research methods advanced-week 8 =ANCOVA

ancova

what is an ancova

includes one or more continous variables (covariates) within the ANOVA, allows to test for differences in group means and interactions just like ANOVA while controlling for (partialling out) effects of covariates

how do covariates influence ANOVA results

with covariates included error variance is reduced as variance due to the covariate is removed (f-ratio)

f=

variance between conditions/ variance with conditions

methods of controlling for covariation

random allocation of participants to conditions to minimize the influence of covariates,

match participants in different conditions to minimise the influence of covariates

statistically : analysis of covariance ANCOVA

reasons to include covariates in ANOVA

serves at least two purposes, reducing within group ‘error' varience (the bottom hald of the ratio/unexplained variance) controlling for the influence of the covariates on the DV (elimiating confounding effects from the covariates)

what can be a covariate

any theoretically reasoned and continous variable can be used as a covariate

assumption 1- relationship between covariate and DV at each level of IV

the relation between the covariate and the DV must be linear at each level of the IV (relationship can be positive or negative) check this by drawing scatterplots to show the relationship between the covariate and DV

assumption 2 -homogentiy of regression slopes

there should be no interaction between the IV and the covariate on the DV. regression slopes are the same direction and similar size

aggression 3- independence of the covariate and the experimental treatments

the covariate doesn’t differ systematically across the levels of the IV . check this assumption: run an ANOVA using the covariate as the dv. we want it not to be significant

spss example

check for homogeneity of regression slopes (iv and covariate interaction)

no significant interaction between IV and VOC indicated that the regression slopes do not differ at different levels of the IV

post-hoc comparisons

if you do not have priori predictions about the differences between the groups, we use post hoc comparisons

reporting an ANCOVA

details of the model, model effects and post hoc comparisons

ancova summary

ANCOVA allows you to examine differences across conditions while controlling for the effects of a covariate. check assumptions about the covariate and its relationswhips with the rest of the data to make sure ancovas can be used. adding a covariate in SPSS largely follows the same pattern as running an ANCOVA. the main difference is in checking the additional assumptions, and including the covariate in the appropriate box when specifying the variables