Suppose that a researcher wants to do a study to assess how scores on the dependent variable heart rate (HR) differ across groups that have been exposed to various types of stress. Stress group membership is originally coded as follows: 

Group 1, no stress/ baseline

Group 2, mental arithmetic

Group 3, pain induction

Group 4, stressful social role play

The basic research questions are whether these four types of stress elicited significantly different heart rates overall, and which specific pairs of groups differed significantly.

a. Set up dummy coded dummy variables that could be used to predict HR in a regression. Note that it might make more sense to use the “No stress” group as the one that all other group means are compared to, rather than the group that happens to be listed last (stressful role play). Write out in words: what contrast between group means is represented by each dummy variable that you have created?

b. Set up effect coded dummy variables that could be used to predict HR in a regression.

In words: how will the numerical results for these effects coded dummy variables (in 1b) differ from the numerical results obtained using dummy coded dummy variables (in 1a)? And what parts of the numerical results will be the same for these two analyses?

c. Set up the coding for orthogonally coded dummy variables that would represent these orthogonal contrasts (assuming that group 1 = mental arithmetic, group 2 = pain, group 3 = stressful role play, and group 4 = baseline)