Broadly defined, multivariate research methods involve the inclusion of more than one outcome in a singular analysis. Instead of conducting a series of univariate analysis, one for each outcome, multivariate analyses consider all the outcomes of interest at the same time. When compared to multiple univariate analysis, the multivariate approach allows for the reduction in Type I error, for an increase in power, and for the relationship between the outcome variables to be expressed. Perhaps most importantly from an applied perspective, the multivariate approach allows the researcher to analyze the data in a way that is most reflective of the actual research context and environment. In education, research scenarios involving multiple outcomes could include examples such as how a character education program impacts student self-efficacy, attitudes, and behavior, or how mentoring influences reading, math, and science performance. Beyond more applied uses of multivariate designs, multivariate analysis can extend to include models such as those specific to testing structural validity of instruments designed to measure latent constructs such as intelligence and personality or to predicting group placement. In other words, multivariate research methods are warranted in most situations where multiple dependent variables are being considered in the same research scenario. In order to appropriately analyze data gathered under a multivariate design, researchers must shift away from univariate analysis into the multivariate analysis framework. The sections in this article are intended as an introduction to the applications, considerations, and mechanics of conducting multivariate research. Although the sections are presented as discrete categories, the topics often overlap and inform each other. The sections are General Overviews of multivariate topics, Multivariate Assumptions, Multivariate Effect Sizes, Multivariate Analysis of Variance (MANOVA), Discriminant Analysis (DA), Canonical Correlation Analysis (CCA), Exploratory Factor Analysis (EFA), Principal Components Analysis and Common Factor Analysis, Factor Retention, Rotation Criteria, Confirmatory Factor Analysis (CFA), Structural Equation Modeling (SEM), Multidimensional Scaling (MDS), and Nonparametric Multivariate Analysis.
The text and articles in this section provide overviews and introductions to major concepts for consideration while conducting multivariate analysis. Huberty and Morris 1989 and Huberty 1994 emphasize the reason for conducting a multivariate analysis instead of a series of univariate analyses. Tabachnick and Fidell 2012 and Stevens 2009 provide comprehensive introductions to understanding and conducting multivariate analysis. Grimm and Yarnold 1995 and Grimm and Yarnold 2000 include introductory chapters on a broad range of multivariate topics written by several experts in the field. Written in a conversational style, Harris 2001 introduces multivariate analysis to the novice researcher, while Johnson and Wichern 2007 provides in-depth chapters for those with stronger statistical backgrounds. Meyers, et al. 2013 presents introductions and step-by-step analysis examples using SPSS (Statistical Package for the Social Sciences). Raykov and Marcoulides 2008 provides several applied examples that include syntax for SPSS, SAS, and MPlus. Loehlin 2004 introduces latent variable models, including factor, path, and structural equation analysis.
Grimm, L. G., and P. R. Yarnold, eds. 1995. Reading and understanding multivariate statistics. Washington, DC: American Psychological Association.
Written for those with little to no exposure to multivariate analyses but a basic understanding of univariate statistics. Includes chapter topics such as path analysis, multidimensional scaling, analysis of cross-classified data, logistic regression, DA, MANOVA, and meta-analysis. Each chapter includes suggestions for further reading and a glossary of terms and symbols.
Grimm, L. G., and P. R. Yarnold, eds. 2000. Reading and understanding MORE multivariate statistics. Washington, DC: American Psychological Association.
An extension of the previous edition focusing on conceptual understanding. Includes chapters on generalizability theory, item response theory, assessing validity of measurement, cluster analysis, SEM, CCA, repeated measures analyses, and survival analysis. Each chapter includes suggestions for further reading and a glossary of terms and symbols.
Harris, R. J. 2001. A primer of multivariate statistics. 3d ed. New York: Psychology Press.
Presented in a conversational style, includes discussion of the theoretical reasoning behind multivariate analysis as well has how the analyses are conducted. Emphasizes the importance of testing the interpretations of latent variables produced through multivariate analyses.
Huberty, C. J. 1994. Why multivariate analyses? Educational and Psychological Measurement 54:620–627.
Overviews the definition and purpose of multivariate analyses. Emphasizes the importance of choosing the appropriate response variables. Refutes the idea of an obligatory multivariate analysis followed by a series of univariate analysis as protection against Type I error.
Huberty, C. J., and J. D. Morris. 1989. Multivariate analysis versus multiple univariate analyses. Psychological Bulletin 105:302–308.
Discusses the methodological argument surrounding multiple ANOVAs versus a MANOVA as it relates to Type I error. Emphasizes that analysis decisions should be based on the established research questions. Multivariate analysis is more appropriate for research questions involving outcome variable selection, variable ordering, and variable system structure.
Johnson, R. A., and D. W. Wichern. 2007. Applied multivariate statistical analysis. 6th ed. Upper Saddle River, NJ: Pearson.
Written from more of a business perspective for those with a stronger statistical background. Presents in-depth chapters on matrix algebra, sampling, and multivariate normal distribution in addition to commonly applied multivariate analyses. Includes examples with SAS syntax and output for two-way MANOVA, PCA, factor analysis, and DA.
Loehlin, J. C. 2004. Latent variable models: An introduction to factor, path, and structural equation analysis. 4th ed. Mahwah, NJ: Lawrence Erlbaum.
Provides a comprehensive overview of latent variable modeling as it pertains to factor analysis, path analysis, and structural equation modeling. Includes both introductory and advanced topics, accessibly presented using path diagrams, applied examples from published research, and illustrative exercises. Both the novice and more advanced user will find the explanations and extensive references useful.
Meyers, L. S., G. Gamst, and A. J. Guarino. 2013. Applied multivariate research: Design and interpretation. Los Angeles: SAGE.
Presented using conversational narrative, provides an introduction of multivariate research to the novice to intermediate user. Includes numerous graphical illustrations including path diagrams and segments of output. Readers will find the step-by-step approach with screenshots of SPSS menus and output helpful to conducting and interpreting analysis.
Raykov, T., and G. A. Marcoulides. 2008. An introduction to applied multivariate analysis. New York: Routledge.
Written as an introductory applied text, covers commonly used multivariate analyses while focusing on necessary methodological considerations such as data screening, meeting assumptions, and missing data. Includes explanations through extensions of univariate concepts. Examples of data analysis in SPSS, SAS, and MPlus included.
Stevens, J. 2009. Applied multivariate statistics for the social sciences. 5th ed. New York: Routledge.
Comprehensive text covering many background topics such as matrix algebra and multiple regression as well as the major multivariate analyses such as MANOVA, DA, factor analysis, CCA, and multivariate categorical data analysis. Each chapter begins with a brief introduction to the topic and includes example data sets with instructions for conducting the analysis and interpreting output in SPSS and SAS.
Tabachnick, B. G., and L. S. Fidell. 2012. Using multivariate statistics. 6th ed. Boston: Pearson Education.
A comprehensive applied review including conceptual background and discussion of analytical decisions, as well as a demonstration of how to conduct multivariate analysis. Demonstrations include DA, logistic regression, survival analysis, CCA, PCA, factor analysis, SEM, and multilevel linear modeling. Includes SPSS and SAS syntax and sample output.
Users without a subscription are not able to see the full content on this page. Please subscribe or login.
- Academic Achievement
- Academic Audit for Universities
- Academic Freedom and Tenure in the United States
- Action Research in Education
- Adjuncts in Higher Education in the United States
- Administrator Preparation
- Advanced Placement and International Baccalaureate Courses
- African American Racial Identity and Learning
- Alternative Certification Programs for Educators
- Alternative Schools
- American Indian Education
- Art Education
- Assessing School Leader Effectiveness
- Assessment, Behavioral
- Assessment, Educational
- Assessment in Early Childhood Education
- Athletics, College
- Augmented Reality in Education
- Beginning-Teacher Induction
- Bilingual Education and Bilingualism
- Blended Learning
- Case Study in Education Research
- Changing Professional and Academic Identities
- Character Education
- Children’s and Young Adult Literature
- Children's Beliefs about Intelligence
- Children's Rights in Early Childhood Education
- Civic and Social Engagement of Higher Education
- Classroom Management
- College Admissions in the United States
- Community Relations
- Comparative Education
- Computer-Based Testing
- Continuous Improvement and "High Leverage" Educational Pro...
- Counseling in Schools
- Critical Perspectives on Educational Innovation and Improv...
- Critical Race Theory
- Crossborder and Transnational Higher Education
- Cross-National Research on Continuous Improvement
- Cross-Sector Research on Continuous Learning and Improveme...
- Culturally Responsive Leadership
- Culturally Responsive Pedagogies
- Culturally Responsive Teacher Education in the United Stat...
- Curriculum Design
- Data Collection in Educational Research
- Data-driven Decision Making in the United States
- Deaf Education
- Desegregation and Integration
- Development, Moral
- Digital Age Teacher, The
- Digital Divides
- Distance Learning
- Distributed Leadership
- Doctoral Education and Training
- Early Childhood Education and Care (ECEC) in Denmark
- Early Childhood Education and Development in Mexico
- Early Childhood Education in Australia
- Early Childhood Education in China
- Early Childhood Education in Europe
- Early Childhood Education in Sub-Saharan Africa
- Early Childhood Education in Sweden
- Early Childhood Education Pedagogy
- Early Childhood Education Policy
- Early Childhood Education, The Arts in
- Early Childhood Mathematics
- Early Childhood Science
- Early Childhood Teacher Education
- Early Childhood Teachers in Aotearoa New Zealand
- Early Years Professionalism and Professionalization Polici...
- Economics of Education
- Education For Children with Autism
- Education Leadership, Empirical Perspectives in
- Education of Native Hawaiian Students
- Education Reform and School Change
- Educational Statistics for Longitudinal Research
- Emotional and Behavioral Disorders
- Epistemic Beliefs
- Equity, Ethnicity, Diversity, and Excellence in Education
- Ethics and Education
- Ethics of Teaching
- Ethnic Studies
- Evidence-Based Communication Assessment and Intervention
- Family and Community Partnerships in Education
- Family Day Care
- Federal Government Programs and Issues
- Finance, Education
- Financial Aid
- Formative Assessment
- Gender and Achievement
- Gifted Education
- Global Mindedness and Global Citizenship Education
- Global University Rankings
- Governance, Education
- Grounded Theory
- Growth of Effective Mental Health Services in Schools in t...
- Higher Education and Globalization
- Higher Education and the Developing World
- Higher Education Faculty Characteristics and Trends in the...
- Higher Education Governance
- Higher Education Graduate Outcomes and Destinations
- Higher Education in China
- Higher Education in Latin America
- Higher Education in the United States, Historical Evolutio...
- Higher Education, International Issues in
- Higher Education Management
- Higher Education Policy
- Higher Education Research
- Higher Education Student Assessment
- High-stakes Testing
- History of Education in the United States
- Inclusive Education
- Indigenous Education in a Global Context
- Indigenous Students in Higher Education in the United Stat...
- Inservice Teacher Education
- Integrating Art across the Curriculum
- Intensive Interventions for Children and Adolescents with ...
- Intersectionality and Education
- Knowledge Development in Early Childhood
- Leadership Development, Coaching and Feedback for
- Leadership Training
- Learning Difficulties
- Learning, Lifelong
- Learning, Multimedia
- Learning Strategies
- Legal Matters and Education Law
- LGBT Youth in Schools
- Linguistic Diversity
- Linguistically Inclusive Pedagogy
- Literacy Development and Language Acquisition
- Literacy, Multiple Documents
- Literature Reviews
- Mathematics Instruction and Interventions for Students wit...
- Mathematics Teacher Education
- Measurement in Education in the United States
- Meta-Analysis and Research Synthesis in Education
- Methodological Approaches for Impact Evaluation in Educati...
- Methodologies for Conducting Education Research
- Mindfulness, Learning, and Education
- Mixed Methods Research
- Multivariate Research Methodology
- Museums, Education, and Curriculum
- Music Education
- Narrative Research in Education
- Numeracy Education
- Online Education
- Organizing for Continuous Improvement in Education
- Organizing Schools for the Inclusion of Students with Disa...
- Pedagogy of Teacher Education, A
- Performance Objectives and Measurement
- Performance-based Research Assessment in Higher Education
- Performance-based Research Funding
- Phenomenology in Educational Research
- Philosophy of Education
- Physical Education
- Podcasts in Education
- Politics of Education
- Portable Technology for Special Education
- Pre-Service Teacher Education
- Problem Solving
- Productivity and Higher Education
- Professional Development
- Professional Learning Communities
- Program Evaluation
- Programs and Services for Students with Emotional or Behav...
- Psychology Learning and Teaching
- Psychometric Issues in the Assessment of English Language ...
- Qualitative Data Analysis Techniques
- Qualitative, Quantitative, and Mixed Methods Research Samp...
- Qualitative Research Design
- Quantitative Research Designs in Educational Research
- Race and Affirmative Action in Higher Education
- Reading Education
- Refugee and New Immigrant Learners
- Reliability in Educational Assessments
- Religion in Elementary and Secondary Education in the Unit...
- Researcher Development and Skills Training within the Cont...
- Response to Intervention
- Restorative Practices
- Scale and Sustainability of Education Innovation and Impro...
- School Accreditation
- School Choice
- School Culture
- School District Budgeting and Financial Management in the ...
- School Improvement through Inclusive Education
- School Reform
- Schools, Private and Independent
- School-Wide Positive Behavior Support
- Science Education
- Secondary to Postsecondary Transition Issues
- Self-Regulated Learning
- Self-Study of Teacher Education Practices
- Severe Disabilities
- Single Salary Schedule
- Single-sex Education
- Single-Subject Research Design
- Social Context of Education
- Social Justice
- Social Network Analysis
- Social Pedagogy
- Social Science and Education Research
- Social Studies Education
- Sociology of Education
- Standards-Based Education
- Statistical Assumptions
- Student Access, Equity, and Diversity in Higher Education
- Student Assignment Policy
- Student Engagement in Tertiary Education
- Student Learning, Development, Engagement, and Motivation ...
- Student Participation
- Student Voice in Teacher Development
- Teacher Evaluation and Teacher Effectiveness
- Teacher Preparation
- Teacher Training and Development
- Teacher Unions and Associations
- Teacher-Student Relationships
- Teaching Critical Thinking
- Technologies, Teaching, and Learning in Higher Education
- Technology Education in Early Childhood
- Technology, Educational
- Technology-based Assessment
- The Bologna Process
- The Regulation of Standards in Higher Education
- Theories of Educational Leadership
- Three Conceptions of Literacy: Media, Narrative, and Gamin...
- Tracking and Detracking
- Traditions of Quality Improvement in Education
- Transitions in Early Childhood Education
- Tribally Controlled Colleges and Universities in the Unite...
- University Faculty Roles and Responsibilities in the Unite...
- Using Ethnography in Educational Research
- Value of Higher Education for Students and Other Stakehold...
- Vocational and Technical Education
- Wellness and Well-Being in Education
- Women's and Gender Studies