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.
Cite this paper
D. Johnson, W. , H. Burton, J. , A. Beyl, R. and E. Romer, J. (2015) A Simple Chi-Square Statistic for Testing Homogeneity of Zero-Inflated Distributions. Open Journal of Statistics
, 483-493. doi: 10.4236/ojs.2015.56050
 Zhang, L., Wu, J.X. and Johnson, W.D. (2010) Empirical Study of Six Tests for Equality of Populations with Zero-Inflated Continuous Distributions. Communications in Statistics—Simulation and Computation, 39, 1196-1211.http://dx.doi.org/10.1080/03610918.2010.489169
 Johnson, W.D., Beyl, R.A., Burton, J.H., Johnson, C.M., Romer, J.E. and Zhang, L. (2015) Use of Pearson’s Chi-Square for Testing Equality of Percentile Profiles across Multiple Populations. Open Journal of Statistics, 5, 412-420. http://dx.doi.org/10.4236/ojs.2015.55043
 Lambert, D. (1992) Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing. Technometrics, 34, 1-14. http://dx.doi.org/10.2307/1269547
 Hall, D.B. (2000) Zero-Inflated Poisson and Binomial Regression with Random Effects: A Case Study. Biometrics, 56, 1030-1039. http://dx.doi.org/10.1111/j.0006-341X.2000.01030.x
 Hausman, J., Hall, B.H. and Griliches, Z. (1984) Econometric Models for Count Data with an Application to the Patents-R&D Relationship. Econometrica, 52, 909-938. http://dx.doi.org/10.2307/1911191
 Lachenbruch, P.A. (1976) Analysis of Data with Clumping at Zero. Biometrische Zeitschrift, 18, 351-356.
 Lachenbruch, P.A. (2001) Comparisons of Two-Part Models with Competitors. Statistics in Medicine, 20, 1215-1234.http://dx.doi.org/10.1002/sim.790
 Tse, S.K., Chow, S.C., Lu, Q.S. and Cosmatos, D. (2009) Testing Homogeneity of Zero-Inflated Poisson Populations. Biometrical Journal, 51, 159-170. http://dx.doi.org/10.1002/bimj.200710490
 Yuen, H.K., Chow, S.C. and Tse, S.K. (2015) On Statistical Tests for Homogeneity of Two Bivariate Zero-Inflated Poisson Populations. Journal of Biopharmaceutical Statistics, 25, 44-53. http://dx.doi.org/10.1080/10543406.2014.919934
 Bedrick, E.J. and Hossain, A. (2013) Conditional Tests for Homogeneity of Zero-Inflated Poisson and Poisson-Hurdle Distributions. Computational Statistics and Data Analysis, 61, 99-106. http://dx.doi.org/10.1016/j.csda.2012.11.009
 Wu, J.X., Zhang, L. and Johnson, W.D. (2012) The Permutation Test as an Ancillary Procedure for Comparing Zero-Inflated Continuous Distributions. Open Journal of Statistics, 2, 274-280. http://dx.doi.org/10.4236/ojs.2012.23033
 Hallstrom, A.P. (2010) A Modified Wilcoxon Test for Non-Negative Distributions with a Clump of Zeros. Statistics in Medicine, 29, 391-400.
 Stoker, T.E., Gibson, E.K. and Zorrilla, L.M. (2010) Triclosan Exposure Modulates Estrogen-Dependent Responses in the Female Wistar Rat. Toxicological Sciences, 117, 45-53. http://dx.doi.org/10.1093/toxsci/kfq180
 Kumar, V., Chakraborty, A., Kural, M.R. and Roy, P. (2009) Alteration of Testicular Steroidogenesis and Histopathology of Reproductive System in Male Rats Treated with Triclosan. Reproductive Toxicology, 27, 177-185.http://dx.doi.org/10.1016/j.reprotox.2008.12.002
 Witorsch, R.J. (2014) Critical Analysis of Endocrine Disruptive Activity of Triclosan and Its Relevanceto Human Exposure through the Use of Personal Care Products. Critical Reviews in Toxicology, 44, 535-555.http://dx.doi.org/10.3109/10408444.2014.910754
 Lankester, J., Patel, C., Cullen, M.R., Ley, C. and Parsonnet, J. (2013) Urinary Triclosan Is Associated with Elevated Body Mass Index in NHANES. PLoS ONE, 8, e80057. http://dx.doi.org/10.1371/journal.pone.0080057
 Benowitz, N.L. (1999) Biomarkers of Environmental Tobacco Smoke Exposure. Environmental Health Perspectives, 107, 249-355.