Optimal sample size allocation for Welch's test in one-way heteroscedastic ANOVA.

Area of Science:

• Statistics
• Biostatistics
• Research Methodology

Background:

• Adequate sample size determination is critical for research planning.
• Sample size calculations must integrate cost and critical factors.
• Welch's test in one-way heteroscedastic ANOVA requires careful group size allocation.

Purpose of the Study:

• To investigate optimal group size allocation schemes for Welch's test in one-way heteroscedastic ANOVA.
• To develop methods for minimizing total cost while maintaining adequate statistical power.
• To present approaches for maximizing statistical power under a fixed cost constraint.

Main Methods:

• The study focuses on allocation schemes for group sizes in Welch's test.
• Optimal allocation strategies are derived for cost minimization and power maximization.
• Numerical investigations are conducted to compare proposed methods with common recommendations.

Main Results:

• Commonly recommended sample size allocation ratios are often not optimal.
• The proposed optimal allocation approaches outperform traditional methods.
• Numerical results demonstrate the superiority of the suggested procedures.

Conclusions:

• Traditional sample size allocation methods for Welch's test can be inefficient.
• Optimal allocation strategies can significantly improve cost-efficiency and statistical power.
• The findings are applicable to cost-effectiveness evaluations in various research fields, including pain centers.