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Understanding Multivariate ANOVA and Related Techniques for Analyzing Multiple Outcomes

This article explores advanced statistical methods such as Multivariate ANOVA (MANOVA) and Repeated Measures ANOVA, highlighting how to simultaneously analyze multiple dependent variables related to demographic factors. It provides concrete examples, like examining adolescent coping styles based on gender and race, and illustrates how Analysis of Covariance (ANCOVA) can adjust for initial group differences. Additionally, it discusses Multiple Regression for predicting language skills and Factor Analysis for grouping behaviors. Meta-analysis is also introduced as a method for synthesizing published research findings.

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Understanding Multivariate ANOVA and Related Techniques for Analyzing Multiple Outcomes

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  1. Intro to Stats Other tests

  2. Multivariate ANOVA • More than one dependent variable/ outcome • Often variables are related • Need a procedure to estimate simultaneously

  3. An example • MANOVA with • gender (2 levels: male, female) • Race (4 levels: caucasian, africanamerican, asianamerican, hispanic) • Grade (5 levels: 8, 9, 10, 11, 12) • DVs • Adolescent coping scale • Seek social support • Focus on solving the problem • Word hard and achieve • Worry • Invest in close friends • Seek to belong • Wishful thinking • Not coping • Tension reduction • Social action • Ignore the problem • Self-blame • Keep to self • Seek spiritual support • Focus on the positive • Seek professional help • Seek relaxing diversions • Physical reaction

  4. Multivariate ANOVA • MANOVA Results With Demographics as Independent Variables

  5. Repeated measures ANOVA • One factor on which participants are tested more than once

  6. An example • Repeated measures ANOVA with • Gender (2 levels: male, female) • Interaction (2 levels: same sex, opposite sex) • Grade level as repeated measure • 11th grade • 12th grade • Multiple outcomes measured in the two grades

  7. Analysis of Covariance • Can equalize initial differences among groups by including a covariate • Helps improve power by reducing problems with random assignment

  8. An example • Women read scenarios about a woman who chooses to have sex or not • ANCOVA with • Relationship condition (4 levels: passion, passion+intimacy+no commitment, passion+intimacy, passion+intimacy+commitment) • Included ratings of acceptability of non-sexual scenario as covariate (to control for baseline ratings of protagonist) • DV: social acceptance (wanted to meet protagonist)

  9. Multiple regression • Can include more than one predictor of an outcome

  10. An example • Multiple regression • Outcome: child language skills • Predictors: • Mother literacy activities • Mother’s level of education • Mother’s age • Amount of shared reading

  11. Factor analysis • How well items “hang” together and form clusters (factors) • Represent factors that are related to one another by a more general construct

  12. An example • Interested in how experiences before 12 influence dating and peer relationships during adolescence • No scale of relationships • Administered 80 items with behaviors from self to partner or from partner to self • Conducted a factor analysis to see what types of behaviors were highly related with one another and formed “clusters” of related behaviors

  13. Meta-analysis • Find all published studies that examine a particular relationship, then pull out and combine effects from all studies

  14. An example • Examined whether elicited emotions (happiness, anger, sadness, anxiety) predict changes in cognitions, emotions, physiology, and behavior • Identified all published studies that included more than one emotion and at least one of the outcomes • Coded factors in each study: college students vs. community members, cover story or not • Also coded the effects – how large was the difference between 2 groups (heart rate in sad versus happy group)

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