Calculate critical values and p-values for Grubbs tests
Description:
This function is designed to calculate critical values for Grubbs
tests for outliers detecting and to approximate p-values
reversively.
Usage:
[q]=grubbsinv(p, n, type, rev)
Arguments:
p: vector of probabilities.
n: sample size.
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.
rev: if set to TRUE, function 'grubbsinv' acts as 'grubbscdf' (grubbscdf
is really wrapper to grubbsinv to omit repetition of the code).
Details:
The critical values for test for one outlier is calculated
according to approximations given by Pearson and Sekar (1936). The
formula is simply reversed to obtain p-value.
The values for two outliers test (on opposite sides) are
calculated according to David, Hartley, and Pearson (1954). Their
formula cannot be rearranged to obtain p-value, thus such values
are obtained by simple bisection method.
For test checking presence of two outliers at one tail, the
tabularized distribution (Grubbs, 1950) is used, and
approximations of p-values are interpolated using 'qtable'.
Value:
A vector of quantiles or p-values.
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.
Pearson, E.S., Sekar, C.C. (1936). The efficiency of statistical
tools and a criterion for the rejection of outlying observations.
Biometrika, 28, 3, 308-320.
David, H.A, Hartley, H.O., Pearson, E.S. (1954). The distribution
of the ratio, in a single normal sample, of range to standard
deviation. Biometrika, 41, 3, 482-493.
