Analyzing Multivariate Repeated Measures Designs: A Comparison of Two Approximate Degrees of Freedom Procedures

Area of Science:

• Statistics
• Psychometrics
• Multivariate Analysis

Background:

• Repeated measures designs are common in psychology and other fields.
• Testing within-subjects effects in such designs can be complex, especially with violations of assumptions.
• The Welch-James (WJ) and Brown-Forsythe (BF) procedures are alternatives to traditional methods when assumptions are violated.

Purpose of the Study:

• To investigate the performance of WJ and BF procedures for within-subjects effects in multivariate repeated measures.
• To evaluate these procedures under departures from covariance homogeneity and normality.
• To compare least-squares and robust estimators for these tests.

Main Methods:

• Empirical Type I error and power rates were simulated.
• The study focused on multivariate groups by trials repeated measures designs.
• Least-squares and robust (trimming/Winsorization) estimators were examined.

Main Results:

• With least-squares estimators, BF and WJ had similar Type I error for the main effect.
• For interactions, BF became conservative and WJ liberal with small samples.
• Robust estimators improved WJ's error control; BF became conservative.
• WJ showed higher power for interactions with heterogeneous covariances.

Conclusions:

• The Welch-James procedure generally offers better Type I error control, particularly with robust estimators and heterogeneous covariances.
• For interaction effects, the WJ procedure is more powerful than the BF procedure under covariance heterogeneity.
• Robust estimators enhance the reliability of these statistical tests in repeated measures analyses.