Lecture 8 - ANCOVA Flashcards
What is ANCOVA?
an extension of ANOVA, where you control for 1 or more covariates
What is a covariate?
A continuous variable that is correlated with the DV, but is not the focus of the study. Can be a possible confound.
Why is ANCOVA better than ANOVA?
- reduces the error variance
- more accurate, increases signal compared to noise
- this can increase your power
What are the 9 assumptions of ANCOVA?
- normality
- homogeneity of variance
- linearity b/w covariates
- linearity b/w covariates and DV
- equal sample sizes
- no multivariate outliers (these can lead to heterogeneity of regression)
- no high correlations b/w different covariates
- homogeneity of regression
- independence of covariate and factor (often ignored)
What is the assumption of homogeneity of regression? How do you check this?
- want slopes for each cell to be the same
- no interaction
- want the interaction in the “Tests of Between-Subjects Effects” to be > .05
- do NOT want interaction b/w covariate and factor (IV)
What is the independence of covariate and factor assumption? How do you check this?
Want the covariate and the IV to be independent.
To check: run an ANOVA with the covariate as the DV and the IV as the IV (fixed factor). Want a non-significant (>.05) effect.
How can you get around the independence of covariate and factor assumption?
With an experimental design with randomly allocated groups , you can assume that the covariates are not related to the groups in any way
How are regression and ANOVA similar and difference?
- can do exactly the same thing!
- ANOVA is a specific case of regression
- diff emphases = diff output
- regression only handles one DV
- ANOVA is multiple regression when you use dummy variables
What does ANCOVA incorporate?
linear regression approaches within an ANOVA
What is in the simplest ANCOVA?
1 DV
1 factor
1 covariate
What is the difference between ANCOVA and ANOVA in terms of testing sig.?
- ANOVA: tests whether main effect for group (alpha) is sig
- ANCOVA: tests whether main effect of group (alpha) is sig after adding in the covariate. Tests groups diffs at average level of the covariate.
What is the difference between the ANOVA and ANCOVA equations? What do the terms in the equations mean?
- ANOVA equation: Yij = u + aj + eij
- ANCOVA: Yij = u + aj + +BXij + eij
- Yij = DV
- Xij = covariate
- B = regression coefficient
- u = grand mean
- aj = main effect for j-th group
- eij = residual
What does it mean if the independence of covariate and factor assumption is not met?
- you are not comparing group means at the average level of the covariate
- cannot equate group diffs with the covariate
How do you check where the group differences are?
- use contrasts (can also use post-hoc tests)
- simple contrasts
- look at sig and CI
What is dummy coding? How many dummy variables do you need for 3 categories?
- when you take categories (eg. 3) and turn it into binary variables
- for 3 categories, you only ever need 2 dummy variables
