Related Experiment Video
Updated: Jun 17, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
On Association Coefficients for 2x2 Tables and Properties That Do Not Depend on the Marginal Distributions
1Psychometrics and Research Methodology Group, Leiden University Institute for Psychological Research, Leiden University, Wassenaarseweg 52, P.O. Box 9555, 2300 RB Leiden, The Netherlands.
Abstract:
We discuss properties that association coefficients may have in general, e.g., zero value under statistical independence, and we examine coefficients for 2x2 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.
Related Concept Videos
Contingency Table
Introduction to Test of Independence
The test statistic for a test of independence is similar to that of a goodness-of-fit test:
Determination of Expected Frequency
Two-Way ANOVA
The two-way ANOVA analysis initially begins by stating the null hypothesis that there is an interaction effect between the two factors of a dataset. This effect can be visualized using line segments formed by joining the means for...
Friedman Two-way Analysis of Variance by Ranks
Probability Histograms
