Huber-Davies test

MuUiple-Rai e Test and Huber-Davies Test for Outliers... 

An alternative approach to identifying the (somewhat ambivalent) rejection of H, in the ANOVA test is to use a different test for outliers. Several such tests are available but one of the most robust appears (Meier 2000) to be Huber s elimination rule that was not originally formulated as an outlier test (Davies 1988). Moreover, this Huber-Davies test is extremely easy to apply. The first step is to rearrange the test measurement values in increasing order (as for the Multiple-Range Test), thus [xj = 5.51 X3 = 5.91 x, = 6.08 Xj = 7.01 X4 = 7.09]. This allows selection of the median value Xjj,ed(= = 6.08 in our case). The absolute values of the differences i.med = In medl 6 then Calculated and arranged also in... 

The methods of robust statistics have recently been used for the quantitative description of series of measurements that comprise few data together with some outliers [DAVIES, 1988 RUTAN and CARR, 1988]. Advantages over classical outlier tests, such as those according to DIXON [SACHS, 1992] or GRUBBS [SCHEFFLER, 1986], occur pri-marly when outliers towards both the maximum and the minimum are found simultaneously. Such cases almost always occur in environmental analysis without being outliers in the classical sense which should be eliminated from the set of data. The foundations of robust statistics, particularly those of median statistics, are described in detail by TUKEY [1972], HUBER [1981], and HAMPEL et al. [1986] and in an overview also by DANZER [1989] only a brief presentation of the various computation steps shall be given here. 

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