MATLAB Program for Two Normal Population Variance Test (F-Test)

This MATLAB program demonstrates how to perform a variance comparison test between two normal populations, known as the F-test. The implementation utilizes statistical concepts to determine whether the variances of two populations are equal. The program begins by defining the hypothesis framework: the null hypothesis (H0) states that the population variances are equal, while the alternative hypothesis (H1) states they are unequal. The core algorithm calculates the variance ratio (F-ratio) by dividing the larger sample variance by the smaller one, ensuring the F-value is always greater than or equal to 1. The program then compares this computed F-ratio against the critical F-value from the F-distribution table at a specified significance level (typically α=0.05). Key MATLAB functions employed include var() for variance calculation and finv() for obtaining critical F-values. The decision rule follows standard statistical practice: if the computed F-ratio exceeds the critical value, we reject the null hypothesis, indicating unequal population variances; otherwise, we fail to reject H0, suggesting equal variances. This program provides researchers and data analysts with a practical tool for variance homogeneity testing, which is crucial for selecting appropriate statistical methods in data analysis workflows. The implementation handles sample data input, automated calculation of test statistics, and clear hypothesis testing outcomes.