Professor David Hand from Imperial College gave an interesting talk about the importance of measurement in statistics. His conclusion was that choice of measurement is not just a question of choosing some representational system to model the world, since several different systems could be used, sometimes giving different statistical conclusions. Hand argued that the choice of measurement is also dependent on pragmatic issues. It depends what question we want answers. It depends partly on what is important to us.
So what about the British and French statisticians? Well, this is a fictional example given by Hand.
Suppose we want to measure the fuel efficiency of two types of car: a Rover and a Renault. We have two examples of each car with a record of fuel consumption. Now, the British measure fuel consumption in miles/gallon. The French measure fuel consumption in litres/kilometer. Now let’s just rescale the British system to be kilometer/litre, so the measures are simply the reciprical of each other (ie French fuel consumption is 1 divided by British and vice versa). So here are some figures along with averages:
Rover
Renault
Car 1
Car 2
Mean fuel consumption
Car 1
Car 2
Mean fuel consumption
British (km/L)
1
4
2.5
2
2
2
French (L/km)
1
0.25
0.625
0.5
0.5
0.5
Now, since the British statistician measures more km/L for the Rover than the Renault, she concludes the Rover is more fuel efficient.
However, since her French counterpart measures less litres consumed per kilometre (L/km) in the Renault, he concludes the Renault is more fuel efficient.
They can’t both be right! What is happening here and which of the two do you think is right?
I’ll place what I think is the right answer in a comment to this post at some point.
The lesson to take from Hand’s talk and this example is that statistics is not a wholly objective system of analysis. It really does depend on the representational system we use and on the pragmatic concerns we have. So when we come to perform a statistical test, we need to be sure we are clear which question we are trying to answer.
November 4, 2006 at 11:55 pm |
The line I take on this is that “meaning” is about potential sensorimotor interactions with the world (along the lines of affordances or Predictive State Representations). A statistical result is too disembodied (in general) to have a meaning. It can only have a meaning by virtue of plugging it into a potential sensorimotor interaction. The statistic does not determine the sensorimotor interaction and some combinations would be incompatible. So, I would rephrase what you and David said as: first choose the operational meaning that is of interest to you and then choose the statistic to suit. In the car example, the meaning (and appropriate statistic) would differ depending on whether you are managing a fleet of cars and care about the total consumption or are a purchaser interested in buying a single car picked at random from the population of Rovers or Renaults.
November 6, 2006 at 3:12 pm |
Hi Ross. That’s interesting because statistics can be viewed in an operational sense, as you describe, when it is a “doing”, and it can also be viewed in a representational sense, in that it’s about other things in the world, when it is a “knowing”. These are just two views of the same thing, although the second is the level a statistician is usually interested in (ie answering questions about things). It’s clear that the use of statistics is dependent on operation, from the first view. However, the second view works at a more abstract level, and perhaps it is this that makes it seem as though statistics is an objective method (ie divorced from the pragmatic issues). The operational view reminds us that this cannot be the case and that any information provided by statistics, on the second view, is only meaningful with respect to the problem we are addressing.
December 20, 2007 at 4:15 pm |
very interesting. i’m adding in RSS Reader