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11.03.2014

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There are all sorts of problems with p-values and confidence intervals and I have no intention (or the time) to cover all those problems right now. As noted before, the change arises primarily from narrowing of the CI intervals owing to AR1 modeling, with changes in the trend estimate being surprisingly slight.
With this they then go on to show that there is large autocorrelation in the measured data and that with a linear trend regression there are very large confidence intervals. Here are simulated data from two independent normally distributed populations testing the confidence intervals and the p-values.


Confidence intervals for trend estimates with autocorrelated observations (unpublished manuscript). Here is one example of a common problem with p-values and how it relates to confidence intervals. But they do not go onto to state the obvious that the models at the moment, being only capable of producing linear trends are inadequate at matching observation with any substantial confidence (80% or more would be good).
This means that you are not describing a linear trend but considering the difference of two points over a fixed time interval after the process has completed.





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