16.Analysis of Errors-I

As mentioned in my earlier post , we start this post with the introduction of two new parameters in error analysis namely – ACCURACY & PRECISION.

1)Accuracy
• Accuracy of a measurement tells us how close the measured value (xi),is close to the true/accepted value.
• Accuracy is measured in Relative error , Absolute error.

2)Precision
• It means reproducibility or repeatability.
It’s the agreement between two or more values of the same set of observations.
Precision is measured in terms of deviation.

To understand these concepts let us take example of an archer and  the target.

88083db2f8b4262fb11329a07f380315
Image 1

The archer’s aim is to hit the bull’s-eye i.e the exact centre of the target board.

Untitled-1

Suppose he shoots 4 arrows, they could land up as follows –
(Green spots ⇒ Region where each arrow hits the board).

CASE I – The arrows shot are far away from the bull’s-eye (centre) but all 4 of them hit the board near a particular spot.Thus, the archer is precise as he hits the target board nearly at the same spot but he is not accurate as he is far away from the target centre – the bull’s eye.

Case1
CASE I – Precise YES.Accurate NO.

 

CASE II – The arrows shot are very near the bull’s-eye but the spots where 4 arrows hit the target board are not very near each other.So, the archer here is accurate but not very precise.

Case2
CASE II – Accurate YES.Precise NO.

CASE III – The arrows shot in this case are both accurate and precise.All 4 arrows are hit in the centre(As they are overlapping, 4 spots cannot be differentiated in the fig below).

Case3
CASE III– Precise YES. Accurate YES.

It shall look like this –

precise_and_accurate
Image 2

How to Remember?

  • aCcurate is  Correct (a bullseye).
  • pRecise is  Repeating (hitting the same spot, but maybe not the correct spot).

Good precision does not ensure a fairly good degree of accuracy but , a good degree of accuracy always ensures an equally good degree of precision.

Thus, if we have many methods to conduct an experiment we choose the one which gives us most accurate and precise results.Suppose, there is an experiment, which can be conducted in four different ways/methods  namely A,B,C & D.We get our results and  we plot them as shown in the figure below –

IMG_2693 copy
Results to the left of True value show -ve error and to the right side show +ve error.

XA XB,XC,XD are the respective mean values.Please note that it is only a matter of  luck that XC is close to true value(thus the accuracy is high), but the individual results are scattered and far away from the true value.Thus,method C cannot be considered as a good way to conduct the experiment.

Scatter is the result of Random error.Thus, in the above figure, we encounter Random error in methods where the results are scattered in both directions (+ve and -ve) from the true value.Systematic error is high where the results are not near the true/accepted value.

So,which method do you think is best suited to conduct our experiment?We would obviously choose method D as it gives us high precision and high accuracy! All the results are near the true/accepted value and both type of errors are minimal.These concepts are very useful in laboratories where high quality work is expected e.g. Proccesses requiring to test high purity of materials.In such cases,a little error could cost millions of dollars !

Now that we looked into the concepts of accuracy and precision, we shall discuss how to measure these parameters in the next post.Till then ,

Be a perpetual student of life…Keep learning !

Good day !

 

References and Further Reading –

1)http://www.mathsisfun.com/accuracy-precision.html

2)http://www.csudh.edu/oliver/che230/textbook/ch05.htm

Image Source –

1)Image 1 -https://www.appannie.com/apps/ios/app/archery-bow-and-arrow-super-archer-free-game/

2)Image 2 -http://www.quickanddirtytips.com/education/math/accuracy-versus-precision

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