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A Comparison of Two Noncentral F Approximations, with Applications to Power Analysis in Set Correlation
Multivariate Behavioral Research
|January 12, 2016
Summary
Researchers evaluated approximations for the noncentral F distribution to create power analysis tables for set correlation. The square root approximation demonstrated slightly better performance and was selected for generating these essential statistical tables.
Area of Science:
- Statistics
- Multivariate Analysis
Background:
- Power analysis for set correlation relies on the noncentral F distribution.
- Existing tables for this distribution are insufficient for practical applications.
Purpose of the Study:
- To compare Laubscher's (1960) square root and cube root approximations of the noncentral F distribution.
- To determine the best approximation for computing power analysis tables for set correlation.
Main Methods:
- A Monte Carlo investigation was conducted using 97 correlation matrices of three sizes.
- 521 power determinations, each based on 1000 samples, were generated.
- A subsample of 205 determinations was compared against exact power values.
Main Results:
- Both square root and cube root approximations were found to be adequate for power analysis.
- The square root approximation showed a slight advantage over the cube root approximation.
- The square root approximation was chosen for the computation of set correlation power tables.
Conclusions:
- The square root approximation provides a reliable method for power analysis in set correlation.
- The study facilitates the creation of necessary power analysis tables for researchers.
- This work addresses a critical gap in the availability of statistical tools for set correlation analysis.
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