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Exact and resampling probability values for measures associated with ordered r by c contingency tables.
Kenneth J Berry1, Janis E Johnston, Paul W Mielke
1Department of Sociology, Colorado State University, Fort Collins, CO 80523-1784, USA. berry@lamar.colostate.edu
Psychological Reports
|October 14, 2006
Summary
Exact and resampling permutation methods are preferred for analyzing sparse contingency tables. These methods provide more accurate probability values than asymptotic methods for ordered r x c tables.
Area of Science:
- Statistics
- Biostatistics
- Data Analysis
Background:
- Contingency tables are frequently used in statistical analysis.
- Measures of association quantify relationships within contingency tables.
- Ordered r x c contingency tables require specific analytical approaches.
Purpose of the Study:
- To describe permutation procedures for computing exact and resampling probability values.
- To evaluate these procedures for measures of association in ordered r x c contingency tables.
- To compare permutation-based probabilities with asymptotic probability values.
Main Methods:
- Development and description of permutation procedures.
- Computation of exact and resampling probability values.
- Comparison with established asymptotic probability values.
- Application to ordered r x c contingency tables.
Main Results:
- Permutation procedures provide exact and resampling probability values.
- Asymptotic probability values were compared to permutation-based values.
- Exact and resampling permutation procedures were found to be preferable for sparse contingency tables.
Conclusions:
- Permutation procedures are valuable for obtaining accurate probability estimates in ordered r x c contingency tables.
- These methods are particularly recommended for sparse tables where asymptotic methods may be unreliable.
- The study highlights the utility of resampling and exact permutation tests in statistical inference.
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