## Accuracy and Uncertainty

A target-based visual metaphor for accuracy and precision. Accuracy is about ‘arrows’ being centred on the target – the true answer. Precision is about arrows being close to each other. However in reality one never knows what the target is or whether one has hit it. One never gets to look up the ‘true answer’. This is where the concept of uncertainty helps.

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’.

A representation of what a measurement tells us. The shading represents the results of an analysis of the likely uncertainty of measurement i.e. how wrong our measurements are likely to have been?

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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.

Kind regards

Michael

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### 4 Responses to “Accuracy and Uncertainty”

1. Nick Day Says:

Happy 400th! Helps me stay sane too.

2. Carole Hegedüs Says:

Hello Michael

I was surprised to read that only 200 people follow this blog; I imagined it might be thousands. Anyway, just to say I really like it and I especially liked the one about EROEI. I forward the postings to my daughters, one of whom teaches maths and I know she has used bits in school.

We met briefly after the end of the winter session, and talked about Ham Hydro. I was with Jean Loveland and she may have contacted you on behalf of our group. Planning permission has been applied for, decision expected at the end of this month. We may need influential support at some stages and we are hoping that we might rely on you.

It’s quite a brave thing, thinking out loud and sending stuff out into the ether with no feedback. So this is feedback.

b/rgds

Carole Hegedüs

• protonsforbreakfast Says:

Carole

Thank you. The blog has around 350 followers but typically 200 people look at it each day. I have lots more to say about EROEI – and it is surprising! I am just busy busy busy!

You can rely in me to support the Ham Hydro scheme. I don’t know its exact EROEI figures or economics, but I know that it is just bonkers not to catch that energy as it flows past. I think the project is deliciously visible and could be enormously valuable in raising consciousness of what could be done in all kinds of other ways.

Every best wish

And well done for typing an umlaut on this funny system

M