ANCOVA

Question 1

What are the key characteristics of the General Linear Model?

Answer 1

• The GLM has 2 key characteristics (doesn’t preclude testing that violates this though)
  
  • Linearity; Variables are assumed to have linear relationships
    
    • Can transform non-linear variables
  • Additivity; effects of a set of variables on an outcome are assumed to be additive
    
    • Can create interaction variables, use moderation
• ANOVA and Regression both use the GLM. ANOVA tends to be used when all predictors are categorical and the outcome is continuous

Question 2

What is ANCOVA?

Answer 2

• ANCOVA is an extension of ANOVA that includes a co-variate (compares 2+ groups on an outcome while controlling for another variable)
  
  • Difference between group means adjusted for covariate;
    
    • ie the covariate score is subtracted from the group scores (
• Purposes:
  
  • Reduces within group error
  • Elimination of confounding variables
  • Controlling for baseline when comparing follow ups
  • Increases sensitivity by explaining some of the unexplained variance (reducing SSerror without changing SStotal)

Question 3

What is a co-variate?

Answer 3

• Covariate = any variable that is measureable and presumed to have a sig relationship on outcome
  
  • Not part of the main experimental manipulation
  • Must be chosen a-priori
• Try to balance predictive power against model complexity
  
  • Adding covariates loses degrees of freedom
  • Number of covariates should be less than
    
    • (10% sample size) - (number of groups - 1)

Question 4

What is the assumption of independence of the covariate?

Answer 4

• There should not be any overlap between the covariate and the treatment
  
  • Covariates do not balance out differences between treatment groups on the covariate
  • Check with t-test or ANOVA (no sig difs in covariate across IV) using IV as predictor for covariate
• Often occurs when participants are not randomly assigned or the covariate levels differ across groups
  
  • Likely to be an issue in quasi experimental designs
• ANCOVA Controversey; Miller and Chapman found many researchers misapplied ANCOVA
  
  • eg; Ie using anxiety as a covariate for depression

Question 5

What is the assumption of homogeneity of the regression slopes?

Answer 5

• The assumption that the relationship between the outcome and the covariate is the same at all levels of the predictor
  
  • ie the overall relationship is true for all groups of participants
• Testing for homogeneity:
  
  • Can be examined using a scatterplot and line of best fit
    
    • Ideally, the lines should be parallel
  • An interaction effect should be non-significant
• Note: sometimes this can be a hypothesis in itself and not necessarily bad

Question 6

How do you test ANCOVA assumptions in SPSS?

Answer 6

• Independence of the Covariate; Run an ANOVA
  
  • Analyse -> GLM -> Univariate
  • Use covariate as dependent, IV as predictor
  • Look for a non-significant F value
• Homogeneity of Regression Slopes; Run Custom ANOVA
  
  • Can be conducted before or after main analysis
  • Analyse -> GLM -> Univariate -> Custom Model
  • Include interation term between covariate and IV
  • Want a non significant interaction term

Question 7

How is ANCOVA output in SPSS interpreted?

Answer 7

• Descriptive Statistics Box; general unadjusted means
• Levene’s Test; Homogeneity of variance test (interpret with caution)
• Test of Between Subjects Effects
  
  • Check covariate significance
  • Check predictor significance (adjusted for covariate)
• Estimated Marginal Means
  
  • Means of groups adjusted for covariate
• Parameter Estimates, Contrasts and Pairwise comparisons;
  
  • Differences between adjusted means of groups against placebos
  • Direct group comparisons and breakdowns

Question 8

How is effect size reported in ANCOVA?

Answer 8

• Effect size (Eta²) needs to be reported separately for each predictor/covariate
  
  • Effect size is calculated based on the SSeffect/SStotal
• A better method is to report Partial Eta²
  
  • Proportion of variance explained uniquely by one variable
  • ie proportion of variance not explained by the covariate
• Can also calculate effect size r from the t-statistics of the contrast