A nonparametric procedure is presented to test the null hypothesis that two independent samples come from the same population against the alternative hypothesis that the samples come from populations differing in variability or “spread.” Extensive tables of critical values are included forn1≤n2≤20. Large sample procedures are presented which include a correction for tied observations. The test is entirely distribution-free under the usual randomization procedures against the null hypothesis that the two distributions are identical. The absence of any normality assumption is a particularly important feature of the test, because its parametric alternative, theFtest for variance differences, is quite sensitive to departures from normality. The test has the additional advantage of being directly applicable to non-numerical ordinal data.