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<p>It is well known that we can compute several chi-squared measures to determine if there is a statistically significant association between the row and column variables. Several of these statistics are subsumed by the Cressie–Read divergence statistic, which depends on the parameter <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11135_2025_2459_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">\(\omega \in \mathbb {R}\)</EquationSource> </InlineEquation>. The Cressie–Read divergence statistics and their subcase, Pearson’s chi-square index, tend to perform poorly when applied to two ordered categorical variables. This reduced performance is partly due to its low power in detecting ordered alternatives to the null hypothesis. In this paper, we consider a different proposal based on the Cressie–Read divergence Statistic family for contingency tables, where both variables have an ordinal nature. Moreover, we consider the role of the double cumulative correspondence analysis in this context.</p>

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Double cumulative correspondence analysis based on an extension of the power divergence family

  • 期刊论文

  • 发表日期：

    2025年11月4日

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  • Antonello D’Ambra,
  • Pietro Amenta

摘要

It is well known that we can compute several chi-squared measures to determine if there is a statistically significant association between the row and column variables. Several of these statistics are subsumed by the Cressie–Read divergence statistic, which depends on the parameter \(\omega \in \mathbb {R}\) . The Cressie–Read divergence statistics and their subcase, Pearson’s chi-square index, tend to perform poorly when applied to two ordered categorical variables. This reduced performance is partly due to its low power in detecting ordered alternatives to the null hypothesis. In this paper, we consider a different proposal based on the Cressie–Read divergence Statistic family for contingency tables, where both variables have an ordinal nature. Moreover, we consider the role of the double cumulative correspondence analysis in this context.