The most recent test for the homogeneity of variance was proposed by O’Neill and Mathews.
If we do not take block size and block effect into account, the ordinary least squares F test with
heuristic degrees of freedom tends to deflate the level of significance. O’Neill and Mathews developed
a weighted least squares version of Levene’s test for the homogeneity of variances for general block
and treatment designs. In the randomized complete block design, the weighted least squares can be
simplified as the ordinary least squares F -test statistics times a multiplier ‘m’. Multiplier ‘m’ takes the
block effect and treatment effect into account and can be found in Table 1 of O’Neill and Mathews.
The weighted least squares (WLS) F -test is based on the absolute value of standardized residuals,
i.e. |yij − y¯i· − y¯·j + y¯··|/
√1 − 1/b. Under the null hypothesis, the WLS F -test statistic converges in