Of course you can. And most all statistical methods for comparing groups can be used, such as ANOVA. But the important thing to keep in mind is your domain for generalization. Among other things, perhaps the most important question is the nature and the equivalence of the populations represented by the subjects and the context you are sampling ... in other words, the assumptions you are making.

For example, you might be doing a cohort analysis. Two years ago, you taught 5th graders in your school math using standard teaching method A. Last year you used method B. This year you use method C. You assume these 3 samples of children are typical samples from the same population (and you compare all three samples on demographic and other possible intervening variables to check this). You assume the context has not changed significantly (the economy has not crashed during this time; the neighborhoods have not changed much; the school itself, the administration, the criteria you are using for comparison have not changed, etc.). Your hypothesis is "Do these three groups differ (on the outcome variable(s))?" If so, you might do post hoc tests to identify which method seems "best". But even still, your findings are only generalizable to the extent that your assumptions are valid, both now and in the future, for students like these, in this school or similar contexts, for this outcome measure, and for these three teaching methods.

Thanks a lot Dear Warren.

Sampieri et al, (2014) en su sexta edición, sugieren trabajar con:

Grupo "A"

Grupo "B"

Grupo "C"

tomando como grupo de control al que tiene mayor número de elementos. y trabajar el grupo A con respecto a B.

Es decir: grupo experimental X1

grupo experimental X2

grupo de control Gc

I thank you all of you for your valuable answers.