A0612
Title: Robustifying an exact test for heteroscedasticity in a two-way layout in variety frost trials with a covariate
Authors: Brenton Clarke - Murdoch University (Australia) [presenting]
Angelika Pilkington - Murdoch University (Australia)
Dean Diepeveen - Murdoch University (Australia)
Abstract: Testing for heteroscedasticity in two-way layouts is often fraught with difficulty. Established tests are often hampered by the test statistic being based on asymptotics when the number of replications per cell can be as low as one. Moreover, as in various frost trials, there is the potential to include one or more covariates. The simple form of heteroscedasticity considered is dichotomous. For example, a group of varieties that may have larger response values can be tested to see if they have increased variance. The considered test is an F-test based on vectors of transformed residuals from the linear model. The exact F-test is shown to be more powerful than the asymptotic likelihood ratio test based on restricted or residual maximum likelihood (REML) available in statistical packages. However, it is, as are both these tests, not robust. Pearson noted the F-test's lack of robustness early last century. The size and power of a robustified F-test based on the Levene statistic formulated from the vectors of transformed residuals without and also with contamination are examined. The implementation of our test is illustrated using wheat data used in various frost trials carried out in Western Australia when a covariate is necessary for the modelling.
