# Can paired samples be treated as un-paired for 1-way ANOVA

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?

• Is the third group tested once or twice? If they are only tested once, how do you get anything for the effect of X? If they are tested twice, then they too can be paired. – Peter Flom Jan 30 '13 at 18:22
• @PeterFlom The third group is only tested once. In this hypothetical scenario, it is not important how the treatment X affects the third group. Even without treatment, the third group has a different level of the parameter P. The research questions are: 1) Is there an effect of treatment X? - Answered by comparing means of the first (non-treated) group and second (treated) groups, by paired t-test. ... – Viktor Jan 30 '13 at 21:55
• 2) We are also interested in the magnitude of the effect. The treatment is considered effective only if the new level of parameter P is the same as in the third (positive control) group of subjects (non-treated). - This would be answered by comparing means of the second group (treated) with the third (unrelated, non-treated), by un-paired t-test, since these groups are unpaired. The problem now is that we will do two comparisons with the second group - i.e. multiple testing with its inherent inflation of the type I error. That is why I saw a need for ANOVA-based approach. – Viktor Jan 30 '13 at 21:56
• As far as I can tell, the third group doesn't help you answer those questions. – Peter Flom Jan 31 '13 at 0:04
• Can this not be broken into two questions, as you've described, and tested independently? 1) is there an effect of treatment with X on P (paired t-test comparing pre and post treatment subjects)? 2) is the effect of treatment adequate (unpaired t-test comparing post-treatment with the control group)? Not ideal, but given the data you have, won't this provide an evaluation of the result? – KirkD_CO Jan 21 '18 at 19:05