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Optimal sample sizes for the design of reliability studies: power consideration
1Department of Management Science, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, Taiwan, 30010, gwshieh@mail.nctu.edu.tw.
Behavior Research Methods
|November 8, 2013
Summary
Determining adequate sample size for intraclass correlation coefficients in multilevel research is crucial. This study finds the Fisher transformation method unreliable for sample size calculations, recommending exact procedures instead.
Area of Science:
- Multilevel statistical modeling
- Psychometrics
- Reliability analysis
Background:
- Intraclass correlation coefficients (ICCs) are vital for assessing group member resemblance in multilevel research.
- Existing literature on sample size determination for ICC hypothesis testing presents incomplete or problematic numerical results.
- The one-way random-effects model is frequently employed in such reliability assessments.
Purpose of the Study:
- To reevaluate and compare the accuracy of an approximate sample size formula based on Fisher's transformation against an exact method for ICCs.
- To provide guidance on necessary sample sizes for ensuring adequate statistical power in hypothesis tests concerning ICCs.
- To offer practical solutions for advance design planning in reliability studies.
Main Methods:
- Comparison of Fisher's transformation-based sample size formula with an exact sample size procedure.
- Evaluation across a wide range of one-way random-effects model configurations.
- Development of computer programs to implement exact sample size algorithms.
Main Results:
- The Fisher transformation method for sample size calculation is deemed appropriate only in limited scenarios.
- The approximate method is not recommended for general application in reliability studies.
- Exact sample size procedures demonstrate superior reliability and applicability.
Conclusions:
- Researchers should exercise caution when using Fisher's transformation for sample size planning related to ICCs.
- Exact sample size procedures are recommended for robust design planning in reliability studies.
- The study provides practical, illustrated methods and computational tools for accurate sample size determination.
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