An influential statistics test recommends a Levene text for homogeneity of variance. A recent note suggests that Levene's test is upwardly biased for small samples. Another report shows inflated Alpha estimates and low power. Neither study utilized more than two sample sizes. This Monte Carlo study involved sampling from a normal population for all combinations of two to seven variances and equal sample sizes from three to twelve. Alpha was upwardly biased for smaller sample sizes; Alpha was upwardly biased for increasing numbers of variances and fixed sample sizes. The Levene technique apparently has little to recommend it besides computational simplicity. (Author)