A Simple Chi-Square Statistic for Testing Homogeneity of Zero-Inflated Distributions

Area of Science:

• Statistics
• Biostatistics
• Data Analysis

Background:

• Zero-inflated distributions are prevalent in statistical analyses, particularly when testing homogeneity across independent groups.
• Standard tests like the median test can be uninformative for distributions with excess zeros or dissimilar shapes.
• Asymmetric and unknown functional forms of zero-inflated data necessitate robust comparison methods.

Purpose of the Study:

• To propose a novel statistical test for comparing zero-inflated distributions.
• To address limitations of existing methods in handling excess zeros and asymmetric data.
• To provide a method for simultaneous comparison of zero proportions and non-zero percentile profiles.

Main Methods:

• A chi-square test is developed for simultaneous assessment of two components: proportion of zeros and percentile profiles of non-zero values.
• The proposed test is applicable to both continuous and discrete data.
• Simulation studies were conducted to evaluate empirical power under various scenarios.

Main Results:

• The proposed chi-square test demonstrates effectiveness in comparing groups with zero-inflated data.
• Simulation results provide insights into the test's power across different data distributions and sample sizes.
• Recommendations for minimum sample sizes are provided to ensure adequate test performance.

Conclusions:

• The novel chi-square test offers a robust and informative approach for analyzing zero-inflated distributions.
• This method enhances statistical homogeneity testing by considering both zero inflation and non-zero value distributions.
• The findings guide researchers in selecting appropriate sample sizes for reliable comparisons.