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Categorical independence tests for large sparse r-way contingency tables.
Paul W Mielke1, Kenneth J Berry
1Department of Statistics, Colorado State University, Fort Collins 80523-1877, USA.
Perceptual and Motor Skills
|November 19, 2002
Summary
A novel nonasymptotic chi-squared technique offers superior analysis for large sparse contingency tables. This method provides more accurate probability values compared to traditional asymptotic chi-squared approaches.
Area of Science:
- Statistics
- Data Analysis
Background:
- Analysis of large sparse r-way contingency tables presents challenges.
- Traditional asymptotic chi-squared methods may produce inaccurate results in such scenarios.
Purpose of the Study:
- To evaluate the properties of a nonasymptotic chi-squared technique for analyzing large sparse r-way contingency tables.
- To compare the nonasymptotic chi-squared technique against asymptotic and exact chi-squared techniques.
Main Methods:
- Application of a nonasymptotic chi-squared technique.
- Analysis of multiple sparse contingency tables (4x5, 5x6, 6x7, 2x2x2).
- Comparison with asymptotic and exact chi-squared methods.
Main Results:
- Asymptotic chi-squared analyses resulted in inflated probability values.
- The nonasymptotic chi-squared technique yielded probability values closer to exact values.
- Demonstrated useful properties for analyzing large sparse contingency tables.
Conclusions:
- The nonasymptotic chi-squared technique is a valuable tool for analyzing large sparse contingency tables.
- It offers improved accuracy over asymptotic chi-squared methods.
- Provides more reliable probability values for sparse data.