Simplified Freeman-Tukey test statistics for testing probabilities in contingency tables

Contingency Tables: Test For Independence

• If we have data that are measurable (eg. height, time, weight, age, test score, etc.) then we can use the coefficient of correlation (r) to measure the strength of the linear association between two sets of data. • If we have two sets of rankings, then we can use Spearman's Rank Order Correlation Coefficient to measure the strength of the association between them. • However, both of these tec...

Accuracy of Power-Divergence Statistics for Testing Independence and Homogeneity in Two-Way Contingency Tables

Chi-Square Test: Analysis of Contingency Tables

The original chi-square test, often known as Pearson’s chi-square, dates from papers by Karl Pearson in the earlier 1900s. The test serves both as a ”goodnessof-fit” test, where the data are categorized along one dimension, and as a test for the more common ”contingency table”, in which categorization is across two or more dimensions. Voinov and Nikulin, this volume, discuss the controversy ove...

Information Identities and Testing Hypotheses: Power Analysis for Contingency Tables

An information theoretic approach to the evaluation of 2 x 2 contingency tables is proposed. By investigating the relationship between the Kullback-Leibler divergence and the maximum likelihood estimator, information identities are established for testing hypotheses, in particular, testing independence. These identities not only validate the calibration of p values, but also yield unified power...

Estimation and Testing in Large Binary Contingency Tables

Very sparse contingency tables with a multiplicative structure are studied. The number of unspecified parameters and the number of cells are growing with the number of observations. Consistency and asymptotic normality of natural estimators are established. Also uniform convergence of the estimators to the parameters is investigated, and an application to the construction of confidence interval...