Repeated Measures Interaction Test with Aligned Ranks.

Area of Science:

• Statistics
• Psychometrics
• Quantitative Psychology

Background:

• Assessing interactions in repeated measures designs is crucial for understanding complex data.
• Non-normal, non-spherical, and heterogeneous data with unequal group sizes pose challenges for traditional statistical tests.
• Robust estimators and aligned ranks offer alternative approaches to handle data violations.

Purpose of the Study:

• To evaluate the Type I error rates of the Welch-James (WJ) and Huynh Improved General Approximation (IGA) tests.
• To examine test performance under non-normal, non-spherical, and heterogeneous conditions with unequal group sizes.
• To compare aligned ranks with least squares and robust estimators for interaction testing.

Main Methods:

• Simulated data from a between- by within-subjects repeated measures design.
• WJ and IGA tests computed using aligned ranks, least squares, and robust estimators (trimmed means, Winsorized variances/covariances).
• Critical values obtained theoretically and via bootstrapping.

Main Results:

• IGA and WJ tests with aligned ranks were valid for equal group sizes and homogeneous covariance matrices.
• Aligned ranks failed to provide a valid test with non-spherical covariance matrices, unequal variances, and unequal group sizes.
• IGA and WJ tests with robust estimators were valid across conditions; least squares showed better Type I error control under heavy-tailed distributions.

Conclusions:

• Aligned ranks are not universally robust for repeated measures interaction tests under violated assumptions.
• IGA and WJ tests utilizing robust estimators offer a valid approach for interaction testing in challenging data conditions.
• Least squares estimators may outperform robust estimators in Type I error control for heavy-tailed distributions.