The Annals of Statistics

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

Shelby J. Haberman

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Abstract

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.

Article information

Source
Ann. Statist., Volume 9, Number 6 (1981), 1178-1186.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345635

Digital Object Identifier
doi:10.1214/aos/1176345635

Mathematical Reviews number (MathSciNet)
MR630101

Zentralblatt MATH identifier
0479.62043

JSTOR
links.jstor.org

Subjects
Primary: 62F05: Asymptotic properties of tests
Secondary: 62H20: Measures of association (correlation, canonical correlation, etc.)

Keywords
Likelihood ratio Pearson chi-square Wishart distribution eigenvalue asymptotic unbiasedness consistency asymptotic power maximum likelihood

Citation

Haberman, Shelby J. Tests for Independence in Two-Way Contingency Tables Based on Canonical Correlation and on Linear-By-Linear Interaction. Ann. Statist. 9 (1981), no. 6, 1178--1186. doi:10.1214/aos/1176345635. https://projecteuclid.org/euclid.aos/1176345635


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