title: A Simple Chi-Square Statistic for Testing Homogeneity of Zero-Inflated Distributions.
abstract: Zero-inflated distributions are common in statistical problems where there is interest in testing homogeneity of two or more independent groups. Often, the underlying distribution that has an inflated number of zero-valued observations is asymmetric, and its functional form may not be known or easily characterized. In this case, comparisons of the groups in terms of their respective percentiles may be appropriate as these estimates are nonparametric and more robust to outliers and other irregularities. The median test is often used to compare distributions with similar but asymmetric shapes but may be uninformative when there are excess zeros or dissimilar shapes. For zero-inflated distributions, it is useful to compare the distributions with respect to their proportion of zeros, coupled with the comparison of percentile profiles for the observed non-zero values. A simple chi-square test for simultaneous testing of these two components is proposed, applicable to both continuous and discrete data. Results of simulation studies are reported to summarize empirical power under several scenarios. We give recommendations for the minimum sample size which is necessary to achieve suitable test performance in specific examples.
authors.affiliation: Department of Biostatistics, Pennington Biomedical Research Center, Louisiana State University, Baton Rouge, LA, USA.
authors.forename: William D
authors.initials: WD
authors.lastname: Johnson
authors.affiliation: Department of Biostatistics, Pennington Biomedical Research Center, Louisiana State University, Baton Rouge, LA, USA.
authors.forename: Jeffrey H
authors.initials: JH
authors.lastname: Burton
authors.affiliation: Department of Biostatistics, Pennington Biomedical Research Center, Louisiana State University, Baton Rouge, LA, USA.
authors.forename: Robbie A
authors.initials: RA
authors.lastname: Beyl
authors.affiliation: Department of Biostatistics, Pennington Biomedical Research Center, Louisiana State University, Baton Rouge, LA, USA.
authors.forename: Jacob E
authors.initials: JE
authors.lastname: Romer
keywords: Asymptotic Chi-Square Test; Equality of Quantiles; Large Sample Test; Nonparametric Test; Percentile Profiles; Zero-Inflated Distributions