Concentration of analytical data as part of data processing in trace element analysis

Abstract

Statistical data evaluation in trace element analysis was mainly influenced by the Normal Law of Error, which is based on the assumption of a Gaussian normal distribution. Supposing that the analytical error of the trace element concentration is negligibly small compared with its true variations in nature, skew distributions may become more important than normal ones. Often, but not always, the lognormal distribution is a good approximation of the skew distribution. Careful investigation of the type of distribution before starting data evaluation in trace element analysis is still frequently overlooked today. In this Department, data concentration is performed on a routine basis by two programmes ZCH-2 and ZCH-3/1. They include a) investigation of the type of distribution by drawing the histogrammes, probability plot for normal and lognormal distribution as Hazen's straight lines, Kolmogorov-Smirnov- and Cramer- van Mises goodness-of-fit tests as well as skewness and kurtosis. Outliers of the normal distribution can be eliminated b) by t-, Nalimov's r-, Grubb's and Dixon's tests. c) As central values for data location, the arithmetic, geometric, and harmonic means and median are calculated. d) The dispersion around the mean is characterized by variance, standard deviation of a single value as well as the mean, relative coefficient of variation, mean deviation from the arithmetic mean, geometric standard deviation, range and 80% inter-decile range. Confidence intervals are given for the arithmetic mean, geometric mean and median. Typical problems of data concentration are the deviation from the normal distribution, comparison of different mean values, outlier elimination, concentrations below detection limit, homogeneity and heterogeneity of the data sample. They are discussed for examples of data series from one of the author's laboratories, e.g. trace element concentrations in air, lead content in dental calculus, toxic heavy metal leaching from ceramic ware and gamma dose rates from an area of higher natural radioactivity in the Federal Republic of Germany. As a conclusion, it is emphasized that the trace element analyst should overcome the “Mystery of the Normal and Quasi-normal Distribution” and include skew data distributions and their statistical treatment into his repertoire of routine procedures as well as in his way of thinking.