Analysis of covariance

When… ANCOVA is an ‘extra’ on an ANOVA ANOVA outcome = number of words learned IV = Sex ANCOVA adds a covariate covariate = size of first language vocabulary

Control Variables that influence the outcome Manipulate Control hold steady randomise enter into the statistical model

Control Hold steady Everyone has same L1 vocab Mean of groups is same for L1 vocab Randomise sometimes you can’t (e.g. Sex) ANCOVA – record L1 vocab and allow statistically

ANCOVA in SPSS Use GLM / Univariate Enter outcome as dependent variable Enter Sex as ‘Fixed’ IV Enter L1 vocab as ‘covariate’

ANCOVA assumptions Linearity relation between covariate and outcome is (roughly) linear ‘Homogeneity of regression ’ relation between covariate and outcome is the same for both Men and Women [relation is the same at each level of the IV]

Checking Homogeneity of regression in SPSS A second ‘run’ through Analyse/GLM/univariate Click the ‘model’ button’ Select IV (Sex) and Covariate and ‘click across’; Now select both together and ‘click across’; Continue as before…. Interaction effect – must not be significant

MANOVA Multiple dependent variables ‘converted’ into one composite DV Assumptions – see Pallant SPSS Survival Guide (similar to Multiple Regression: Linearity, Mahalanobis distances) Plus homescedasticity (use Box’s M with a conservative p-value) Further reading: Tabachnik & Fidell