Determine what range represents 95% of a skewed data set I have a set of reference wetlands and experimentally manipulated wetlands and I am comparing many water quality variables between them. My thought was to first identify which of the manipulated wetlands fall outside of the natural range for each variable by calculating the mean and standard deviation for the natural wetlands and then seeing which of the experimental wetlands fell more than 2 standard deviations outside of this range, in order to identify wetlands that have water chemistry that falls outside of 95% of natural wetlands.
However, many of my variables are positively skewed. Is there a better way than the 2x the standard deviation to identify upper and lower values that encapsulate 95% of the range?
Note: My question is somewhat similar to this one, but different enough that I think it stands alone (standard deviation to describe variation in positively skewed data)
 A: No matter how you cut it, it's not often useful to use a symmetric interval to define normal ranges in asymmetric data - assuming of course that those data are filtered free of non-normal observations. Here I mean "normal" in the sense of not abnormal. While we don't often condone discarding outliers, the point is that if you are defining a cut off to define abnormal cases you had best make sure the ranges of normal are in fact calculated from normal values. If you actually know which cases are normal and which are abnormal, then you can look at discrete predictive metrics, like a ROC to define an optimal threshold of abnormal.
That said, it's quite easy to calculate an asymmetric interval representing the range of normal from non-abnormal data, i.e. what one expects with a "central" 95%. Two approaches immediately come to mind: first is to simply calculate the 2.5th and the 97.5th quantile, i.e. which values at which 2.5% and 97.5% of the sample fall below that value. Alternately, you can simply log transform the value, if the resulting distribution has an approximately symmetric distribution, you can treat the distribution as log normal and define empirical normal rules based on the transformed sample.
