# One or Two way Repetaed Measure ANOVA

I have a doubt due to the fact that I found different analysis in the literature for basically the same design. If we have 2 conditions (Treatment Vs. Placebo) and we evaluate at different time points the dependent variable (plasma concentrations lets say), would it be more appropriate to use a 1 way repeated or a 2 Way repeated measure. Is time a factor even if I'm not interested in considering it as a factor ?! Its a within-subject design, therefore, each Subj. undergo treatment and then Place or the other way around at different days. Thank you very much.

• I think this is just a terminology issue, with different people describing the same thing differently. You have one between subjects factor and one within subjects factor no matter what you call the design. Commented Feb 22, 2018 at 11:42

As you have repeated measures for each subject, you can assume correlation for each subject measurements, then the most appropriate method would be one-way random effect model. The model is posed:

$$y_{ijk}=\mu+a_i+b_{ij}+\epsilon_{ijk}$$

Each measurement $y_{ijk}$ (the $k^{th}$ measurement of the $j^{th}$ subject in the $i^{th}$ group) is composed of the general mean $\mu$, the fixed effect of the group $a_i$, the random effect of the subject $b_{ij}$ and the measurement error $\epsilon_{ijk}$.

You can read more here and here, I also suggest using R package lme4.

• Agreed, in terms of the model. My point is that some would still call this a two-way ANOVA as you have a fixed between-subjects effect and a random within-subjects effect. You would (or could) get an F value for each. Hence, the two-way label. Commented Feb 22, 2018 at 13:30
• The question is exactly the between-subjects effect. If it's a fixed effect then I agree with you, but as the subjects get measured repeatedly and they differ from one group to the other, it's more likely to be a random effect. Commented Feb 22, 2018 at 13:36
• In your model, the treatment effect is fixed. This is the fixed between-subjects effect. I agree that the effect for subjects is random and needs to be. In classic ANOVA terminology, a factor can be both fixed or random. Just because it is random (the subject factor) doesn't mean that it is not a factor in the ANOVA sense of the term. Hence, the two-way rather than one-way distinction. I agree with you in terms of how the model should be estimated. Commented Feb 22, 2018 at 13:43
• I'm only trying to provide context for why the literature seems to describe this as both a one-way and two-way model and I think the discussion between us has illustrated that. Commented Feb 22, 2018 at 13:43