The Morgan-Pitman Test of Equality of Variances and its Application to Machine Learning Model Evaluation and Selection

Argimiro Arratia; Alejandra Cabaña; Ernesto Mordecki; Gerard Rovira-Parra

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arXiv · 2509.12185

The Morgan-Pitman Test of Equality of Variances and its Application to Machine Learning Model Evaluation and Selection

Argimiro Arratia·Alejandra Cabaña·Ernesto Mordecki·Gerard Rovira-Parra

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Abstract

Model selection in non-linear models often prioritizes performance metrics over statistical tests, limiting the ability to account for sampling variability. We propose the use of a statistical test to assess the equality of variances in forecasting errors. The test builds upon the classic Morgan-Pitman approach, incorporating enhancements to ensure robustness against data with heavy-tailed distributions or outliers with high variance, plus a strategy to make residuals from machine learning models statistically independent. Through a series of simulations and real-world data applications, we demonstrate the test's effectiveness and practical utility, offering a reliable tool for model evaluation and selection in diverse contexts.

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Argimiro Arratia, Alejandra Cabaña, Ernesto Mordecki, Gerard Rovira-Parra. 2025-09-15. The Morgan-Pitman Test of Equality of Variances and its Application to Machine Learning Model Evaluation and Selection. https://arxiv.org/abs/2509.12185

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