Mixed-model pairwise multiple comparisons of repeated measures means.

Area of Science:

• Statistics
• Psychometrics
• Data Analysis

Background:

• Traditional statistical methods for repeated measures data often assume specific covariance structures.
• Mixed-model approaches offer flexibility by allowing data-driven modeling of covariance structures.
• This flexibility is crucial for complex experimental designs, such as Between-Subjects x Within-Subjects designs.

Purpose of the Study:

• To evaluate the performance of mixed-model approaches for testing pairwise differences in marginal means within a Between-Subjects x Within-Subjects design.
• To compare Type I error and power rates of simultaneous and stepwise multiple comparison procedures under violated assumptions.
• To identify robust statistical procedures for analyzing unbalanced repeated measures data.

Main Methods:

• Utilized SAS (1999) PROC MIXED for mixed-model analysis of repeated measures data.
• Investigated Type I error and power rates under conditions violating normality and covariance homogeneity assumptions.
• Applied J. P. Shaffer's (1986) step-down and Y. Hochberg's (1988) step-up Bonferroni procedures with an unstructured covariance matrix.

Main Results:

• Shaffer's (1986) sequentially rejective step-down and Hochberg's (1988) sequentially acceptive step-up Bonferroni procedures showed superior Type I error control.
• These Bonferroni-based procedures also exhibited greater power in detecting true pairwise differences.
• The findings were consistent across various investigated conditions, including unbalanced designs.

Conclusions:

• Mixed-model analysis, particularly with unstructured covariance, provides a robust framework for repeated measures data.
• Specific Bonferroni-based multiple comparison procedures offer reliable error control and enhanced power in complex designs.
• These methods are recommended for researchers analyzing unbalanced repeated measures data where assumptions may not hold.