Univariate and Multivariate Methods for the Analysis of Repeated Measures Data

Table of Contents

• 1. INTRODUCTION
• 2. EXPLORING THE DATA
• 3. TIME BY TIME ANOVA
• 4. UNIVARIATE APPROACH TO REPEATED MEASURES
  • 4.1 Repeated Measures ANOVA
  • 4.2 Testing For Compound Symmetry
• 5. MULTIVARIATE APPROACH TO REPEATED MEASURES
  • 5.1 Profile Analysis
  • 5.2 Assumptions of Profile Analysis
  • 5.3 Testing For Multivariate Normality
  • 5.4 Testing For The Equality of Covariance Matrices
  • 5.5 Hypothesis Tests for Profile Analysis
• 6. THE GENERALISED MULTIVARIATE ANALYSIS OF VARIANCE
  • 6.1 Growth Curves
  • 6.2 Hypothesis Tests For Growth Curves
  • 6.3 Testing Polynomial Adequacy
  • 6.4 Testing For The Equality of Growth Curves
• 7. CONCLUSION
• REFERENCES
• APPENDIX A

Objectives and Key Themes

This thesis explores both univariate and multivariate approaches to the analysis of repeated-measures data. The objective is to demonstrate various methods for analyzing data with correlated observations, highlighting the advantages and disadvantages of each approach. The text explores the issue of violating the independence assumption in traditional analysis of variance when dealing with repeated measures.

• Univariate and Multivariate Approaches to Repeated Measures Analysis
• Violation of Independence Assumption in Repeated Measures
• Advantages and Disadvantages of Different Approaches
• Application of Methods to a Real-World Example (Milk Bacteria Study)
• Interpretation of Results and Statistical Significance

Chapter Summaries

The thesis begins with an introduction to the topic of repeated measures data and its significance. Chapter 2 delves into the exploration of the data, examining patterns and characteristics. Chapter 3 focuses on Time by Time ANOVA, a traditional approach to analyzing repeated measures data. Chapters 4 and 5 explore univariate and multivariate approaches respectively, including Repeated Measures ANOVA, Profile Analysis, and the assumptions associated with these methods. Chapter 6 delves into the generalized multivariate analysis of variance, exploring growth curves and hypothesis testing. The thesis concludes with a summary of findings and interpretations.

Keywords

This thesis focuses on the analysis of repeated measures data, exploring both univariate and multivariate methods. Key terms include repeated measures ANOVA, profile analysis, generalized multivariate analysis of variance, compound symmetry, multivariate normality, covariance matrices, growth curves, and statistical significance. The text also examines real-world applications through a case study involving milk bacteria production in vaccinated and non-vaccinated cows.