Week 4 ANCOVA Flashcards
to address the learning aims of week 4 lecture including: Assumptions of ANCOVA Why do we check for Homogeneity of Regression? Interpretation: Main effects & Covariates
When do we use ANCOVA?
- ANCOVA may be used as an extension to any type of ANOVA design, including MANOVA
- It is used when you want to statistically control for a covariate(s).
What is a Covariate?
- A covariate (CV) is a variable that must be related to the DV, which research suggests may impact on the findings.
- when we say control we are saying we are removing the effect of that variable (the CV) on the DV.
What does it mean to Statistically control for Covariates?
*when we say control we are saying we are removing the effect of that variable (the CV) on the DV.
Which is more Powerful ANOVA or ANCOVA?, and why?
*ANCOVA is more powerful than ANOVA because it removes the amount of error variance apportioned by the CV on the DV – think about this and remember the f-test statistic of ANOVA.
When & Why do we use ANCOVA?
ANCOVA can be used as part of:
- One way between groups ANOVA – One-way ANCOVA
- Two way between groups ANOVA – Two-way ANCOVA
- Multivariate ANOVA – MANCOVA
What does ANCOVA actually test for?
To test for differences between group means when we know that an extraneous variable affects the outcome variable. Used to control known extraneous variables.
*We use ANCOVA to test differences between group means when we know that another variable (CV) may impact on outcome variable (DV).
In what way are the principles of ANCOVA are quite similar to ANOVA
- ANOVA’s equation of the value of variance apportioned to the numerator (between subjects) divided by the value apportioned to the denominator (within subject effect).
- Removing error variance from the denominator will increase the overall value. Resulting equation’s value will be larger.
How is ANCOVA different from ANOVA?
*You can control for a known extraneous variable or in repeated measures, where you want to control for the baseline measure in a 2nd administration of a variable. *ANCOVA assesses change in the outcome with the removal of the impact of the baseline to see true differences.
What are the advantages of ANCOVA?
- ANCOVA reduces Error Variance
- By explaining some of the unexplained variance (SSR) the error variance in the model can reduce the within/ error variance (noise).
How does ANCOVA provide Greater Experimental Control?
By controlling known extraneous variables, we gain greater insight into the effect of the predictor variable(s).
Increases power to detect significant differences
How do you decide which Covariates to control for?
- decisions are derived from the theoretical and empirical literature
- I need to know my research area well, have a strong theoretical basis to argue for covariate use.
What properties should Covariates have?
- Covariates should be continuous variables that are measured reliably and need to be correlated significantly with the DV.
- Logically - this makes sense. Having a covariate that is not significantly correlated would do little in allowing adjustment of the DV to occur.
What points should I consider when using more than one Covariate?
- Each covariate should only share a moderate amount of variance
- Each should contribute uniquely to the variance
- They must be measured before the treatment or experimental manipulation, so the covariates are not influenced by the treatment . That is, you don’t unintentionally control for some of the treatment effect in the analysis.
What are the assumptions of ANCOVA?
- ANCOVA assumes covariates are measured reliably & are valid.
- Covariates should be suitable for the intended population
- Covariates should correlate well with the DV but not with each other.
- since overlapping covariates would contribute little to a reduction in error variance
- Should be a linear relationship between the DV and covariates as well as between covariates
What needs to happen with the Homogeneity of regression slopes?
- The relationship between covariate & DV for each group must be the same across groups.
- Unequal slopes indicate an interaction between covariate and treatment.
- adjustments are made on the DV according to the overall correlation with the CV. Different slopes across the groups would make the adjustments uninterpretable.
When is ANCOVA often used?
ANCOVA is often used to evaluate the impact of an intervention while controlling for pre-test scores
The example in the lecture introduced ANCOVA as a means of evaluating the impact of an intervention while controlling for pre-test scores. Can you remember the design?
Variables:
IV – Categorical - (2 groups Maths Building, Confidence Building)
*DV – 1 Continuous - Fear of Statistics after intervention
*Covariate (CV) - Baseline measure of Fear of Statistics prior to participating in the intervention groups
The IV was the intervention, what was that?
IV – Student Gp (1) receives maths skills intervention Student Gp (2) receives confidence building intervention
The DV was the fear of stats after the intervention (time 2), why was the covariate CV – Scores on Fear of Statistics – Test Time1?
By controlling the Scores on Fear of Statistics – Test Time1, i.e. reducing this to er for all participants, the effect on each intervention is clearly identifiable, without the confusion of the original fear of stats (the CV)
What would I do if my covariate and DV had a very weak correlation?
Reconsider, if it is not going to reduce error variance? What’s the point of using it?
How do I check for interactions between covariate and treatment?
Inspect scatterplot – are the 2 lines similar in their slope? Alternatively, we can also test this statistically if we write the syntax OR build terms in GLM
What does Hills suggest when requesting scatterplots?
- I can request a scatterplot for each group, and compare them
- I can look at the 2 groups simultaneously to see if there is a difference in slopes.
How do I test Homogeneity of Regression slopes?
either by graph or by building a custom model.
e.g. UNIANOVA fost2 BY group WITH fost1
/METHOD=SSTYPE(3) /INTERCEPT=INCLUDE
/CRITERIA=ALPHA(0.05) /DESIGN=group fost1 fost1*group
What would I do if the Assumption – Homogeneity of regression slopes is violated?
Consider again – not going to reduce error variance? So little point of using it.