An alternative test for the equality of variances for several populations in randomised complete block design

In the last 50 years, eight major modifications and extensions of Levene’s test and Bartlett’s test had been developed for Randomized Complete Block Design (RCBD). The improvement from these works can be divided mostly into three categories as follows: (i) adjust fixed block effects and degrees of freedom in FF 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 normality assumption, all tests either suffer from severe inflation of Type I error rate or lose statistical power to detect heterogeneity of variances.In this paper, we consider the problem of homogeneity of variance in Randomized Complete Block Design (RCBD) and develop a new Fmax-test for the equality of variances in RCBD. The Type I error of this new test is well controlled and the power is higher than eight other tests when the number of treatment groups is larger than the number of blocks. Under normality assumption, none of the eight other tests are consistent top-performer. Our new Fmax-test either outperforms or is comparable to the top-performer of the other eight tests. The new Fmax-test can be recommended for future use by practitioners in cases such as sensory monadic testing with more than 10 products and blood glucose variability testing.