Abstract
In the analysis of two-way contingency tables, the degree of departure from independence is measured using measures of association between row and column variables (e.g., Yule’s coefficients of association and of colligation, Cramér’s coefficient, and Goodman and Kruskal’s coefficient). On the other hand, in the analysis of square contingency tables with the same row and column classifications, we are interested in measuring the degree of departure from symmetry rather than independence. Over past years, many studies have proposed various types of indexes based on their power divergence (or diversity index) to represent the degree of departure from symmetry. This study proposes a two-dimensional index to measure the degree of departure from symmetry in terms of the log odds of each symmetric cell with respect to the main diagonal of the table. By measuring the degree of departure from symmetry in terms of the log odds of each symmetric cell, the analysis results are easier to interpret than existing indexes. Numerical experiments show the utility of the proposed two-dimensional index. We show the usefulness of the proposed two-dimensional index by using real data.
Highlights
For two-way contingency tables, an analysis is generally performed to see whether the independence between the row and column classifications holds
This study proposes a two-dimensional index to measure the degree of departure from the symmetry model in terms of the log odds of each symmetric cell with respect to the main diagonal of the table
By using the weighted geometric mean indexes of the diversity index as the elements of the proposed two-dimensional index, the proposed two-dimensional index has more useful properties than the index proposed by [13], which measures the degree of departure from the symmetry model
Summary
For two-way contingency tables, an analysis is generally performed to see whether the independence between the row and column classifications holds. For the analysis of square contingency tables with the same row and column classifications, there are many issues related to symmetry rather than independence. In the analysis of two-way contingency tables, the degree of departure from independence is assessed by using measures of association between the row and column variables. In the analysis of square contingency tables with the same row and column classifications, we are interested in measuring the degree of departure from the symmetry model. This study proposes a two-dimensional index to measure the degree of departure from the symmetry model in terms of the log odds of each symmetric cell with respect to the main diagonal of the table. By measuring the degree of departure from symmetry in terms of the log odds of each symmetric cell, the analysis results are easier to interpret than existing indexes.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
