Optimum sample size allocation to minimize cost or maximize power for the two-sample trimmed mean test

Area of Science:

• Biostatistics
• Statistical Methods
• Research Methodology

Background:

• Sample size determination is critical in study planning, influenced by study objectives, budget, and data characteristics.
• Heterogeneous variances and non-normality pose challenges in statistical testing, particularly for two-group comparisons.
• Yuen's two-group test is a robust method for comparing means, but requires careful sample size considerations.

Purpose of the Study:

• To develop novel sample size formulas for Yuen's two-group test addressing heterogeneous variances and non-normality.
• To provide methods for minimizing total cost or maximizing statistical power in study design.
• To optimize sample size allocation ratios for enhanced research efficiency and validity.

Main Methods:

• Development of sample size formulas based on standard deviation and sample size ratios.
• Formulas designed to minimize total cost, total sample size, or the sum of both, for a given statistical power.
• Optimization of sample size allocation ratios to maximize statistical power for a fixed total cost.
• Validation through simulations assessing Type I errors and power of Yuen's test with generated samples.

Main Results:

• The proposed sample size formulas effectively control Type I errors.
• The formulas achieve the desired statistical power under specified conditions of variance and normality.
• Simulation results confirm the validity and efficacy of the developed procedures.

Conclusions:

• The developed formulas offer a flexible approach to sample size determination for Yuen's two-group test.
• These methods aid researchers in optimizing resource allocation (cost and sample size) while maintaining statistical rigor.
• The findings have significant implications for designing experimental studies and guiding future research in statistical methodology.