dixonTest {dixonTest} | R Documentation |
Dixons Outlier Test (Q-Test)
Description
Performs Dixons single outlier test.
Usage
dixonTest(x, alternative = c("two.sided", "greater", "less"), refined = FALSE)
Arguments
x |
a numeric vector of data |
alternative |
the alternative hypothesis.
Defaults to |
refined |
logical indicator, whether the refined version
or the Q-test shall be performed. Defaults to |
Details
Let denote an identically and independently distributed
normal variate. Further, let the increasingly ordered realizations
denote
.
Dixon (1950) proposed the following ratio statistic to detect
an outlier (two sided):
The null hypothesis, no outlier, is tested against the alternative,
at least one observation is an outlier (two sided). The subscript
on the
symbol indicates the number of
outliers that are suspected at the upper end of the data set,
and the subscript
indicates the number of outliers suspected
at the lower end. For
it is also common to use the
statistic
.
The statistic for a single maximum outlier is:
The null hypothesis is tested against the alternative, the maximum observation is an outlier.
For testing a single minimum outlier, the test statistic is:
The null hypothesis is tested against the alternative, the minimum observation is an outlier.
Apart from the earlier Dixons Q-test (i.e. ),
a refined version that was later proposed by Dixon can be performed
with this function, where the statistic
depends on
the sample size as follows:
: | |
: | |
; | |
: | |
The p-value is computed with the function pdixon
.
References
Dixon, W. J. (1950) Analysis of extreme values. Ann. Math. Stat. 21, 488–506. doi:10.1214/aoms/1177729747.
Dean, R. B., Dixon, W. J. (1951) Simplified statistics for small numbers of observation. Anal. Chem. 23, 636–638. doi:10.1021/ac60052a025.
McBane, G. C. (2006) Programs to compute distribution functions and critical values for extreme value ratios for outlier detection. J. Stat. Soft. 16. doi:10.18637/jss.v016.i03.
Examples
## example from Dean and Dixon 1951, Anal. Chem., 23, 636-639.
x <- c(40.02, 40.12, 40.16, 40.18, 40.18, 40.20)
dixonTest(x, alternative = "two.sided")
## example from the dataplot manual of NIST
x <- c(568, 570, 570, 570, 572, 578, 584, 596)
dixonTest(x, alternative = "greater", refined = TRUE)