This function is designed to calculate critical values for Grubbs tests for outliers detecting and to approximate p-values reversively.
qgrubbs(p, n, type = 10, rev = FALSE)
pgrubbs(q, n, type = 10)vector of probabilities.
vector of quantiles.
sample size.
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.
if set to TRUE, function qgrubbs acts as pgrubbs.
A vector of quantiles or p-values.
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 uniroot.
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.
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.