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We modified the robust analysis of variance (RANOVA) method to calculate sampling uncertainty of selected trace elements determined in soil samples from two heterogeneous remote historic metal ore mining areas. Classical RANOVA is down-weighting the outlying values by replacing them during the calculation process with mean  ± c·σ    r  . Because the arithmetic mean is greatly influenced by outliers, it cannot represent a robust statistic. The main novel contribution of this work is use of median value that is independent on outliers and replace all extreme values during the calculation process with median  ±  2· σ    r  . In our work, 18 duplicate, composite soil samples were collected, digested with aqua regia in a closed microwave system, and analyzed twice for selected trace elements. To extract homogenous groups within sampling areas and make the results more accessible for interpretation, a cluster analysis was done. Subsequently, histograms of each element were prepared and statistical tests were applied to determine the normal distribution of datasets. For abnormally distributed elements, the outlying values were identified by four different methods: boxplot, mean  ± c·σ    r  , mean  ± c·σ , and median  ±  2· σ    r  . For five elements, the amount of outliers identified by the median ± 2· σ    r   procedure was less than 10 %, and for these elements, the sampling uncertainty was computed using a modified RANOVA method. The sampling uncertainty computed with this method was 28.9 % for Cd, 15.2 % for Co, 14.5 % for Mn, 12.7 % for Ni, and 16.3 % for Zn, whereas that computed with a traditional model was 16.7 % for Cd, 9.2 % for Co, 20.5 % for Mn, 17.9 % for Ni, and 16.3 % for Zn.   Electronic supplementary material  The online version of this article (doi:10.1007/s10661-016-5584-9) contains supplementary material, which is available to authorized users.

Heterogeneous areas—identification of outliers and calculation of soil sampling uncertainty using the modified RANOVA method