Background and threshold: critical comparison of methods of determination

Different procedures to identify data outliers in geochemical data are reviewed and tested. The calculation of [mean±2 standard deviation (sdev)] to estimate threshold values dividing background data from anomalies, still used almost 50 years after its introduction, delivers arbitrary estimates. The boxplot, [median±2 median absolute deviation (MAD)] and empirical cumulative distribution functions are better suited for assisting in the estimation of threshold values and the range of background data. However, all of these can lead to different estimates of threshold. Graphical inspection of the empirical data distribution using a variety of different tools from exploratory data analysis is thus essential prior to estimating threshold values or defining background. There is no good reason to continue to use the [mean±2 sdev] rule, originally proposed as a 'filter' to identify approximately 2½% of the data at each extreme for further inspection at a time when computers to do the drudgery of numerical operations were not widely available and no other practical methods existed. Graphical inspection using statistical and geographical displays to isolate sets of background data is far better suited for estimating the range of background variation and thresholds, action levels (e.g., maximum admissible concentrations-MAC values) or clean-up goals in environmental legislation.