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Dergiler / Fundamental Journal of Mathematics and Applications / 2026 / Volume: 7 Issue: 3

The Most Powerful Member of the Power-Divergence Family for the Independence Model in Contingency Tables

Gokcen Altun(ANKARA HACI BAYRAM VELI UNIVERSITY)0000-0003-4311-6508
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Yayın Tarihi
2024-09-30
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Two applications are given to demonstrate the usefulness of the PD(0.4) test statistic over the chi-square test statistic {contingency tables}.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The family of power-divergence (PD) test statistic contains many well-known test statistics used in the analysis of the contingency tables under the independence model.
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Temel Bulgular & Veri:According to the simulation results, we recommend the PD(0.4) test statistic for the small sample size based on its power and type-I error rates.
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Sonuç & Katkı:Two applications are given to demonstrate the usefulness of the PD(0.4) test statistic over the chi-square test statistic {contingency tables}.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Goodness-of-fit test statistics · Independence model · Power-divergence family

Abstract

The family of power-divergence (PD) test statistic contains many well-known test statistics used in the analysis of the contingency tables under the independence model. In this work, we compare the various test statistics for the independence model. The type-I and type-II errors of the test statistics are obtained and compared via simulation study considering the different degree of freedoms and sample sizes. According to the simulation results, we recommend the PD(0.4) test statistic for the small sample size based on its power and type-I error rates. Two applications are given to demonstrate the usefulness of the PD(0.4) test statistic over the chi-square test statistic {contingency tables}.

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Bu Makaleye Atıf Yap

Altun, G. (2024). The Most Powerful Member of the Power-Divergence Family for the Independence Model in Contingency Tables. Fundamental Journal of Mathematics and Applications, Volume: 7 Issue: 3. https://doi.org/10.33401/fujma.1432348

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