* Note that in Section 3.6 the book does the Brown Forsythe test for just two groups using a t-test. With two groups use of the t-test is equivalent to the use of the F-test that we used in notes in the class. We have done it in terms of the F-test as this automatically handles more than two groups. * BROWN-FORSYTHE/MODIFIED LEVENE TEST IN SAS. The later versions of SAS have a Brown-Forsythe option in ANOVA. If you run an anova the residuals as the respons an with hovtest=bf you get the same test that we developed by finding the d's (deviations of residuals from the median) and running a one-way anova on the d's. To illustrate consider the Kishi data with the developments in the notes where we obtained d directly by obtaining the medians and using them. Then using proc anova; class group; model d =group; run; yielded The ANOVA Procedure Dependent Variable: d Sum of Source DF Squares Mean Square F Value Pr > F Model 2 14.5820939 7.2910469 1.78 0.1865 Error 28 114.4087282 4.0860260 The F-test of 1.78 with a p-value of .1865 is the Brown-Forsythe test. We can also use proc anova data=result; class group; model resid=group; means group/hovtest=bf; but notice I have now used hovtest=bf rather than levene as done in class. This first ANOVA, which I had left out of the class notes, gives Dependent Variable: resid Residual Sum of Source DF Squares Mean Square F Value Pr > F Model 2 1.1466860 0.5733430 0.05 0.9512 Error 28 320.0978299 11.4320654 Corrected Total 30 321.2445159 The F-test here is testing the hypothesis that the expected value of the residuals is equal across groups. It should be if the model is correct as the true errors have mean 0. So, not surprisingly this is non signficiant. The second part of this anova is testing equality of variances of the residuals, which with Brown-Forsythe option is doing exactly what we did by creating the d's earlier. Brown and Forsythe's Test for Homogeneity of resid Variance ANOVA of Absolute Deviations from Group Medians Sum of Mean Source DF Squares Square F Value Pr > F group 2 14.5821 7.2910 1.78 0.1865 Error 28 114.4 4.0860