Difference in Difference of Group Means-Treatment and Control

[willfla29]

I believe this is a simple question, but extensive searching has not revealed the answer. I am trying to determine the extent of convergence between two groups caused by exposure to treatment. I have values for my dependent variable for Group A and B in the control group and the treatment group, but they are NOT the same people (e.g. between subjects design). How do I compare statistically the difference between the mean values of Group A and B in the control group with the difference of mean values of Group A and B in the treatment group?

This is not a simple difference-of-means, but may be some other variety of that test that I am not familiar with.

Thanks in advance!

[Clyde Schechter]

I find your question confusing. The two groups A, and B: are these, respectively, the treatment and control groups? Or are A and B defined by some other factor, and treatment/control status varies within each? Also, you refer to "convergence between two groups caused by exposure to treatment). Do you have information going back before the intervention, some baseline data? If so, are the people who are in group A before the intervention the same as the people in group A after the intervention, and likewise for group B?

The "usual" design in this situation is that there is a treatment group and a control group, whose outcomes are assessed before intervention. Then one group gets the intervention and the other does not, and the groups are re-assessed. If the variable group designates treatment vs. control, and the variable pre_post distinguishes pre-intervention vs post-intervention assessments, the difference in differences can be estimated by regressing the outcome on i.group##i.pre_post. The coefficient of the interaction term is the estimator. The particular type of regression to use depends on the nature of the outcome variable. And if the same people are involved both pre- and post-, you need to use a method that takes into account the repeated measures (e.g. an xt- command, or an me-command).

[willfla29]

Sorry, let me clarify. Group A and B are defined by another factor (it's party affiliation: Democrats and Republicans). I am attempting to see if exposure to a prime decreases the difference between the groups on dependent variable X, but I only have partisans assigned to the control group and treatment group: only one observation of X per person. The data looks like this:


Party/Treatment Assignment/Value
D/Control/5
D/Treatment/2
R/Control/3
R/Treatment/1

So I want to know if the difference between Dems and Reps in the control (5-3=2) is statistically different than the difference between Dems and Reps in the treatment (2-1=1).

[Clyde Schechter]

Since you only have one observation per person, there is no need to worry about repeated measures, So an ordinary regression will do the trick. Assuming "Value" is an ordinary continuous variable and you expect the assumptions of ordinary least squares linear regression to apply you just need

regress value i.Party##i.Treatment

The Party#Treatment interaction coefficient estimates the difference in differences, and its statistical significance can be assessed by the associated p-value.

Please note that you need the double ## in the regression command, but the coefficient will be labeled with a single # sign.

If Value is a count variable, you might want to look into Poisson or negative binomial models instead of linear regression. The use of the interaction term will be the same in any case.

[willfla29]

Thanks...I figured it was straightforward but hadn't dealt with this before.