The picture above presents a well-known visual metaphor for accuracy and precision. The idea is that firing an arrow at a target is like making a measurement. And accuracy is a qualitative measure of how close a measurement is to the centre of the target – ‘the true answer’.
However in any real-world measurement, one can never know the “true answer”! If we did know the ‘true answer’, then there would have been no need to make the measurement!
In the real world, we fire our arrows i.e. we make our measurements – and that is it! We would like to know how far away our arrows fell from the target – but that is not possible! There is no way to compare them with the ‘true answer’.
So in the real world, what interests us is the answer to the question “How far from the target could our arrows have fallen?” or equivalently we need to ask “How wrong could we have been?”. We can work out an answer to this latter question without knowing the mystical ‘true value’.
Assessing the uncertainty of measurement is hard. It involves looking at all the factors that go into a measurement and asking how each factor could have affected the final estimate of the answer. We can then work out how wrong we could possibly have been.
However “how wrong we could possibly have been” is unlikely to be a useful number. To work out that answer we have to assume that ‘everything went wrong’ i.e. we have to assume that all the factors which affected the measurement were all – by chance – at the limit of what they could have been in a way that moved our estimate furthest away from the ‘true answer’.
What we really want to know is how wrong are we likely to have been?.
The answer to “How wrong are we likely to have been?” is called the measurement uncertainty, and this is the most useful assessment of how far our estimate lies from the mystical and unknowable ‘true answer’.
This is the 400th post on this blog, which as I write has had around 140,000 ‘page impressions’, corresponding to around 200 visitors each day. If you are reading this then I would just like to say ‘Thank you’. Writing these articles helps me stay sane – and the thought that anyone reads them makes staying sane seem like a worthwhile activity.
See you at 500.