Analysis of Categorical Data with Logistic Regression and the Cochran-Mantel-Haenszel Tests in Biological Experiments

The choice of statistical test is a fundamentally important one when analyzing experimental data. Here, we consider the question of categorical data, defined by their properties (for example color) rather than by continuous numbering. Using simple and complex example datasets generated from Caenorhabditis elegans research, we conduct a statistical analysis of (1) a rare cellular event involving the formation of a neuronal extrusion called an exopher, and of (2) a variable behavioral response across a timescale. Two tests we use here are the Cochran- Mantel-Haenszel (CMH) test and logistic regression. These two tests pose practical challenges to researchers that include lack of easy access to statistical software and the need for prior programming knowledge. To this end we provide step-by-step tutorials and example code. We emphasize the flexibility of logistic regression in handling both simple and complex datasets, emphasizing the capacity of logistic regression to provide more comprehensive insights into experimental outcomes than simpler tests like CMH. By analyzing real biological examples and demonstrating their analysis with R code, we provide a practical guide for biologists to enhance the rigor and reproducibility of categorical data analysis in experimental studies.