The scaling of dispersion and correlation: A comparison of least-squares and absolute-deviation statistics

In conventional measures of dispersion and correlation, the use of squared deviations from the mean causes a disproportionate influence of outliers. We have compared various conventional and unconventional measures of dispersion and correlation through repeated computer trials, taking large numbers of samples from populations of specified distributions. Under the normal distribution, the standard deviation and Pearson correlation provide the most stable estimates of dispersion and correlation. However, in other cases involving outliers within normal distributions, double exponential distributions, or skewed distributions, measures of dispersion and correlation involving absolute deviations from the mean are clearly more stable than arc conventional formulae.