Chi-Square Test MATLAB Implementation with Source Code

This document provides a comprehensive overview of chi-square test implementation in MATLAB. The chi-square test is a fundamental statistical method used to assess whether there's a significant discrepancy between expected and observed frequencies across one or more categorical variables. This hypothesis testing technique finds applications in diverse fields including biology, economics, and psychology research. For MATLAB implementation, the process typically involves two key functions: 1. The crosstab function generates contingency tables that summarize frequency distributions between categorical variables 2. Custom chi-square test functions (or built-in alternatives) calculate the test statistic and corresponding p-value The core algorithm follows these steps: - Construct observed frequency matrix from raw data - Compute expected frequencies under the null hypothesis - Calculate chi-square statistic: χ² = Σ[(Observed - Expected)² / Expected] - Determine degrees of freedom: (rows-1)*(columns-1) - Compare calculated statistic to chi-square distribution for p-value determination Important implementation considerations: - Requires sufficient sample size (typically >5 observations per cell) - Assumes independent observations between categories - Applicable only to categorical data, not continuous variables - For 2x2 tables with small samples, consider Fisher's exact test instead The provided MATLAB code includes proper error checking for assumptions and generates comprehensive outputs including test statistics, p-values, and degrees of freedom. This implementation serves as a reliable tool for statistical analysis and research validation across various disciplines.