Example 74.2 Robust ANOVA

The classical analysis of variance (ANOVA) technique based on least squares assumes that the underlying experimental errors are normally distributed. However, data often contain outliers due to recording or other errors. In other cases, extreme responses occur when control variables in the experiments are set to extremes. It is important to distinguish these extreme points and determine whether they are outliers or important extreme cases. You can use the ROBUSTREG procedure for robust analysis of variance based on M estimation. Typically, there are no high leverage points in a well-designed experiment, so M estimation is appropriate.

The following example shows how to use the ROBUSTREG procedure for robust ANOVA.

An experiment was carried out to study the effects of two successive treatments (T1, T2) on the recovery time of mice with certain diseases. Sixteen mice were randomly assigned into four groups for the four different combinations of the treatments. The recovery times (time) were recorded (in hours) as shown in the following data set recover.

   data recover;
      input  T1 $ T2 $ time @@;
   datalines;
   0 0 20.2  0 0 23.9  0 0 21.9  0 0 42.4
   1 0 27.2  1 0 34.0  1 0 27.4  1 0 28.5
   0 1 25.9  0 1 34.5  0 1 25.1  0 1 34.2
   1 1 35.0  1 1 33.9  1 1 38.3  1 1 39.9
   ;

The following statements invoke the GLM procedure ( Chapter 39, The GLM Procedure ) for a standard ANOVA.

   proc glm data=recover;
       class T1 T2;
       model time = T1 T2 T1*T2;
   run;