Just quote a comment from the Economist, may be you can get inspired from this.
sanmartinian wrote: Jul 1st 2011 11:17 GMT
Congrats on this much needed and very well designed study.
Despite my remark below, this does a lot of credit to this piece and to the Economist.
Without detracting a single thought of what I just wrote above, I'd like, however, to add my theoretical words of caution against these multiple scale analyses.
They are very common nowadays. They are also very useful. They are mathematically very wrong too.
Scale measurements cannot be added, subtracted or averaged as these studies have to do. You can add, subtract, etc. physical measures like length, weight, numbers of people and money in circulation and so on.
A simple example I always give to explain this idiosyncrasy is as follows: Temperature is a scale; not a physical measurement (not even when measured in Kelvin units that supposedly measure energy levels).
If you have two buckets, each containing a gallon of water one at 50oF and the other at 100oF, and you mix them up you don't get one gallon of water at 150oF.
You get two gallons of water at 75oF.
Volume of water is addable, temperature measurements aren't (although an artifice makes them average-able).
Same with most indicators used in the study.
To obtain mathematically correct results you'd have to use quaint, still juvenile and ruddy clumsy maths techniques called DEA or MOLP.
For the time being I don't advise it.
But I do advise to use 200 year old Chevalier de Borda's method. Not fully correct, either but closer to right results than doing maths operations on scales.
I repeat nothing I've said at the end detracts from the deserved congrats on the usefulness and novelty of the study presented here.