MATLAB Code Implementation for Mathematical Modeling

Mathematical modeling is a crucial methodology for solving real-world problems using mathematical tools, where normality testing of data distribution represents a common step in the modeling process. MATLAB, as a powerful mathematical computing software, provides multiple approaches to implement normality tests.

Significance of Normality Testing Many statistical methods (such as t-tests, ANOVA, etc.) in mathematical modeling rely on the assumption that data follows a normal distribution. Conducting normality tests validates whether data meets this prerequisite, ensuring the accuracy of subsequent analyses.

Implementation Methods in MATLAB Graphical Testing: Visually assess data normality through Q-Q plots or histograms using MATLAB's plotting functions. Statistical Testing: Implement tests like Kolmogorov-Smirnov, Lilliefors, or Shapiro-Wilk (requiring either built-in functions or custom implementations).

MATLAB's built-in function `normplot` generates normal probability plots, while statistical toolbox functions like `kstest` or `lillietest` perform direct hypothesis testing. For complex scenarios, users can enhance test robustness by integrating Monte Carlo simulations through iterative sampling algorithms.

Interpreting Test Results If the p-value exceeds the significance level (e.g., 0.05), the null hypothesis of normal distribution is generally accepted. Otherwise, data transformation or non-parametric methods should be considered. MATLAB's computational efficiency enables rapid testing even with large-scale datasets through vectorized operations.

By appropriately selecting testing methods and correctly interpreting results, modelers can ensure data reliability, thereby improving the final model's explanatory power and predictive performance through validated statistical foundations.