Simplified Estimation and Testing in Unbalanced Repeated Measures Designs

Area of Science:

• Statistics
• Experimental Design
• Psychometrics

Background:

• Repeated measures designs are common in various scientific fields.
• Unbalanced data and complex error structures pose analytical challenges.
• Existing methods often require strong assumptions about the error covariance structure.

Purpose of the Study:

• To propose a simple, unbiased estimator for unbalanced repeated measures designs.
• To develop robust statistical inference methods (confidence intervals, hypothesis tests) using bootstrap techniques.
• To evaluate the performance of the proposed estimator and bootstrap methods via simulation.

Main Methods:

• Development of a novel, model-free estimator for unbalanced repeated measures.
• Application of bias-corrected and accelerated (BCa) bootstrap for confidence intervals.
• Utilizing naive percentile bootstrap for Wald-type tests, addressing small sample limitations.
• Simulation studies under various error distributions (normality and non-normality).

Main Results:

• The proposed estimator and its variance estimator are unbiased under weak assumptions.
• The simple estimator shows only a minor efficiency loss compared to block-structured estimators.
• Bootstrap methods provide reliable confidence intervals and hypothesis testing, particularly when normality assumptions fail or sample sizes are small.
• The methods are validated using data from a task switch experiment.

Conclusions:

• The proposed simple estimator offers a practical and robust approach for unbalanced repeated measures analysis.
• Bootstrap techniques enhance the reliability of statistical inference in challenging scenarios.
• The findings support the use of this estimator in complex experimental designs, such as those with many cells and participants.