ANCOVA Flashcards
(17 cards)
Traditional ANCOVA
Traditional ANCOVA just adds a “main effect” of the continuous CV to the model
We want to account for the effect that our CV is having on our DV
If we don’t account for the CV, then there will be more unexplained variance in the model, which will make our test less powerful
Non-traditional version of ANCOVA
Includes the interaction between the IV(s) and the CV; this is robust against the violation of one of the assumptions (homogeneity of regression slopes), but is technically just a linear model (i.e., it’s not commonly referred to as ANCOVA)
Benefits of ANCOVA
Reducing the error variability in the model by explaining this portion of variance in the DV that the covariate can explain.
Make more powerful test and give better chance of detecting the effect of our IVs
What is a covariate
A (continuous) variable that we think might influence our DV
If we make poor choices of covariates, then we can come to misleading conclusions
Covariates should be based on knowledge (e.g., literature, expertise, etc.), and be things that we think might influence the DV, while being distinct from our IV(s)
ANCOVA assumptions - independence
CVs to be independent from our IVs - that is, our CV doesn’t differ across the levels of our IV
Similar to multicollinearity, we want to avoid situations where the variables that predict the DV (i.e., the IV(s) and CV(s)) to share variance with each other
If the assumption is violated It’s hard to know what effect the IV is having, and what effect the CV is having
IV and CV can’t be the same - we can’t control for what we are manipulating
ANCOVA Assumptions
DV (and CV) should be at the scale level
Data should be normally distributed
The ones for whatever type of ANOVA you’re using:
Equal Variances for BS and Mixed ANOVA
Sphericity for WS and Mixed ANOVA (though can be avoided with Linear mixed effects models)
Equality of covariance matrices for Mixed ANOVA (though can be avoided with linear mixed effects models)
Two ones unique to ANCOVA:
Independence between the IV and the CV
Homogeneity of regression slopes
Independence between the IV and the CV
We want the CV to be roughly equal across the levels of the IV
How do we test if our covariate is independent from the IV
We can run an ANOVA
For this check, the covariate would be treated as the dependent variable rather than a covariate
If the ANOVA is non-significant, this suggests that the covariate is independent of the IV
Variance of the covariate is not explained by the independent variable
If the ANOVA is significant, this may suggest that the covariate is not independent of the IV
Variance of the covariate is explained by the independent variable
Homogeneity of regression slopes
We want the relationship between the CV and the DV to be roughly equal across the levels of the IV
Essentially, we want there to be no interaction between the CV and the IV on the DV
How do we test for homogeneity of regression slopes
We can add the interaction term between the CV and IV into our ANCOVA
If the interaction is non-significant, this suggests that the assumption is met
No interaction between the CV and IV
Do we want the independence between the IV and DV assumption test and the homogeneity of regression slopes test to be significant or not
Non-signficiant
What do you do if the homogeneity of regression slopes assumption is violated (interaction is significant)
Use the linear model that was used to test HoRS with the interaction term to test main effects of IV and the effect of the CV - ignoring the interaction
How would you write up the model - interaction
The interaction term between IV and CV was also included in the model to account for the violation of homogeneity of regression slopes.
How would you write up the model - controlling
An ANCOVA was conducted to compare the effect of IV on DV after controlling for CV
When to use each model
Assumption violated = use the model with the interaction
Assumption met = Standard ANCOVA without the interaction
How to write up the ANOVA including the covariate
Including is when there is the interaction
Would state: after controlling for the covariate, the IV had a sig effect
Would not state the interaction. Just the main effect the the IV and the main effect of the CV separately
How to write up the ANOVA without the covariate
Only looking at the effect of the IV
