A Modified Hall-Padmanabhan Test for the Homogeneity of Scales

We consider a simple adaptive test for the homogeneity of scales due to Hall and Padmanabhan (1997) which is based on the ratio of adaptively trimmed sample variances. We develop a modification of this test that has the form of a combined bootstrap test and that is obtained within the nonparametric combination of dependent tests framework (Pesarin, 2001). We considered other approaches for the combination of tests concluding that the Liptak method is the most suitable one for the problem at hand. We compare the modified test with the original one in terms of robustness of significance level and power in a simulation study which considers distributions that range from symmetric to skewed and from light to heavy tailed ones. We show that the modified test is more powerful than the original one under heavier than normal tailed and very skewed distributions. A practical application to detect difference in scale of energy intake of lactating and non pregnant and not lactating women is presented.

We consider a simple adaptive test for the homogeneity of scales due to Hall and Padmanabhan (1997) which is based on the ratio of adaptively trimmed sample variances. We develop a modification of this test that has the form of a combined bootstrap test and that is obtained within the nonparametric combination of dependent tests framework (Pesarin, 2001). We considered other approaches for the combination of tests concluding that the Liptak method is the most suitable one for the problem at hand. We compare the modified test with the original one in terms of robustness of significance level and power in a simulation study which considers distributions that range from symmetric to skewed and from light to heavy tailed ones. We show that the modified test is more powerful than the original one under heavier than normal tailed and very skewed distributions. A practical application to detect difference in scale of energy intake of lactating and non pregnant and not lactating women is presented. Copyright © Taylor & Francis Group, LLC.