5. ANCOVA

Question 1

ANCOVA

Answer 1

An ANCOVA is run to control for any known extraneous variables. These are continuous variables that effect the dependent (outcome) variable but are not part of the experimental manipulation.

Question 2

Advantages of ANCOVA

Answer 2

Reduce Error Variance:​ It reduces error variance by explaining some of the unexplained variance (SSR) in a model.

Greater Experimental Control:​ It also gives greater experimental control as controlling for extraneous variables gives a greater insight into the effect of predictor (independent) variables. It can enhance or dilute them.

Question 3

Assumptions

Answer 3

Relationship between DV and covariant

Covariant should be independent of the treatment effect

Homogeneity of regression slopes

Question 4

Relationship between DV and covariant

Answer 4

The outcome (dependent) variable and covariant should have a linear relationship (e.g. same direction or different direction). Can check this with a scatterplot.

Question 5

Covariant should be independent of the treatment effect

Answer 5

we do not want these things to share variance otherwise they could be part of the same bigger variable. You can do this by running a ANOVA with conditions as dv and covariant as the iv. We are looking for a non-significant result indicating that the variables are independent of one another.

Question 6

Homogeneity of Regression Slopes

Answer 6

there should not be a difference between the relationship between the covariant and the dependent variable between conditions. We can check this by plotting each condition as a regression slope on scatterplot (via the model dialog within univariant model). If there is a difference, assumption is violated and this needs to be reported in paper. You can test formally by running a custom model which tests for an interaction between iv and the covariant. If the interaction is significant, then the assumption is violated.

Question 7

ANCOVA as Regression

Answer 7

ANOVA can be run as a regression by dummy coding the variables (you do this by assigning value of 1 to target condition and 0 to all other conditions for total number of conditions). You then add the dummy variables as predictors (the control will be the constant). Similarly, you can run an ANCOVA this way, you simply run a hierarchical regression, adding the covariant in the first step and the predictors in the second step. By doing this we get the effect of the treatment over the effect of the covariant.