Increased power with modified forms of the Levene (Med) test for heterogeneity of variance

While the conventional Levene (Med) test is a widely used and robust test f or detecting heterogeneity of variance, it does not take notice of either t he linear dependencies among the residuals involved or the possibility of a mean (or median)-variance relationship. This paper explores the substantia l improvements in power possible by investigating the benefits both of remo ving such linear dependencies (structural zeros) and of modeling (even roug hly) such relationships.