Making Sense of Factor Analysis

Marjorie A. Pett, MStat, DSW, is a Research Professor in the College of Nursing at the University of Utah, Salt Lake City, Utah, having been on the faculty since 1980. By her own admission, she is a "collector" of academic degrees: BA (Brown University), MS in sociology (University of Stockholm, Sweden), MSW (Smith College), DSW (University of Utah), and MStat (Biostatistics) (University of Utah). Dr. Pett has a strong commitment to facilitating the practical application of statistics in the social, behavioral, and biological sciences, especially among practitioners in health care settings. She has designed and taught graduate courses to students from a variety of disciplines at the beginning and advanced levels, including research design and data management, parametric and nonparametric statistics, biostatistics, multivariate statistics, instrument development, and factor analysis. She has tried to approach the teaching of statistics with humor and from a clinician's perspective and has been the recipient of several distinguished teaching awards both at the College and University levels. Her most recent research interests include the development of client-centered assessment tools and interventions to evaluate and enhance health-related quality of life (HRQoL) for persons with intellectual disabilities. She is the author of numerous research articles and chapters, and is an author of the Sage publication, Making Sense of Factor Analysis: The Use of Factor Analysis for Instrument Development in Health Care Research. When not engaged in research, writing, or teaching, Marge is a (now retired) state soccer referee, devotee of tennis, an avid (high handicap) golfer, student of Italian and French, reader of mystery novels, grandmother to three, mother to two, and wife to (only) one. Dr John Sullivan has been a professor of management for over 26 years at San Francisco State University. His specialty is HR strategy and designing world class HR systems and tools for Fortune 200 firms. He has worked with over 200 different businesses and organizations in more than 30 countries around the world as a speaker or advisor. He has written a weekly column for ERE for over eleven years. Overall, he has written ten books, dozens of white papers and over 700 articles. He was the chief talent officer for Agilent (the 40,000+ employee HP spin off). He has appeared on the CBS and ABC national nightly news, CNN and in various publications including Fortune, the Economist, CIO, BusinessWeek, the WSJ, the Washington Post, Money, Time and every major HR magazine. Fast company called him the Michael Jordan of hiring. He was listed among the 40 most influential people in HR. Tom Peters cites and utilizes his work in his latest book Re-Imagine.

1. An Overview of Factor Analysis Characteristics of Factor Analysis Exploratory Vs. Confirmatory Factor Analysis Assumptions of Exploratory Factor Analysis Historical Developments of Factor Analysis Uses of Factor Analysis in Health Care Research Decision-Making Process in Exploratory Factor Analysis 2. Designing and Testing the Instrument Types of Measurement and Frameworks The Use of Latent Variables in Instrument Development Identifying Empirical Indicators of Latent Variables Using Qualitative Research Methods to Identify Empirical Indicators Additional Qualitative Approaches to Identifying Empirical Indicators Development of the Instrument Scoring the Instrument Pilot Testing the Instrument Determining the Number of Subjects 3. Assessing the Characteristics of Matrices Characteristics and Types of Matrices Tests of Matrices Review of the Process 4. Extracting the Initial Factors Evaluating the Correlation Matrix Sources of Variance in Factor Analysis Models Determining the Factor Extraction Method Selecting the Number of Factors to Retain Comparing the Two-Factor Solution Using PCA and PAF 5. Rotating the Factors Achieving a Simple Structure Types of Rotations Mapping Factors in Geometric Space Orthogonal Rotations Oblique Rotations Comparing the Orthogonal and Oblique Solutions Advantages and Disadvantages of the Oblique Solution Choosing Between Orthogonal and Oblique Rotations Summary of the Process of Rotations 6. Evaluating and Refining the Factors Evaluating and Refining the Factors Assessing the Reliability of an Instrument Evaluating the Internal Consistency of an Instrument Estimating the Effects on Reliability of Increasing or Decreasing Items Cronbach's Coefficient Alpha Assessing Reliability Using Cronbach's Alpha: A Computer Example Two Additional Reliability Estimates: Temporal Stability and Equivalence 7. Interpreting Factors and Generating Factor Scores Interpreting the Factors Naming the Factors Interpreting and Naming the Four Factors on the CGTS Scale Determining Composite Factor Scores 8. Reporting and Replicating the Results When to Report the Results What to Include in the Report An Exemplar of a Published Report Replicating the Factors in Other Studies Conclusions Appendix A: Concerns About Genetic Testing Scale Appendix B: SAS Commands and Generate Output Appendix C: Output for 20-item CGTS Scale Appendix D: Tables for the Chi-Square and Normal Distributions Appendix E: Unraveling the Mystery of Principal Component Extraction References Index About the Authors