Another Proof of Pearson’s Theorem Using Symbolic Computation in Python
Jose Armando Ortega, Arturo Portnoy, Wolfgang Rolke · Scatterplot · 2025
In his seminal 1900 paper, Karl Pearson introduced the chi-square (χ2) test, a foundational tool in modern statistics. The chi-square test provides a formal method for assessing the goodness of fit between observed and expected frequencies in categorical data, laying the groundwork for hypothesis testing in statistical inference. This innovation transformed statistical methodology, offering a systematic approach to checking whether observational data is in agreement with a scientific theory. In this work, we present a detailed proof of Pearson’s theorem using Python to find a pattern, which leads to a conjecture, which in turn leads to a proof by direct computation, leveraging matrix properties and the power of symbolic computation offered by Google Colab to offer a modern computational perspective on these classical results, enhancing their accessibility for contemporary statistical analysis.