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I'm looking to test for a difference between populations A and B. Each population is made of three time series which can be modeled well with a Gaussian or Gaussian mixture, and each have 55 data points. An example A and B are below, and in total I have a few thousand comparisons like this.

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What's biologically relevant is the "intensity" of each curve. This can mean either the peak value, area under the curve, or something similar. My problem is that I have a small sample size (3 in each group). If sample size was larger I'd be happier to reduce each curve to a single number (e.g. maximum, area-under-the-curve, etc.) and then perform something equivalent to a t-test. However this throws out a lot of the limited information I have. It's also inappropriate to just take more data points from each curve, since points from a single curve are clearly not independent.

Is there a way to test for the difference in "intensity" between A and B (peak value, area under the curve, etc.) that preserves as much information as possible? Could I do something like take multiple points from each time series and perform a repeated-measures ANOVA, i.e. keep more data points and try to account for the non-independence?

R Greg Stacey
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  • In case anyone's interested, my solution is to follow Rob Hyndman's answer [here](http://stats.stackexchange.com/questions/3616/what-is-the-best-statistical-test-for-a-time-series?rq=1) where he suggests parametric bootstrapping. I'm going to assume a mixed Gaussian model for both groups A and B, bootstrap a distribution for the Gaussian parameters, and then test how likely it is that parameters in A and B are equal. In my case I think it's appropriate to test whether the height of the Gaussians are equal. Of course, If anyone can comment on how valid this sounds, that would be wonderful... – R Greg Stacey Feb 26 '16 at 23:42

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