Additional Stuff

Question 1

How is ANOVA and Dummy-Coded Multiple Linear Regression similar

Answer 1

• Both use least squares estimator
• SS_total = Variation explained by model + Variation not explained by model
  
  • LR: SS_reg or SS_{Due to Mean Difference}
  • ANOVA: SS_res or SS_{Not due to Mean Difference}
• Both have the same omnibus hypothesis
  
  • LR: None of the IVs explains any variation in the DV
  • ANOVA: No differences between group means
    
    • Expressed differently

Dummy-coding is one way to investigate group differences (but they are not linear contrasts because the values do not sum to zero). Contrasts are more flexible.

Question 2

How do we think of Sum of Squares and orthogonality in a two-way between-subject

Answer 2

Assuming balanced design

• All groups have same mean = Grand Mean
  
  • No deviation
• Main effects
  
  • Deviation mean for each group from grand mean
  • Square of these deviation mean is a measure of variaton in observed scores due to group
    
    • SS_factor
• Orthogonal = Uncorrelated
  
  • SS_{contrasts sum of squares} = SS_{factor ​}
    
    • Hence, all group differences are explained in one possible way

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