Grubbs tests for one or two outliers in data sample
Description:
Performs Grubbs' test for one outlier, two outliers on one tail,
or two outliers on opposite tails, in small sample.
Usage:
[pval,G,U] = grubbstest(x,type,opposite,twosided)
Arguments:
x: a numeric vector or matrix of data values. Matrices are treated
columnwise (each column as independent set).
opposite: a logical (default 0) indicating whether you want to check not the value
with largest difference from the mean, but opposite (lowest,
if most suspicious is highest etc.)
type: Integer value indicating test variant. 10 is a test for one
outlier (side is detected automatically and can be reversed
by 'opposite' parameter). 11 is a test for two outliers on
opposite tails, 20 is test for two outliers in one tail. Default 10.
two.sided: Logical value indicating if there is a need to treat this
test as two-sided. Default 0.
Details:
The function can perform three tests given and discussed by Grubbs
(1950).
First test (10) is used to detect if the sample dataset contains
one outlier, statistically different than the other values. Test
is based by calculating score of this outlier G (outlier minus
mean and divided by sd) and comparing it to appropriate critical
values. Alternative method is calculating ratio of variances of
two datasets - full dataset and dataset without outlier. The
obtained value called U is bound with G by simple formula.
Second test (11) is used to check if lowest and highest value are
two outliers on opposite tails of sample. It is based on
calculation of ratio of range to standard deviation of the sample.
Third test (20) calculates ratio of variance of full sample and
sample without two extreme observations. It is used to detect if
dataset contains two outliers on the same tail.
The p-values are calculated using 'grubbscdf' function.
Value:
G,U: the value statistic. For type 10 it is difference between
outlier and the mean divided by standard deviation, and for
type 20 it is sample range divided by standard deviation.
Additional value U is ratio of sample variances with and
withour suspicious outlier. According to Grubbs (1950) these
values for type 10 are bound by simple formula and only one
of them can be used, but function gives both. For type 20 the
G is the same as U.
pval: the p-value for the test.
Author(s):
Lukasz Komsta, ported from R package "outliers".
See R News, 6(2):10-13, May 2006
References:
Grubbs, F.E. (1950). Sample Criteria for testing outlying
observations. Ann. Math. Stat. 21, 1, 27-58.
