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Chapter 16

Chapter 16. Integrating What You Have Learned: The General Linear Model. The Relationship Among Major Statistical Methods. The general linear model. Review of the Principles of Multiple Regression. Multiple correlation ( R ) Proportionate reduction in error ( R 2 ). The General Linear Model.

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Chapter 16

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  1. Chapter 16 Integrating What You Have Learned: The General Linear Model

  2. The Relationship Among Major Statistical Methods • The general linear model

  3. Review of the Principles of Multiple Regression • Multiple correlation (R) • Proportionate reduction in error (R2)

  4. The General Linear Model • Actual value of Y • Error term (e) • The general linear model and multiple regression

  5. Bivariate Regression and Correlation as Special Cases of Multiple Regression • Bivariate regression • Special case of multiple regression • Bivariate correlation • Special case of multiple regression

  6. The t Test as a Special Case of ANOVA • t test • Two groups • ANOVA (F ratio) • More than two groups • Parallels in their basic logic • Numeric relationship of the procedures

  7. Links Between the t Test for Independent Means and ANOVA

  8. The t Test as a Special Case of the Significance Test for the Correlation Coefficient • Correlation coefficient • Degree of association between two variables • t test • Significance of the difference between the two population means • Both use the t distribution to determine significance

  9. The t Test as a Special Case of the Significance Test for the Correlation Coefficient • Group differences as associations among variables • Numerical predictor variables versus two-category nominal variable that divides the groups

  10. Relation Between Correlation and t Test for Independent Means

  11. ANOVA as a Special Case of the Significance Test of Multiple Regression • ANOVA for two groups as a special case of the significance of a bivariate correlation • ANOVA Correlation/Regression SSWithin = SSError SSTotal =SSTotal SSBetween = SSTotal – SSError R2 = r2

  12. ANOVA as a Special Case of the Significance Test of Multiple Regression • ANOVA for more than two groups as a special case of multiple correlation • Nominal coding

  13. Choice of Statistical Tests • t test, ANOVA, and correlation can all be done as multiple regression • However, each usually used in specific research contexts • Correlation and regression automatically give estimates of effect size and not just significance

  14. Controversies • What does causality mean? • Regularity theory of causality • Generative theory of causality

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