Testing for Constant Variances

The difference-from-nominal chart should be accompanied by a test that checks whether the variances for each product type are identical (homogeneous). Levene’s test of homogeneity is particularly appropriate for short run applications because it is robust to departures from normality; refer to Snedecor and Cochran (1980). You can implement Levene’s method by using the GLM procedure to construct a one-way analysis of variance for the absolute deviations of the diameters from averages within product types.

proc sort data=Old;
   by Prodtype;
run;

proc means data=Old noprint;
   var Diameter;
   by Prodtype;
   output out=Oldmean (keep=Prodtype diammean) mean=diammean;
run;

data Old;
   merge Old Oldmean;
      by Prodtype;
   absdev = abs( Diameter - diammean );
run;

proc means data=Old noprint;
  var absdev;
  by Prodtype;
  output out=stats n=n mean=mean css=css std=std;
run;

title;
proc glm data=Old outstat=glmout;
   class Prodtype;
   model absdev = Prodtype;
run;

A partial listing of the results is displayed in Figure 15.214. The large -value (0.3386) indicates that the data do not reject the hypothesis of homogeneity.