Analysis of Co-Variance Flashcards
What is ANCOVA?
ANOVA but with a control variable (covariate).
What are covariates?
These are variables that are related to the DV but can’t be manipulated.
When would you use ANCOVA?
To control for continuous factors that could influence the outcome variable - more suitable for experimental research. CV should be independent of treatment..
What is the most important condition for an ANCOVA?
That the IV and covariate be independent of each other. Can’t be comorbid.
What are some interpretational issues with ANCOVA?
ANCOVA removes the variance due to the CV but it doesn’t control for CV.
Adding a CV should only be done if IV is independent from the CV. Most appropriate experiment should be with randomised allocation.
What happens if the covariate is significantly related to the DV?
ANCOVA adjusts the group means by the covariate-DV relationship.
Any comparisons are now carried out on these adjusted means.
What are the two main advantages of using an ANCOVA?
It increases test sensitivity.
It eliminates confounds - attempts to maximise and explore an IVs true effect. It is often used to improve weak research designs but this can lead to weaker IV effect sizes and it should only be seen as descriptive model building.
What are the extra assumptions that must be taken into account for ANCOVAs?
Homogeneity of regression slopes.
Reliability of covariates.
Define homogeneity of regression slopes.
The relationship between each CV and DV should be the same for each level of the IV.
What can you do if homogeneity of regression slopes is not met?
You can use multilevel modelling or hierarchical regression with an interaction term.
Explain the reliability of covariates assumption.
No error is assessed or removed from the CV - it is assumed that the Cvs are measured without any error.
we want to ensure that our CVs have high internal consistencies if they come from multi-item scales.
What is the statistic and cut-off point for a reliable covariate?
Cronbach’s Alpha.
Has to be larger than 0.7.
What can you do if the reliability of covariates assumption is violated?
Can use bootstrap to obtain robust model parameters and post-hoc tests (has to be done in R).
Can use change scores, randomised-block design or simple blocking.
How can you establish that ANCOVA is appropriate?
Check correlations between COVARIATE and IV before conducting the ANCOVA.
Conduct a T-test or ANOVA (depends on the number of levels).
Correlations should be non-significant.
What effect size is used for an ANCOVA?
Partial eta-squared.
What are the small, medium, large cut-off points for partial eta-squared?
- 01 - small.
- 06 - medium.
- 14 - large.
What do we have to report when conducting an ANCOVA?
- The correlations - F, df, p, np-squared.
Run ANCOVA… - Descriptive statistics.
- Homogeneity of variance.
- Variance explained.
- Main effects - F, df, p, np-squared (for IV).
- Follow-up tests. Use estimated means as these are adjusted for the effect of the covariate.
- Assess the covariate - F, df, p, np-squared. Should be significant (this means it is a useful covariate).
- Check homogeneity of regression slopes - this has to be done last otherwise the results will change - should be non-significant.
When assessing the covariate should this be significant or non-significant?
Significant - means it was a useful covariate.
How do we interpret the graphs for the homogeneity of regression slopes?
The lines should be fairly parallel for the assumption to be met.
Should the interaction be significant or non-significant for homogeneity of regression slopes to be met?
Non-significant.
Still report analysis but have to interpret with caution.
How can ANCOVA be run in regression?
By using dummy coding of categorical predictors.
