doubleGrubbsTest function

Grubbs Double Outlier Test

Performs Grubbs double outlier test.

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.

Returns

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:

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

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

The p-value is computed with the function pdgrubbs.

Examples

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

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") .