Was Quetelet’s Average Man Normal?

Quetelet’s data on Scottish chest girths are analyzed with eight normality tests. In contrast to Quetelet’s conclusion that the data are fit well by what is now known as the normal distribution, six of eight normality tests provide strong evidence that the chest circumferences are not normally distributed. Using corrected chest circumferences from Stigler, the χ2 test no longer provides strong evidence against normality, but five commonly used normality tests do. The D’Agostino–Pearson K2 and Jarque–Bera tests, based only on skewness and kurtosis, find that both Quetelet’s original data and the Stigler-corrected data are consistent with the hypothesis of normality. The major reason causing most normality tests to produce low p-values, indicating that Quetelet’s data are not normally distributed, is that the chest circumferences were reported in whole inches and rounding of large numbers of observations can produce many tied values that strongly affect most normality tests. Users should be cautious using many standard normality tests if data have ties, are rounded, and the ratio of the standard deviation to rounding interval is small.