Estimating Common Parameters of Lognormally Distributed Environmental and Biomonitoring Data: Harmonizing Disparate Statistics From Publications

The progression of science is driven by the accumulation of knowledge and builds upon published work of others. Another important feature is to place current results into the context of previous observations. The published literature, however, often does not provide sufficient direct information for the reader to interpret the results beyond the scope of that particular article. Authors tend to provide only summary statistics in various forms, such as means and standard deviations, median and range, quartiles, 95% confidence intervals, and so on, rather than providing measurement data. Second, essentially all environmental and biomonitoring measurements have an underlying lognormal distribution, so certain published statistical characterizations may be inappropriate for comparisons. The aim of this study was to review and develop direct conversions of different descriptions of data into a standard format comprised of the geometric mean (GM) and the geometric standard deviation (GSD) and then demonstrate how, under the assumption of lognormal distribution, these parameters are used to answer questions of confidence intervals, exceedance levels, and statistical differences among distributions. A wide variety of real-world measurement data sets was reviewed, and it was demonstrated that these data sets are indeed of lognormal character, thus making them amenable to these methods. Potential errors incurred from making retrospective estimates from disparate summary statistics are described. In addition to providing tools to interpret other people's data, this review should also be seen as a cautionary tale for publishing one's own data to make it as useful as possible for other researchers.