Effect size comparison for populations with an application in psychology

Area of Science:

• Behavioural Science
• Statistical Methods
• Research Methodology

Background:

• Effect size estimates are crucial for precise estimation and power analysis in behavioral studies.
• Sample size planning is often constrained by limited resources, necessitating optimal allocation.
• Population variances significantly influence effect size variance, impacting study precision.

Purpose of the Study:

• To define a general effect size for comparing two population characteristics.
• To optimize the variance of this general effect size under sampling budget constraints.
• To develop a method for determining optimum sample sizes for populations with differing variances.

Main Methods:

• A general effect size is defined for comparing two population characteristics.
• Sequential theory is employed to determine optimum sample sizes for minimum variance.
• The developed method is distribution-free and does not require prior knowledge of population parameters.

Main Results:

• The sequential method successfully optimizes sample size allocation under budget constraints.
• The method achieves minimum variance for the general effect size.
• Simulation studies validate the mathematical justification and effectiveness of the sequential approach.

Conclusions:

• The developed sequential method offers an efficient approach to sample size optimization in effect size comparisons.
• This distribution-free method has broad applicability in behavioral and other research fields.
• Accurate sample size planning is paramount for reliable effect size estimation and power analysis.