I have data from an experiment in which participants were randomly assigned to one of two groups and asked a series of opinion questions. One group, the control, was not presented with any additional context beyond a brief introduction and the questions themselves. The other group, the treatment group, was given a textual stimulus providing more information.
There is a single key question, let's call it
CHOICE, which serves as the main question that I am trying to answer.
CHOICE is always one of two answers,
B. I want to know if being in the treatment group had any statistically significant effect on the answer that respondents gave for
I have read through chapter 8 of Experimental and quasi-experimental designs for generalized causal inference (Shadish, Cook, and Campbell) for some guidance on how to analyze such a randomized assignment experiment. On page 251, they write:
Randomization equates groups on expectations of every variable before treatment, whether observed or not.... Randomization ensures that confounding variables are unlikely to be correlated with the treatment condition a unit receives.
As I understand this (and the rest of the chapter), when I run my logistic regressions on this data, I should not be controlling for other factors because I risk biasing my estimates. I.e. I should be using the formula
CHOICE ~ GROUP rather than
CHOICE ~ GROUP + AGE + INCOME + GENDER + ....
If this is correct, can someone explain why in more detail? If not, how should I be addressing this? Thanks!
P.S. In case it's relevant, I am using