Bayesian sample size determination for coefficient of variation of normal distribution

Area of Science:

• Statistics
• Statistical inference
• Bayesian statistics

Background:

• Sample size determination is crucial in statistical research.
• Bayesian methods generally yield smaller sample sizes than classical techniques.
• The average length criterion is a conventional Bayesian approach for sample size determination.

Purpose of the Study:

• To apply key Bayesian sample size determination techniques to the coefficient of variation for normal distributions.
• To compare the performance of Bayesian methods against frequentist approaches.
• To evaluate the efficiency of Bayesian sample size determination.

Main Methods:

• Utilized Bayesian sample size determination techniques.
• Focused on the coefficient of variation for normal distributions.
• Compared results with frequentist methods.

Main Results:

• The average coverage criterion yielded smaller sample sizes than the worst outcome criterion.
• Bayesian methods require smaller sample sizes than frequentist approaches for equivalent efficiency.
• Demonstrated the effectiveness of Bayesian techniques in reducing sample size requirements.

Conclusions:

• Bayesian sample size determination is efficient for the coefficient of variation.
• Bayesian methods offer a statistically sound approach to reduce sample sizes.
• This research supports the use of Bayesian methods for more economical study designs.