How to compare differences between groups, when measured values have decreasing trend

Question

I'm currently performing challenging analysis and I'm not sure how to continue.

I have three separate groups which had different procedures. In each of them there are four measurements (subjects were measured for cortisol level 4 times during the day). In simple case, it would lead to two way ANOVA (please correct me, if I'm wrong), but there is a catch. Measured variable (Cortisol) has decreasing trend, so If I measure cortisol in the morning before intervention, it should be similar in all groups, but how to capture differences in cortisol levels later, when some intervention has been performed? Cortisol values are naturally lower in the morning than at noon and I need to test if there is difference in intervention.

Answer 1

Even if the variable was something else than cortisol and you did not know what trend to expect beforehand, a regular two-way ANOVA would not be appropriate because observations at different times are not independent from each other.

Instead, if you had measured your participants at two distinct time points, you should at least consider a repeated-measures ANOVA (see Best practice when analysing pre-post treatment-control designs and related questions) and look at the interaction between time and group/procedure. A simple trend is not necessarily an issue, that's the reason why you should focus on the interaction.

Now, since you have several measures (not only before/after) and they are ordered by time, you can do better than that. People sometimes start with a repeated measures ANOVA and then test for a linear trend with contrasts but that does not properly account for correlations between measures that are closer in time. Another recent question, Comparing two sets of time-series (physiological measures), focuses on much larger series but has a lot of relevant ideas you could adapt to your situation.