Lecture 12: ANCOVA Flashcards
What is ANCOVA
Analysis of covariance
What are covariates (CV)
A new predictor variable. A continuous variables that are not of primary interest but could be a confounding variable. By adding the CV we can reduce error/residual in the model
What is the least squares estimate
The regression line that is closest to all of the data points, minimized the squares between data points and the line
Principle of parsimony
You want the best prediction based on the simplest model
What happens to the f-value when we control for effects of covariates and why
The f-value increases because the unexplained variance (MSmodel) decreases after adding a covariates
What are the assumptions of the ANCOVA
- Continuous variable
- Random sample
- Normally distributed
- Equal variance within groups
—> these are the same as ANOVA - Independence of covariate and treatment effect
- Homogeneity of regression slopes
How do we check for homogeneity in JASP
Levene’s test, descriptive stats (check if the SD’s are the same or not)
How do we check for normality in JASP
Q-Q plot —> see if the data points are approximately on the line
How do we check independence for ANCOVA in JASP
Use ANOVA and put CV as DV and the IV in ‘fixed factors’, then check the p-value (if bigger than 0.05 then not violated)
How do we check homogeneity of regression slopes for ANCOVA with JASP
Descriptive plots —> CV on horizontal axis, IV on ‘separate lines’, check if the lines are parralel
Or
Use ‘model’ —> click both variables and put both in ‘model terms’ (remove these again if you want to read results for ANCOVA analysis)
What is the function of the least squares estimate
It adds 2 prediction options: 1) covariates, 2) covariates + group means
What are marginal means
Estimated group means, while keeping the covariate equal across the groups (controlling for CV)
These means are used for follow-up tests such as contrasts and post-hoc analyses
