% 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. % %