qgrubbs {outliers}

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

qgrubbs(p, n, type = 10, rev = FALSE)
pgrubbs(q, n, type = 10)

Arguments

p

vector of probabilities.

q

vector of quantiles.

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 qgrubbs acts as pgrubbs.

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 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.

Value

A vector of quantiles or p-values.

Author(s)

Lukasz Komsta

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.

See Also

grubbs.test