A procedure for testing homogeneity of variances is proposed. The procedure uses weighted regression on the sample variances and the sample means, using the reciprocal of the sample standard deviations as the weights. The procedure is based on the assumption that data sets with larger means tend to have larger variances. When applied to real data sets, the procedure is better at detecting differences in the variances than Bartlett's test, Levene's test, or other standard tests for homogeneity of variances. Extensive simulations indicate that the procedure is robust to distributional form provided that the distributions are symmetric. The power of the procedure is greater than that of Bartlett's test, Cochran's test, or the F-max test when the samples are from normal distributions. In addition, the procedure is much more powerful than Levene's test for nonnormal symmetrical distributions. The procedure is particularly sensitive to small differences in the population variances. The procedure is not recommended when fewer than four or five variances are being compared.