Performs Grubbs single outlier test.
grubbsTest(x, alternative = c("two.sided", "greater", "less"))A list with class "htest" containing the following components:
a character string indicating what type of test was performed.
a character string giving the name(s) of the data.
the estimated quantile of the test statistic.
the p-value for the test.
the parameters of the test statistic, if any.
a character string describing the alternative hypothesis.
the estimates, if any.
the estimate under the null hypothesis, if any.
a numeric vector of data.
the alternative hypothesis.
Defaults to "two.sided".
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 a single maximum outlier can be proposed:
$$ x_{(i)} = \left\{ \begin{array}{lcl} \mu + \epsilon_{(i)}, & \qquad & i = 1, \ldots, n - 1 \\ \mu + \Delta + \epsilon_{(n)} & & \\ \end{array} \right.$$
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 a single minimum outlier, the model can be proposed as
$$ x_{(i)} = \left\{ \begin{array}{lcl} \mu + \Delta + \epsilon_{(1)} & & \\ \mu + \epsilon_{(i)}, & \qquad & i = 2, \ldots, n \\ \end{array} \right.$$
The null hypothesis is tested against the alternative, H\(_{\mathrm{A}}: \Delta < 0\).
The p-value is computed with the function pgrubbs.
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").
data(Pentosan)
dat <- subset(Pentosan, subset = (material == "A"))
labMeans <- tapply(dat$value, dat$lab, mean)
grubbsTest(x = labMeans, alternative = "two.sided")
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