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Lemme run a thought process by you. It's supposed to be a pedagogical illustration of what we miss when averaging over individuals (or systems), instead of analysing individual time series. Related to this mini-MOOC, ergodicity, etc. Possibly stupid. > mattiheino.com/2018/10/25/nam…
> There are good theoretical reasons from cybernetics/synergetics/complexity theory to assume that systems behave in a certain way prior to shifting states. First slide is @FredHasselman's (google.com/url?sa=t&rct=j…) for background. Assume this is what goes on. >
> So, there's a baseline stability, followed by instability, which stabilises on a better level of functioning. Of course, the whole real process is invisible to us as observers. Let us cover the important bit with an additional veil of BLACK BOX. >
> Now, taking the time-honoured pre-post design, what we see is something like this, which is all well and good if we only care about increase/decrease. But often we'd like to learn about the process, to come up with better ways of dealing with it (ncbi.nlm.nih.gov/pmc/articles/P…) >
> Let's add a measurement point. Turns out we see something very familiar to people dealing with behaviour change interventions: An initial effect tapering off somewhat during long-term follow-up. >
> Maybe that wasn't fair. Let's assume we have a bunch of individuals, all of whom have the same pre- and post-levels. They differ in the wild fluctuations, which we average like the other time points. Still being misled on the process. >
> Let's add measurement points, which happen to not coincide with the critical period. Still getting the wrong conclusion of a linear growht trajectory. >
> What if we add more time points, this time managing to include the critical period? Alas, our wrong view of the process is just fortified. >
> What if we looked at the individual trajectories before averaging? NOW we see that something funky's going on. >
> This was the result of trying to illustrate something ultra-simply to my very tired brain. It may be obvious, but it may or may not also be wrong – is it?

Any comments or improvement suggestions? (ping @EikoFried @aaronjfisher @FredHasselman @Chris_Noone_ @FelixNaughton)
(to be clear, I'm also open to "not even wrong")
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