(i)] = μ + Δ + ε[(j)] for j = n-1, n

with ε \approx N(0,σ). The null hypothesis, H_0: Δ = 0 is tested against the alternative, H_{\mathrm{A}}: Δ > 0.

For testing two minimum outliers, the model can be proposed as

x[(i)] = μ + Δ + ε[(j)] for j = 1, 2 and x[(i)] = μ + ε[(i)] for i = 3, ..., n

The null hypothesis is tested against the alternative, H_{\mathrm{A}}: Δ < 0.

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

### 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

Grubbs, F. E. (1950) Sample criteria for testing outlying observations. Ann. Math. Stat. 21, 27–58.

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.

### Examples

    data(Pentosan)
    dat <- subset(Pentosan, subset = (material == "A"))
    labMeans <- tapply(dat$value, dat$lab, mean)
    doubleGrubbsTest(x = labMeans, alternative = "less")

[Package PMCMRplus version 1.7.0 Index]