Two sample comparisons including zero-inflated continuous data: A parametric approach with applications to microarray experiment

Micro-array experiments are important fields in molecular biology where zero values mixed with a continuous outcome are frequently encountered leading to a mixed distribution with a clump at zero. Comparison of two mixed populations, e.g. of a control and a treated group; of two groups with different types of cancer, to name a few, are often encountered in these contexts. Fairly skewed distribution of the continuous part coupled with small sample sizes are issues of main concern to be attended for the quality of inference in such situations while popularly used nonparametric methods rely on asymptotic distribution of the underlying test statistics which are valid only under large sample sizes. We address the aforementioned issues via a newly proposed exact test for location-scale family distributions and Generalized pivot quantity (GPQ) based parametric test procedures for non-location-scale distributions. Simulation based assessment showed their superior performance with respect to size and power in comparison to the popular two-part tests (Wilcoxon rank sum, t-test, Kolmogrov-Smirnov, Ansari-Bradley and Sigel-Tukey) more prominently for small sample sizes.