Week 11: ANCOVA Flashcards
ANCOVA is a…
statistical control procedure
Secondary variables are controlled methodologically by..
Elimination, constancy or making them into an IV
What do we do if we cannot control for secondary variables methodologically?
We can statistically control it by removing the variance associated with it using ANCOVA
What are we essentially doing in ANCOVA?
We are adjusting everybody’s scores on the DV to be what we think it would be if everyone had the same score on the co-variate
E.g. we could look at post-test scores to see what they would look like if everyone had the same score at pretreatment (this makes it a lot easier to see the treatment effect)
What is the major benefit of ANCOVA?
It allows a more sensitive test of treatment effects
- Removing the variance that is due to differences in the covariate will reduce the amount of unexplained variance
What does ANCOVA produce?
Main effect of treatment: tests whether the means of the groups are significantly different after controlling for the effect of the CV on the DV
Main effect of covariate: tests whether the CV is significantly related to the DV (is the slope of the regression line for the DV-CV relationship significantly different to 0)
Interaction between the treatment and CV: tests whether the relationship between the CV and the DV (whether the slopes are equal) is the same for all treatment groups
Why is the main effect of covariate important?
If it is not significant, we do not need to control for it as it is not related to the DV
What is a super important assumption of ANCOVA?
Parallel relationships between the covariate and DV for both groups
Slopes = same, this means we can identify differences by picking any point to identify their DV scores at any point on the CV
What happens if we have different slopes for each group?
Going to have different size differences at each level of the covariate
If it is not equal, you need to come up with a good reason as to why you compare groups at certain values of the covariate (because the size of the difference will change)
ANCOVA does not include..
An interaction term - assumes the slopes are the same for all groups
What does include an interaction term?
ANCOHET
What is ANCOHET?
Analysis of Covariance of Heterogenous slopes
- Explicitly tests whether the slopes are homogenous or not
What if we have a non-significant interaction in ANCOHET?
Then we have homogeneity of slopes
Can revert to ANCOVA (some say to, some say not to) as the assumption has been met
What if we have a significant interaction in ANCOHET?
Then the slope between the DV and CV are not the same for each group
Introduces a problem with interpretation of the main effect as the difference between groups will change depending on what level of the CV you assess it on
What are the assumptions of ANCOVA and ANCOHET?
- Linear relationships between the CV and DV
- Normal distribution of scores, homogeneity of variance and independence of residuals
- Homogeneity of regression: The regressions between the CV and DV have the same slope for each treatment group
Are there any differences between the two techniques and the assumption of homogeneity of regression?
Yes.
ANCOVA assumes and ANCOHET explicitly tests
What would be our ideal? and how can we test it?
Independence between CV and IV
Can be determined by performing a one way ANOVA with the CV (as the DV) and IV
If significant: not independent
Non-significant: independent
How do you set the data up in jamovi?
1 x row per participant
1 x column per vairable
What design and analysis would we use to turn the CV into an IV?
Two factor ANOVA model
- Will have main effects and interaction effect
- Can do tests of simple main effects
How do you do an ANCOVA in jamovi?
Linear models - general linear models
IV - fixed factors
DV - DV box
Covariate - covariates box
Ask for a simple contrast under factors coding
How do you do an ANCOHET analysis in jamovi?
Do it in the same way as an ANCOVA
BUT
Then go into the model component of the analysis
- Highlight the IV and CV
- Then click on the bottom arrow and ask for a 2 way interaction
What does ANCOHET produce?
Main effect for group Main effect of covariate Interaction effect - if sig = report ANCOHET - if non-sig = can revert to ANCOVA
How do you use ANCOVA to conduct a step-down analysis following MANOVA?
The DV that is deemed the most important (based on theory) is tested first in a univariate ANOVA
- The remaining DVs are then successively tested in univariate ANCOVAs, using the first DV as a covariate
If the subsequent ANCOVA’s are significant, it can be interpreted as:
- This DV is adding important information
Non-significant:
- The DV does not add anything that has not already been accounted for by the initial DV
What is the ANCOVA step down analysis called?
The Roy-Bargmann analysis
