Set correlation (SC) is a generalization of the multivariate linear model, extending the concept of multiple correlation analysis to handle multivariate data. It offers a flexible framework for analyzing the relationship between two sets of variables, X and Y, and includes measures of association, significance tests, and power analysis. SC can be applied to contingency tables, where it assesses the overall association and specific hypotheses about the details of the association through nominal scale coding and partialling.
Zwick and Cramer (1986) described four methods for analyzing two-way contingency tables: Pearson chi-square, multivariate analysis of variance (MANOVA), canonical analysis, and correspondence analysis. These methods produce equivalent results. SC is introduced as an additional option, offering greater flexibility and information yield.
The article illustrates the application of SC to a fictitious survey on abortion attitudes, comparing it with the methods described by Zwick and Cramer. SC uses different coding methods (dummy, effects, and contrast coding) to represent group membership and perform specific comparisons. The analysis of the relationship between religion and abortion response shows that SC can identify the source of the association, which is the greater rate of "No" responses from majority religions compared to minority religions.
The discussion highlights the advantages of SC, including its ability to handle nominal scales, systematic hypothesis testing, and robustness to nonnormal data. SC can also be applied to higher-order contingency tables and multi-way frequency tables, making it a versatile tool for multivariate data analysis.Set correlation (SC) is a generalization of the multivariate linear model, extending the concept of multiple correlation analysis to handle multivariate data. It offers a flexible framework for analyzing the relationship between two sets of variables, X and Y, and includes measures of association, significance tests, and power analysis. SC can be applied to contingency tables, where it assesses the overall association and specific hypotheses about the details of the association through nominal scale coding and partialling.
Zwick and Cramer (1986) described four methods for analyzing two-way contingency tables: Pearson chi-square, multivariate analysis of variance (MANOVA), canonical analysis, and correspondence analysis. These methods produce equivalent results. SC is introduced as an additional option, offering greater flexibility and information yield.
The article illustrates the application of SC to a fictitious survey on abortion attitudes, comparing it with the methods described by Zwick and Cramer. SC uses different coding methods (dummy, effects, and contrast coding) to represent group membership and perform specific comparisons. The analysis of the relationship between religion and abortion response shows that SC can identify the source of the association, which is the greater rate of "No" responses from majority religions compared to minority religions.
The discussion highlights the advantages of SC, including its ability to handle nominal scales, systematic hypothesis testing, and robustness to nonnormal data. SC can also be applied to higher-order contingency tables and multi-way frequency tables, making it a versatile tool for multivariate data analysis.