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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
Chapter 16

Integrating What You Have Learned: The General Linear Model

review of the principles of multiple regression
Review of the Principles of Multiple Regression
  • Multiple correlation (R)
  • Proportionate reduction in error (R2)
the general linear model
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 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
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
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 coefficient1
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 as a special case of the significance test of multiple regression
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

anova as a special case of the significance test of multiple regression1
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
choice of statistical tests
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
Controversies
  • What does causality mean?
    • Regularity theory of causality
    • Generative theory of causality