| grubbsTest {PMCMRplus} | R Documentation |
Grubbs Outlier Test
Description
Performs Grubbs single outlier test.
Usage
grubbsTest(x, alternative = c("two.sided", "greater", "less"))
Arguments
x |
a numeric vector of data. |
alternative |
the alternative hypothesis.
Defaults to |
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 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.
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.. doi:10.1007/s10182-011-0185-y.
Examples
data(Pentosan)
dat <- subset(Pentosan, subset = (material == "A"))
labMeans <- tapply(dat$value, dat$lab, mean)
grubbsTest(x = labMeans, alternative = "two.sided")