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A Quick, Compact, Two-Sample Dispersion Test

The common “F test” for testing the equality of two population variances is very sensitive to the normality assumption, yet many introductory statistics books do not stress this sensitivity. Several alternative dispersion tests have been developed that do not assume normality, but these are rarely discussed other than in nonparametric statistics texts. Additionally, these tests generally require tables of critical values or software to calculate p values. We propose a simple graphical procedure, requiring no tables or software, that compares absolute deviations of one sample to another. With equal sample sizes, if one sample has the five largest absolute deviations, we conclude that its population has greater dispersion. We believe the simplicity of this test makes it a viable alternative to the often misleading F test and to other tests.