This may be too simple a question for this forum - it is possibly a very basic statistics question as commonly found in biomedical research. But since scientists often lack good understanding of statistics, I would appreciate a lot if I could hear the thoughts from expert statisticians on this forum and be educated a little bit.
I want to test if the treatment X affects the parameter P in a sample group of subjects. The design is paired: each subject is tested with no treatment (negative control) and with treatment X (order is randomized). To analyze such data, a paired t-test is obvious. However, I also have a positive control group - which is a separate independent group of subjects with sort of intrinsically different level of P, the one we would expect if treatment X works. So now I have three groups of measurements - two are paired, and one is un-paired. For three groups, I would need to use 1-way ANOVA. However, this will treat three groups as independent. How can I test if there is a difference in means between these three groups. Which test to use? Is it always appropriate to treat paired samples as un-paired? I understand that this leads to lower power, however - is this the only problem with this approach and is it still correct?