ST_deandixon

Arguments

v:: vector of numerical values
p:: statistical confidence level (%) as a string or the level of significance (α) as a decimal value, "95%", "99%", "99.9%" or 0.05, 0.01, 0.001 resp (see examples).
outlierfree :: input vector with the detected outlier removed; unchanged if the test does not identify an outlier
outlier :: detected outliers as a scalar vector; [] if no outlier is detected

Description

Performs the basic Dean-Dixon outlier test. It sorts the distribution in ascending or descending order, then takes the minimum and maximum values (xi) and calculates the respective Q value for both xi values. This is compared with the critical value from a table (Q_crit). If one of the two or both Q values greater than the corresponding (Q_crit value, one or both xi values are outliers.

$\begin{eqnarray} Q = \frac{\left | x_{i+1}-x_i \right |}{\left | x_n-x_i \right |} \quad ; \quad Q > Q_{crit} \quad \Rightarrow \quad x_i = \text{outlier} \quad ; \quad x = \text{values} \end{eqnarray}$

Only one outlier can be found on each side.

Apply this test ONLY one time to your data.

Do use ST_deandixon ONLY with NORMAL distributed data and with sample sizes from 3 through 30 values! For more than 30 values use Pearson-Hartley "ST_pearsonhartley()" or better the generalized Extreme Studentized Deviate test according to Rosner "ST_esd()" instead.

Examples

data = [6 8 14 12 35 15];
of = ST_deandixon(data, "95%")      // outlier-free values
[of, o] = ST_deandixon(data, "95%") // outlier and outlier-free values
[of, o] = ST_deandixon(data, 0.05)  // outlier and outlier-free values

Authors

Hani A. Ibrahim - hani.ibrahim@gmx.de

Bibliography

Lohringer, H., "Grundlagen der Statistik", Oct, 10th, 2012, http://www.statistics4u.info/fundstat_germ/cc_outlier_tests_4sigma.html

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