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PMCMRplus (version 1.9.3)

doubleGrubbsTest: 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.

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.

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 \(x_{(1)} \le x_{(2)} \le \ldots \le x_{(n)}\). Then the following model for testing two maximum outliers can be proposed:

$$ x_{(i)} = \left\{ \begin{array}{lcl} \mu + \epsilon_{(i)}, & \qquad & i = 1, \ldots, n - 2 \\ \mu + \Delta + \epsilon_{(j)} & \qquad & j = n-1, n \\ \end{array} \right.$$

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

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

$$ x_{(i)} = \left\{ \begin{array}{lcl} \mu + \Delta + \epsilon_{(j)} & \qquad & j = 1, 2 \\ \mu + \epsilon_{(i)}, & \qquad & i = 3, \ldots, n \\ \end{array} \right.$$

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

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.. 10.1007/s10182-011-0185-y.

Examples

Run this code
# NOT RUN {
data(Pentosan)
dat <- subset(Pentosan, subset = (material == "A"))
labMeans <- tapply(dat$value, dat$lab, mean)
doubleGrubbsTest(x = labMeans, alternative = "less")
# }

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