# How to determine normal variability and understand whether other values may be clinically relevant?

I have been examining asymmetry in a new measure of brain pathology in a large sample of 300 clinically normal individuals. Many of these variables are normally distributed, some have a bit of a skew due to 4 or 5 outliers.

We have been wondering how we can determine whether this variability is just normal or whether there is some level that may be indicative of true asymmetry. The easiest way would be mean ±2 standard deviations, but that may be a bit simplistic.

Are there other ways to figure this out? This is the first dataset measuring this pathology, so we cannot compare it to another sample.

See here for an example:

• Do you mean something like outlier detection?
– Dave
Apr 18 at 16:49
• If you want to measure non-normality you can use (e.g.) skewness and kurtosis or (more unusual, but better) L-moments. DIstributions don't divide into sheep (normal) and goats (not normal), and even those that look close to normal usually show some small departures from normality, which may or may not be important. The fraction within 2 SD from the mean is not a good measure of whether a distribution is close to normal; back in 1965 Pearson and Tukey showed that it is remarkably constant across a range of distributions. Apr 18 at 17:52
• Question implies both that you have one variable ("a new measure of brain pathology") and that you have several variables ("many variables"). Which is it? Are you referrring to variation between subsets? Why not show us the data? Apr 18 at 17:54
• "Clinically interesting" isn't a question statistics can address. (It is meaningless without a definition.) Are you perhaps asking how to test whether the center of a distribution is nonzero?
– whuber
Apr 18 at 19:10
• The graph is modern in style but says nothing much directly about approximation to a normal distribution. I'd suggest that side-by-side normal quantile plots (many other names: normal probability plots, probit plot) would be a good idea. I say side-by-side but superimposing them might not be too crazy. Posting the data, or say a smaller sample, would allow experiment (subject to any constraints on your sharing them). Apr 19 at 15:46