PMCMRplus (version 1.9.6)

doubleGrubbsTest: Grubbs Double Outlier Test

Description

Performs Grubbs double outlier test.

Usage

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

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.

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 $x_i(1\le i\le k)$. Further, let the increasingly ordered realizations denote $x_{(1)}\le x_{(2)}\le \dots \le x_{(n)}$. Then the following model for testing two maximum outliers can be proposed:

$$x_{(i)}=\{\begin{array}{lcl}\mu +{ϵ}_{(i)},& & i=1,\dots ,n-2\\ \mu +\mathrm{\Delta }+{ϵ}_{(j)}& & j=n-1,n\end{array}$$

with $ϵ\approx N(0,\sigma )$. The null hypothesis, H${}_0:\mathrm{\Delta }=0$ is tested against the alternative, H${}_{\mathrm{A}}:\mathrm{\Delta }>0$.

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

$$x_{(i)}=\{\begin{array}{lcl}\mu +\mathrm{\Delta }+{ϵ}_{(j)}& & j=1,2\\ \mu +{ϵ}_{(i)},& & i=3,\dots ,n\end{array}$$

The null hypothesis is tested against the alternative, H${}_{\mathrm{A}}:\mathrm{\Delta }<0$.

The p-value is computed with the function pdgrubbs.

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.. tools:::Rd_expr_doi("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")