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Journals / Cumhuriyet Science Journal / 2021 / Cilt: 42 - Sayı: 2

A study on Freeman-Tukey test statistic under the symmetry model for square contingency tables

Gökçen ALTUN
Pages
413–421
Publication Date
2022-10-12
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The results of simulation study and artificial data study show that Freeman- Tukey’s 𝑇2 test statistic does not converge to chi-squared distribution for both sparse and nonsparse square contingency tables.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The symmetry model is the basic model in the analysis of square contingency tables.
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Key Findings & Data:Multiple test statistics have been developed for the goodness of fit test.
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Conclusion & Impact:The results of simulation study and artificial data study show that Freeman- Tukey’s 𝑇2 test statistic does not converge to chi-squared distribution for both sparse and nonsparse square contingency tables.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

The symmetry model is the basic model in the analysis of square contingency tables. Multiple test statistics have been developed for the goodness of fit test. Freeman-Tukey test statistics is appropriate to be used in large samples. However, the required sample size to use the Freeman- Tukey test statistics is not clear. In this paper, the asymptotic properties of Freeman-Tukey test statistic are discussed via extensive Monte-Carlo simulation study. The Freeman-Tukey test statistic is compared with members of power-divergence family test statistic under the symmetry model. The results of simulation study are evaluated based on the Type-I error and power of a test. The results of simulation study and artificial data study show that Freeman- Tukey’s 𝑇2 test statistic does not converge to chi-squared distribution for both sparse and nonsparse square contingency tables.

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Cite This Article

ALTUN, G. (2022). A study on Freeman-Tukey test statistic under the symmetry model for square contingency tables. Cumhuriyet Science Journal, Cilt: 42 - Sayı: 2, 413–421. https://ajindex.com/articles/477633

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