Effect sizes for experimental research

Area of Science:

• Statistics
• Experimental Design
• Quantitative Research Methods

Background:

• Scientific reporting standards necessitate effect size estimates alongside significance tests.
• Statistical best practices require quantifying the uncertainty of effect size estimates, often using standard errors.

Purpose of the Study:

• To review effect sizes commonly used in experimental research.
• To provide formulas for the standard error of various effect sizes.
• To cover effect sizes for treatments with single and multiple degrees of freedom.

Main Methods:

• Literature review of effect size measures in experimental statistics.
• Derivation and presentation of standard error formulas for selected effect sizes.
• Focus on effect sizes applicable to both simple (single degree of freedom) and complex (multiple degrees of freedom) treatment structures.

Main Results:

• Comprehensive overview of key effect size metrics.
• Formulas for calculating standard errors for each effect size are presented.
• Discussion includes effect sizes for fixed and random effects in multifactorial designs.

Conclusions:

• Accurate reporting of effect sizes and their uncertainty enhances the interpretability and reproducibility of experimental findings.
• The presented formulas facilitate the correct statistical analysis and reporting of experimental results.
• This work serves as a valuable resource for researchers seeking to implement best practices in statistical reporting.