Using Exact Tests from Algebraic Statistics in Sparse Multi-Way Analyses: An Application to Analyzing Differential Item Functioning

Shishir Agrawal, Luis David Garcia Puente, Minho Kim and Flavia Sancier-Barbosa

The American Statistician, 2025, vol. 79, issue 1, 10-22

Abstract: Asymptotic goodness-of-fit methods in contingency table analysis can struggle with sparse data, especially in multi-way tables where it can be infeasible to meet sample size requirements for a robust application of distributional assumptions. However, algebraic statistics provides exact alternatives to these classical asymptotic methods that remain viable even with sparse data. We apply these methods to a context in psychometrics and education research that leads naturally to multi-way contingency tables: the analysis of differential item functioning (DIF). We explain concretely how to apply the exact methods of algebraic statistics to DIF analysis using the R package algstat, and we compare their performance to that of classical asymptotic methods.

Date: 2025
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DOI: 10.1080/00031305.2024.2388526

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