A question about hygiene and where it led

I love the idea of surrogate measures.  I love it where the "thing" (thing 1) you are trying to measure is hard or impossible to observe and/or quantify, and someone recognises another "thing" (thing 2) which can be measured and which is demonstrably correlated with thing 1.  One needs to be aware of the value of surrogate measures in quantitative O.R. ... but also be wary of the dangers of relying on them.  If they are used, then they need to be explained, and their correlation be clear both statistically and to the (possibly) non-numerate client. 

So it was a delight to me to read in this week's New Scientist magazine of an obvious surrogate measure in response to a question posed by a reader.  The question asked was: if there are three WC stalls in a washroom, which stall is most hygienic?  The first one you pass, the second or the furthest from the door?  The questioner was relating hygiene to usage, so the question becomes one of which stall has the most usage?  And the question doesn't have to be limited to three stalls - the question applies for any N>=2 stalls.

One reply observed that because most washrooms are cleaned regularly, then the risk of infection is much less than using shared equipment in an office (landline telephone handsets and computer keyboards were cited as particularly unhygienic).  Another suggested that those who use the washroom for a few moments peace and quiet will tend to get to the "security" of the furthest stall.  

And then there was the respondent who gave us a surrogate measure.  Which stalls use most toilet rolls?  As a regular cleaner of washrooms, this respondent had observed that the least used stall was invariably the first one.  So, instead of watching the use of stalls by people, measure the use of rolls in each one.  Simple, easy to do, and quite obviously correlated ... unless you can think of a reason why the rate of usage should also vary between stalls.

I suspect that when N is large, there might be variations in this conclusion - why walk too far? - but the question was about N=3 and so the variation in distance to stalls is not significant.


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