9 GLM: Testing hypotheses using contrasts

Question 1

When do you use dummy coding in regression?

Answer 1

When you want to use a categorical variable as a predictor.

Question 2

How can dummy coded variables be interpreted in a regression model?

Answer 2

Unstandardised beta is always an estimate of change in DV for 1-unit change in IV. Dummy coding allows us to make that one unit difference the difference between groups.

Question 3

What would happen if you put in all levels of a categorical IV as separate dummy coded variables?

Answer 3

You’d have a problem with multicollinearity (IVs being related).

Question 4

In a regression equation with dummy coded variables, what is the intercept?

Answer 4

The mean of the reference group (the group coded 0).

Question 5

What is the advantage of using standard-form contrast coefficients?

Answer 5

The contrast estimate is interpretable, as the mean difference between the two lots being compared.

Question 6

Why are Cohen’s contrasts useful?

Answer 6

They make beta coefficients directly interpretable as mean differences between lots.

Question 7

In Cohen’s contrasts, at least one of the lots must be ________ so the coefficients still sum to __, and the difference between the groups must be __.

Answer 7

In Cohen’s contrasts, at least one of the lots must be negative so the coefficients still sum to zero, and the difference between the groups must be 1.

Question 8

How do Cohen’s contrasts make unstandardised betas interpretable?

Answer 8

Unstandardised betas give the change in the DV for a 1-unit change in the IV. If the difference between the lots is 1, the beta will be a mean difference. (But the contrasts have to be put into new variables first, before entering them into the regression.)

Question 9

What’s the point of doing contrasts in regression, rather than in ANOVA?

Answer 9

In regression, you can run contrasts (Cohen’s) that control for other variables.