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8 articles for “Square Contingency Table”
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Research ArticleOpen accessPhrase in the titleMeasure of Departure from Conditional Partial Symmetry for Square Contingency TablesYusuke Saigusa, Nobuki Fukumoto, Tomoyuki Nakagawa, Sadao TomizawaFor square contingency tables, asymmetry of conditional probability in part of the off-diagonal cells isconsidered with respect to the main diagonal. A measure is proposed torepresent the degree of departure from the symmetric structure and gives theapproximate confidence interval. Some numerical experiments are performed toillustrate the validity and usefulness of the proposed measure. Japaneseoccupational data are analyzed using the measure. …Journal of Mathematics and Statistics, Vol. 18, Issue 1 · 4 Oct 2022 · 5,561 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleGeometric Mean Type Measure of Marginal Homogeneity for Square Contingency Tables with Ordered CategoriesTomoyuki Nakagawa, Toshiki Takei, Aki Ishii, Sadao TomizawaFor square contingency tables, some studies have developed the weighted arithmetic mean type measure to represent the degree of departure from the marginal homogeneity. The present paper proposes (1) the cumulative partial marginal homogeneity model which has the weaker restriction than the marginal homogeneity model and (2) the measure to represent the degree of departure from the proposed model. The … …Journal of Mathematics and Statistics, Vol. 16, Issue 1 · 11 Aug 2020 · 6,620 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleMeasure of Departure from Partial Symmetry for Square Contingency TablesYusuke Saigusa, Kouji Tahata, Sadao TomizawaFor square contingency tables, the present paper newly considers the partial symmetry model which indicates that there is a symmetric structure of probabilities for at least one of pairs of symmetric cells. It also proposes the measure to express the degree of departure from the partial symmetry model. Examples are given. …Journal of Mathematics and Statistics, Vol. 12, Issue 3 · 9 Aug 2016 · 7,416 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleDecomposition of Marginal Homogeneity into Logit and Mean Ridits Equality for Square Contingency TablesKiyotaka Iki, Kouji Tahata, Sadao TomizawaProblem statement: For square contingency tables with ordered categories, if the Marginal Homogeneity (MH) model holds, then the probability that X selected at random from the row marginal distribution is less than Y selected independently at random from the column marginal distribution equals the probability that X is greater than Y. However, the converse does not hold. We are interested … …Journal of Mathematics and Statistics, Vol. 6, Issue 1 · 31 Mar 2010 · 7,297 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleDecompositions for Ordinal Quasi-Symmetry Model in Square Contingency Tables with Ordered CategoriesKouji Yamamoto, Satoru Shinoda, Sadao TomizawaProblem statement: For square contingency tables with ordered categories, this study considers four kinds of extensions of the marginal homogeneity model and gives decompositions for the ordinal quasi-symmetry model. The decompositions are extensions of some existing decompositions. Approach: This study gives a decomposition theorem that the ordinal quasi-symmetry model holds if and only if the quasi-symmetry model and the proposed … …Journal of Mathematics and Statistics, Vol. 7, Issue 4 · 28 Oct 2011 · 7,152 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleMeasure of Departure from Average Cumulative Symmetry for Square Contingency Tables with Ordered CategoriesKouta Miyazawa, Sadao Tomizawa, Kouji TahataProblem statement: For square contingency tables with ordered categories, we are interested in considering a structure of weak symmetry when Bowker's symmetry model does not hold and in measuring the degree of departure from weak symmetry. Approach: The present study considered the average cumulative symmetry model that has a weaker restriction than the structure of symmetry. It also gave a … …Current Research in Biostatistics, Vol. 1, Issue 1 · 30 Jun 2010 · 7,621 accessesView PDFCite
Research ArticleOpen accessIn the keywordsThe Analysis of High Dimensional Contingency Table with InteractionsKeorapetse Sediakgotla, Lesego Gabaitiri, Keamogetse Setlhare et al.This paper is focused on the analysis of categorical data in a 2 × c × K contingency table. The theoretical frame work of a 2 × c design is extended to 2 × c × K with provision for testing interactions among subsets of either lower or upper columns of the designated table. The developed chi square tests for … …American Journal of Applied Sciences, Vol. 14, Issue 8 · 30 Aug 2017 · 7,651 accessesView PDFCite
Research ArticleOpen accessIn the keywordsAnalysis of Unaided Vision Data using New Decomposition of SymmetryKouji Yamamoto, Sadao TomizawaProblem statement: First, this study considers how the structure of symmetry for probabilities is decomposed into two structures. Secondly, this study infers the structure of unknown probabilities which indicates how the right eye is better (or worse) than the left eye for three kinds of data on unaided distance vision of (1) women in Britain, (2) students in an university … …Current Research in Medicine, Vol. 3, Issue 1 · 25 Feb 2012 · 7,449 accessesView PDFCite