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I have an experiment where animals are exposed to a temperature change and then a continuous response variable is measured at set time points after the change. I have a baseline, 8 hours after change, 24 hours after change, 4 days after change, etc. There is clearly a decline in the response variable over time, but I would like to determine the earliest timepoint at which this decline is significantly different from the baseline.

Each animal only provided one measurement at one timepoint. Therefore since I'm not measuring in the same animal over time, I believe a repeated measures ANOVA would be inappropriate. In my Googling, I've come across the term "repeated cross section" which I think would be an accurate term for this study, but I can't figure out what kind of test would be appropriate to answer my question. Any help from the stats gurus of the world?

This question Validity of pseudo-panel data constructed from repeated cross sectional data as a panel data seemed promising, but I don't have panel data and I'm not sure the question is relevant here. Is a marginal model the best approach? I don't have any covariates. Animals were same species, age, similar sizes, etc.

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You do have a repeated measurement design, since you repeatedly measured each animal over time. A mixed model can solve this. Code each time point as a factor, the animals are random effects. Then simply test every change from one time point to another to check for significant differences.

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  • $\begingroup$ When you say "you repeatedly measured each animal over time", this does not seem accurate. Perhaps I was not clear in my question. A single individual was measured once. So for example, timepoint 1 = individuals A-C. Timepoint 2 = individuals D-F. Timepoint 3 = individuals G-I. Individual A was measured at timepoint 1 only. Not at timepoints 2, 3, or later. $\endgroup$
    – CephBirk
    Feb 15, 2019 at 15:02
  • $\begingroup$ @CephBirk My mistake, in that case you do not have repeats, so a regular ANOVA can be used, if the other assumptions are met. $\endgroup$ Feb 15, 2019 at 15:21

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