The improvement from these works can be divided mostly into three categories as follows: (i) ad-just fixed block effects and degrees of freedom in F test, (ii) improve the power of variance homogeneity tests, and (iii) develop a robust test that can be applied to non-normal distributions. Surprisingly, very little attention has been paid to the homogeneity of within treatment variance when the number of treatment groups is large and the number of blocks is relatively small. Even under normal-ity assumption, all tests either suffer from severe inflation of Type I error rate or lose statistical power to detect heterogeneity of vari-ances.