What test to compare three groups with data before and after an intervention? I am writing a proposal for a study. I have 3 groups:  


*

*Group A- receiving specialized intervention technique

*Group B- receiving regular intervention 

*Group C- control/receiving no intervention


I want to compare each group's mean on a standardized test pre and post intervention to see if the specialized intervention increased means on the standardized test. What test do I use? 
 A: You can use repeated measures ANOVA for this.  However, if that feels too advanced, another option would be to get difference scores for each group (i.e., subtract pre from post for each person).  Then you can use a simple one-way ANOVA on the three sets of difference scores.  
A: Repeated measures ANOVA will work. ANCOVA is another option. The ANOVA of difference scores and ANCOVA test the same null hypothesis in the context of a randomized experiment, but ANCOVA is usually more powerful. 
The trade-off has to do with the size of the error term in ANCOVA vs the extra parameter needed for the regression slope in ANCOVA which is assumed to be 1 in the ANOVA. The error term is smaller in ANCOVA and that increases the MS_error, which increases the F ratio. But, there is one less degree of freedom for the numerator, which makes p values slightly larger.
The bottom line is that, between the two, ANCOVA is usually more powerful. See Maxwell and Delaney, chapter 9 for more details.
Here is another reference: "Pretest-posttest designs and measurement of change" by Dimitrov and Rumrill (2003).
