Chapter 16

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# Chapter 16 - PowerPoint PPT Presentation

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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Presentation Transcript
Chapter 16

Integrating What You Have Learned: The General Linear Model

Review of the Principles of Multiple Regression
• Multiple correlation (R)
• Proportionate reduction in error (R2)
The General Linear Model
• Actual value of Y
• Error term (e)
• The general linear model and multiple regression
Bivariate Regression and Correlation as Special Cases of Multiple Regression
• Bivariate regression
• Special case of multiple regression
• Bivariate correlation
• Special case of multiple regression
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
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
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
• 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

• ANOVA for more than two groups as a special case of multiple correlation
• Nominal coding
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
Controversies
• What does causality mean?
• Regularity theory of causality
• Generative theory of causality