Normal or log-normal: That is the question!

Because of the gemeral preference of the normal distribution, we were asked to find examples of data that followed a normal distribution, but did not match a log-normal distribution. Interestingly, original measurements did not yield any such examples.

Even the classic example of the height of women used to demonstrate the normal distribution (Snedecor and Cochran, 1989) fits both distributions equally well, with parameters 62.54 2.38 inches the normal, and with 62.48 inches x/ 1.039 the log-normal distribution. This is in line with the findings discussed more extensively by Aitchison and Brown (1957, p. 102f) in support of a log-normal distribution for most anthropometric and biological measurements. The examples of normally, but not log-normally distributed data we found consisted of differences, sums, means or other functions of original measurements. These considerations raise the question about the role of symmetry for quantitative variation in nature.

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