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7.8 Tests for Equality of Variances

Two-sample t-tests and one-way ANOVA tests that required the assumption of equal population variances were discussed earlier in the chapter. Support for the assumption may be obtained from scrutiny of displays of the data in the form of individual value plots or boxplots. Minitab provides formal tests of the null hypothesis of equal variances. Consider again the magnesium assay data in Table 7.6, stored in Magnesium.MTW. Use of Stat > Basic Statistics > 2 Variances . . . provides a test of the null hypothesis that the two population variances are the same, i.e. the null hypothesis , versus the alternative hypothesis that they are not, . The null hypothesis is equivalent to H_{0}: s_{1} = s_{2}, which in turn is equivalent to H_{0} : s_{1}/s_{2} = 1. The dialog is shown in Figure 7.40. The alternative hypothesis is equivalent to H_{1} : s_{1} ? s_{2}, which in turn is equivalent to H_{1} : s_{1}/s_{2} ? 1. In completing the dialog the reader is urged to use the Graphs . . . button to select either an individual value plot or boxplot of the data.