Week 9-ANCOVA Flashcards
What does ANCOVA stand for?
■ ANalysis of COVAriance
■ So it is from the ANOVA family but has a some fairly unique facets
What are Covariates?
■ Covariates are simply variables that are associated with your DV but are not part of your experimental manipulation
■ E.g. effect of alcohol (randomly allocated to the placebo/low dose/high dose group) on
working memory
What do you not do in ANCOVA?
–Throw in as many covariates as possible to see if that changes your result (seen as P Hacking)
–Put in categorical variables
■ Racial group
■ Last level of education
- However people do this all the time: ANCOVA is probably the most abused form of statistical test!
What should we use ANCOVA for?
■ We should use them to eliminate confounds
■ In any experiment there will be things influencing your DV. Often
these are a nuisance and not what you are investigating
■ A thorough literature review should identify the important
■ Eliminating confounds means you are more likely to see an effect
of your IV on the DV
■ You increase the power of your analysis
■ So fewer participants will be needed to detect a significant effect
■ Reduce error variance, so the ratio of variance accounted for by
the IV compared to error variance increases
covariates (if any)
What are the assumptions of ANCOVA?
■ homogeneity of variance (if between subs)
■ Sphericity (if within subs) ratio/interval data although ordinal data is also used
■ Homogeneity of covariance matrices if mixed
■ Independence of the covariate and the IV effect
■ Homogeneity of regression slopes
What’s the difference between ANOVA and ANCOVA?
-ANOVA=error variance + variance accounted for by the IV
-ANCOVA=error variance + variance accounted for by the IV AND COVARIATE VARIANCE
ANCOVA Assumptions: What is meant by’Independence of the covariate and the IV effect’?
■ The covariate should be not be different across the IV groups
■ So if you did a ANOVA on the covariate (DV) and group (IV) there would be no significant effect
■ Over utilised- Common in non-
random assignment=Flawed conclusions
■ Under utilised=Increased power
■ Think of this in a similar way to multicollinearity in multiple regression analyses – we want to avoid variables which predict the DV (the IV and covariate) to share variance with each other.
How can we check for the Independence of the covariate and the IV effect?
■ We can run a one way ANOVA to ensure the covariate is independent of the IV
– For this check, the covariate would be treated as the dependent variable rather than a covariate.
■ If the ANOVA is nonsignificant, this suggests that the covariate is independent of the IV
– Variance of the covariate is not explained by the independent variable (i.e., scores on the covariate do not significantly vary between conditions in the IV).
■ If the ANOVA is significant, this may suggest that the covariate is not independent of the IV
– Variance of the covariate is explained by the independent variable (i.e., scores on the covariate do significantly vary between conditions in the IV).
ANCOVA Assumptions: What is meant by ‘Homogeneity of regression slopes’?
■ The relationship between the covariate and the DV is consistent across groups
■ If age was negatively associated with working memory in the placebo it would have to be negatively associated with working memory in the low and high dose conditions
