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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.

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  • $\begingroup$ 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. $\endgroup$
    – dbwilson
    Commented Feb 22, 2018 at 11:42

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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.

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    $\begingroup$ 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. $\endgroup$
    – dbwilson
    Commented Feb 22, 2018 at 13:30
  • $\begingroup$ 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. $\endgroup$
    – Spätzle
    Commented Feb 22, 2018 at 13:36
  • $\begingroup$ 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. $\endgroup$
    – dbwilson
    Commented Feb 22, 2018 at 13:43
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    $\begingroup$ 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. $\endgroup$
    – dbwilson
    Commented Feb 22, 2018 at 13:43

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