Log-normal Distributions across the Sciences: Keys and Clues
E. Limpert, Werner A. Stahel, MARKUS ABBT · BioScience · 2001
As the need grows for conceptualization, formalization, and abstraction in biology, so too does mathematics' relevance to the field (Fagerström et al. 1996). Mathematics is particularly important for analyzing and characterizing random variation of, for example, size and weight of individuals in populations, their sensitivity to chemicals, and time-to-event cases, such as the amount of time an individual needs to recover from illness. The frequency distribution of such data is a major factor determining the type of statistical analysis that can be validly carried out on any data set. Many widely used statistical methods, such as ANOVA (analysis of variance) and regression analysis, require that the data be normally distributed, but only rarely is the frequency distribution of data tested when these techniques are used. The Gaussian (normal) distribution is most often assumed to describe the random variation that occurs in the data from many scientific disciplines; the well-known bell-shaped curve can easily be characterized and described by two values: the arithmetic mean x and the standard deviation s, so that data sets are commonly described by the expression x ± s. A historical example of a normal distribution is that of chest measurements of Scottish soldiers made by Quetelet, Belgian founder of modern social statistics (Swoboda 1974). In addition, such disparate phenomena as milk production by cows and random deviations from target values in industrial processes fit a normal distribution.