Sample sizes in the multivariate analysis of repeated measurements

Area of Science:

• Biostatistics
• Experimental Design
• Statistical Power Analysis

Background:

• Repeated measurements experiments are common in various scientific fields.
• Determining appropriate sample sizes is crucial for obtaining reliable results.
• Existing methods may not fully address complex variance-covariance structures in repeated measures.

Purpose of the Study:

• To develop and present methods for sample size determination in repeated measures experiments.
• To address scenarios with arbitrary positive-definite error variance-covariance matrices.
• To ensure adequate statistical power for detecting differences between treatment means.

Main Methods:

• Assumes multivariate normality of repeated measures.
• Utilizes power considerations for Hotelling's T2 test.
• Focuses on detecting specified differences between treatment means.
• Provides tabulated sample sizes for equal variance-unequal covariance structures.

Main Results:

• Presents sample size calculations for comparing multiple treatments under repeated measures.
• Demonstrates the utility of these sample sizes for general variance-covariance structures.
• Offers practical guidance through illustrative examples.

Conclusions:

• The proposed sample size determination methods are applicable to complex repeated measures designs.
• These methods enhance the reliability of detecting treatment effects.
• The findings support robust experimental design in biostatistics and related fields.