The Data Transformation on CRD with Unequal Variance

Abstract

The objective of this research is to compare the ability of some methods based on Box-Cox and/or weighted transformation, to cope with the problem on heterogeneity of variances. The data are simulated under CRD with the fixed effect model and balanced design. Number of treatments (k) and replications (n) are as follows : (k,n) =  (3, 5), (3, 10), (5, 10), (5, 12), (5, 20). Normal and lognormal distribution are considered. The degree of heterogeneity of variance are set at 3 levels, small (less than 2 times of least variance), medium (less than 5 times of least variance), and large (less than 10 times of least variance). Each situation are replicated 1,000 times to compare the ability of those methods, Levene’s test is used to test for homogeneity of variance and Shapiro-Wilk’s test is used to test for normality. Results of this study revealed that the original Box-Cox transformation and modified Box-Cox transformation can solve the non-normality problem but not the unequal variance problem. On the other hand, weighted method can solve the unequal variance problem but not the normality problem. Findings exhibit the more appropriate way which is applying Box-Cox transformation together with weighted method.