A Note on Confidence Intervals for Two-Group Latent Mean Effect Size Measures.

Area of Science:

• Statistics
• Psychometrics
• Educational Research

Background:

• Confidence intervals are crucial for estimating the precision of effect size measures.
• Latent mean effect sizes are valuable for comparing groups on unobserved constructs.
• Existing methods for confidence intervals of latent means can be complex.

Purpose of the Study:

• To present practical delta method implementations for confidence intervals of latent mean effect sizes.
• To illustrate these methods with a real-world example in early education.
• To provide supporting computational syntax for reproducibility.

Main Methods:

• The delta method is applied to derive standard errors for latent mean effect size estimators.
• Statistical modeling software (LISREL) syntax is provided for implementation.
• A hypothetical dataset from a kindergarten reading study is used for demonstration.

Main Results:

• The delta method provides a feasible approach for obtaining confidence intervals for latent mean effect sizes.
• The provided LISREL syntax facilitates the application of these methods.
• The example illustrates the practical utility in educational contexts.

Conclusions:

• Delta method implementations offer a valuable tool for researchers estimating latent mean effect sizes.
• These methods enhance the interpretability and reliability of effect size estimates in comparative studies.
• The study supports the use of these techniques in educational and psychological research.