Week 11: ANCOVA

Question 1

ANCOVA is a…

Answer 1

statistical control procedure

Question 2

Secondary variables are controlled methodologically by..

Answer 2

Elimination, constancy or making them into an IV

Question 3

What do we do if we cannot control for secondary variables methodologically?

Answer 3

We can statistically control it by removing the variance associated with it using ANCOVA

Question 4

What are we essentially doing in ANCOVA?

Answer 4

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)

Question 5

What is the major benefit of ANCOVA?

Answer 5

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

Question 6

What does ANCOVA produce?

Answer 6

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

Question 7

Why is the main effect of covariate important?

Answer 7

If it is not significant, we do not need to control for it as it is not related to the DV

Question 8

What is a super important assumption of ANCOVA?

Answer 8

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

Question 9

What happens if we have different slopes for each group?

Answer 9

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)

Question 10

ANCOVA does not include..

Answer 10

An interaction term - assumes the slopes are the same for all groups

Question 11

What does include an interaction term?

Answer 11

ANCOHET

Question 12

What is ANCOHET?

Answer 12

Analysis of Covariance of Heterogenous slopes

- Explicitly tests whether the slopes are homogenous or not

Question 13

What if we have a non-significant interaction in ANCOHET?

Answer 13

Then we have homogeneity of slopes

Can revert to ANCOVA (some say to, some say not to) as the assumption has been met

Question 14

What if we have a significant interaction in ANCOHET?

Answer 14

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

Question 15

What are the assumptions of ANCOVA and ANCOHET?

Answer 15

• 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

Question 16

Are there any differences between the two techniques and the assumption of homogeneity of regression?

Answer 16

Yes.

ANCOVA assumes and ANCOHET explicitly tests

Question 17

What would be our ideal? and how can we test it?

Answer 17

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

Question 18

How do you set the data up in jamovi?

Answer 18

1 x row per participant

1 x column per vairable

Question 19

What design and analysis would we use to turn the CV into an IV?

Answer 19

Two factor ANOVA model

• Will have main effects and interaction effect
• Can do tests of simple main effects

Question 20

How do you do an ANCOVA in jamovi?

Answer 20

Linear models - general linear models
IV - fixed factors
DV - DV box
Covariate - covariates box

Ask for a simple contrast under factors coding

Question 21

How do you do an ANCOHET analysis in jamovi?

Answer 21

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

Question 22

What does ANCOHET produce?

Answer 22

Main effect for group 
Main effect of covariate 
Interaction effect 
- if sig = report ANCOHET 
- if non-sig = can revert to ANCOVA

Question 23

How do you use ANCOVA to conduct a step-down analysis following MANOVA?

Answer 23

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

Question 24

What is the ANCOVA step down analysis called?

Answer 24

The Roy-Bargmann analysis