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Subjects were randomized into treatment and control groups. Within the treatment group, subjects were randomized to receive the treatment under condition A or B (mutually exclusive groups). For all subjects, we have pre- and post-measures of the outcome.

We can easily test the effect of the treatment (both conditions pooled) or for a treatment effect under condition A or B (in separate models that use the same control group).

I'm looking for a formal test of difference for the coefficients from the two treatment effect models under the mutually exclusive conditions A and B. These coefficients come from separate models that have the same control group and randomized mutually exclusive treatment (condition) groups. How can I test whether the effect of treatment under condition A is different from the effect of the treatment under condition B?

Edit: Stata code based on accepted answer

* If control and treatment conditions are in a (0,1,2) categorical variable
anova y i.treatments
contrast ar2.treatments
test 1.treatments = 2.treatments

* Alternatively, if treatment conditions are (0,1) and (0,1) in regression
regress y treatment1 treatment2
test treatment1 = treatment2
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Testing whether the effect of condition A is different from the effect of condition B is the same as testing whether the mean of condition A is different from the mean of condition B. You can do this in a standard one-way ANCOVA (adjusting for pre-treatment scores), where you specify a contrast between A and B or just perform all pairwise comparisons.

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  • $\begingroup$ Thanks, the contrast got me on track. Reading about that, I also discovered how to do it with Stata's test command in regression. I added my sample code to the question. $\endgroup$
    – dcoy
    Nov 12, 2021 at 0:53
  • $\begingroup$ You can include the pretreatment scores as covariates in either the ANOVA (to make it an ANCOVA) or in the regression. This will increase power without affecting the bias of the estimates. $\endgroup$
    – Noah
    Nov 12, 2021 at 6:23

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