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**On association coefficients for \(2\times 2\) tables and properties that do not depend on the marginal distributions.**
*(English)*
Zbl 1284.62762

Summary: We discuss properties that association coefficients may have in general, e.g., zero value under statistical independence, and we examine coefficients for \(2\times 2\) tables with respect to these properties. Furthermore, we study a family of coefficients that are linear transformations of the observed proportion of agreement given the marginal probabilities. This family includes the phi coefficient and Cohen’s kappa. The main result is that the linear transformations that set the value under independence at zero and the maximum value at unity, transform all coefficients in this family into the same underlying coefficient. This coefficient happens to be Loevinger’s \(H\).

### MSC:

62P15 | Applications of statistics to psychology |

### Keywords:

agreement indices; resemblance measures; correction for chance; correction for maximum value; phi coefficient; Cohen’s kappa; Hubert-Arabie adjusted rand index; Yule’s \(Q\); Loevinger’s \(H\); Cole’s \(C _{7}\)
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\textit{M. J. Warrens}, Psychometrika 73, No. 4, 777--789 (2008; Zbl 1284.62762)

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### References:

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