More measurement insights from Archie Cochrane in his book __Effectiveness and Efficacy__ (1972):

“Once the idea of a skewed distribution became partially accepted, there was considerable pressure, conscious and unconscious, to provide the physicians with a simple rule to tell them what it all meant and someone (I have been unable to discover who it was) introduced the concept of 'normal limits' and defined them as lying within plus or minus two standard deviations from the mean. Theoretically there is nothing to support this idea. It is merely the statement of an assumption that 5 per cent of the population when described quantitatively by any test are abnormal. It also assumes that deviations from the mean in either direction are equally important and that doctors should take action if the results fall outside these limits, to say nothing of assuming that standard deviations are meaningful when calculated on very skew distributions, and the very oddly selected populations on which the calculations are based.”

“The only alternative to this unsatisfactory approach, as far as I know, is that suggested by Dr Elwood and myself. **The idea is that for simple univariate analyses the object should be to establish the point or points on the distribution at which therapy begins to do more good than harm.** Elwood has demonstrated the application of this approach in his investigation of the distribution of haemoglobin levels in the population as an indication for giving iron therapy. … It is very sobering to reflect how few distributions have been investigated at all in this way.” (pages 41-43)

*These quotes capture the tension between variable definitions (in scales/instruments) based on measurement versus variable definitions (in scales/instruments) based on statistics.*