Independence In Two-way Contingency Tables Research Articles

Tests for Independence in Two-Way Contingency Tables Based on Canonical Correlation and on Linear-By-Linear Interaction

Tests for independence of rows and columns in an $r \times s$ contingency table are developed from canonical correlation analysis and from models of linear-by-linear interaction. The resulting test statistics are asymptotically equivalent under the null hypothesis. They are consistent and asymptotically unbiased. Approximate critical values are available from existing tables. The proposed tests are most appropriate when the matrix of joint probabilities is well approximated by a matrix of rank 2. Against some alternatives which may arise in such tables, the proposed statistics have greater asymptotic power than conventional chi-square tests of independence.

On Pearson's Chi-Squared Statistic for Independence in Two-Way Contingency Tables

Abstract This article discusses a representation of Pearson's chi-square for independence in two-way contingency tables in terms of conditional probabilities of two categorical random variables and proposes a functional interpretation of Pearson's chi-square. This representation is suggested for use in the teaching of statistical independence between categorical variables.

On Pearson's Chi-Squared Statistic for Independence in Two-Way Contingency Tables

On Pearson's Chi-Squared Statistic for Independence in Two-Way Contingency Tables

Testing independence in two-way contingency tables with data subject to misclassification.

The misclassification process is represented by a stochastic matrix containing the probabilities that an individual who belongs in one cell is counted as belonging to another (or perhaps the same) cell. These probabilities are supposed known. If misclassification in the row direction is independent of that along the column variable then the size of the usual chi-square test is unchanged. It is shown how to calculate loss of power in this case and also how to calculate the change in size of the test if the errors are not independent. A modified test criterion is suggested when errors are not independent and a numerical example is included.