Weighted Least Squares ANOVA, Single-Factor

ANOVA, Single-Factor, Using WLS Regression Approach When Normality Satisfied but Homoscedasticity Not Satisfied

The following SAS program provides the statistics for testing equality of means using the weighted least squares approach. This approach is used when there is evidence for heteroscedasticity, but no evidence that the normality assumption is violated. The example used here is the surface coating of optical lens example. data one; input coating haziness; if coating = 1 then x1 = 1; else x1 = 0; if coating = 2 then x2 = 1; else x2 = 0; if coating = 3 then x3 = 1; else x3 = 0; if coating = 4 then x4 = 1; else x4 = 0; x = 1; label coating = "Lens Surface Coating" haziness = "Lens Haziness after Abrasion"; cards; 1 8.52 1 9.21 1 10.45 1 10.23 1 8.75 1 9.32 1 9.65 2 12.50 2 11.84 2 12.69 2 12.43 2 12.78 2 13.15 2 12.89 3 8.45 3 10.89 3 11.49 3 12.87 3 14.52 3 13.94 3 13.16 4 10.73 4 8.00 4 9.75 4 8.71 4 10.45 4 11.38 4 11.35 ; proc boxplot; plot haziness*coating; title "Side-by-Side Boxplots of Response Variable"; title2 "by Levels of Treatment"; ; proc sort;by coating; ; proc means;by coating; var haziness; output out=coatsd stddev=sdcoat; ; data two;set coatsd; w = 1/(sdcoat*sdcoat); ; data three;merge one two;by coating; ; proc glm; model haziness = x1 x2 x3 x4 / noint; weight w; title "Full Model"; title2 "WLS Approach"; ; proc glm; model haziness = x / noint; weight w; title "Reduced Model"; ; run;