Week 9 - ANCOVA Flashcards
ANCOVA is a means to…
Specify the correct model for Y by not ignoring known sources of variance
By removing all known sources of variance we make the analysis more sensitive by reducing the error term
Remove systematic and extraneous error
Fisher and ANCOVA
Designed to reduce the error term in true experiments by removing variance from nuisance (nonfocal) variables that are measured before randomisation
Benefits of ANCOVA
Increase precision
Increase statistical control
ANCOVA is combination of
Regression and ANOVA formally
ANCOVA contains
Categorical Grouping variable and at least one continuous variable
When is ANCOVA problematic
When people apply it to pre-existing groups or quasi experimental designs without adjusting their thinking
- Covariate with be confounded with Y (Randomisation remove this)
- Would reduce power
- Would remove variance in Y
- Homogeneity likely to be violated
Best thing to do is to incorporate a better quasi-experimental design
Role of randomisation
Break the link of correlation (Systematic link) between initial competence and group assignment
Problems with Randomisation Without using ANCOVA
Distribute the differences between experimental (treatment) groups Inflates the error term with the variation from external causes (factors other than the focal X's) Lower power (lower chance to reject null when actually false - type 2 error)
How to increase low power
Increase sample size
increase power of manipulation/ sensitivity to the measure
Limit to what you can do
How to ANCOVA increase power
By lowering the error term with the inclusion of extracting sources of variance that are irrelevant to the focal X (Why some poeple intially high or low on the focal X factor)
Steps of ANCOVA (4)
1) Take measure of peoples current (y) before randomisation using a reliable and valid test
2) Expect certain amount of variance between participants
3) Randomly assign people to experimental group, then apply conditions
4) Re-measure the participant level on (Y) at the end of the experiment
Where does initial variance go?
Go into the error term if not included in the model
Covariate
The initally measure variance (X)
Pre-existing, non focal sources of variance
ANCOVA partial out initial competence by using it as a predictor
Can be any variable that expected to effect Y (Aptitude test, initial competence, nuisance variable)
Nuisance variable we want to partial out
Problem with Mixed subject design
Error will still contain all or part of initial competence (By not including initial measure)
Leftover after Initial Competence (Covariate)
The post test score that is not accounted for by the pre-test measure (individual difference)
Notes for using Covariate
Ideally no overlap with the Focal X
- if this happens can swallow up the effect of the focal X(Can also happen by being linked to the Y)
Essential design elements for ANCOVA (3)
1) True experiment (Manipulation and random assignment important)
2) Covariate should be measured before randomisation (Definitely before treatment)
3) X should not have an effect on the covariate (If 1 and 2 are true it wont)
What ANCOVA does not do
Adjust for within group variables (no between subject group to adjust for)
Key Assumptions of ANCOVA
Homogeneity of regression slopes
- Must be interaction between Covariate (Continuous) and X (Categorical)
- Imply that difference in covariate and Y across slopes of X
- If slopes not the same for levels of X, not appropriate to pool them (Slopes should be the same)
Does not include product term (interaction term)
What to do when homogeneity of regression slopes is violated
Run analysis with seperate regression slopes
Can use hierarchical or random effects ANOVA
