Precision vs Accuracy

[crokett]

A colleague and I had an argument about this and agreed that a neutral third party would be the arbitrator. His posit is that precision is often interchanged with accuracy but that is incorrect. He says that you can have precision without accuracy. For example, PI is 3.14. A more precise answer is 3.14159. He says that 3.23675 is more precise than 3.14. I say it is not because it is inaccurate to start with.

There is lunch riding on this one.

[shoottx]

When all else fails go to http://en.wikipedia.org/wiki/Accuracy_and_precision

[jussi]

The way I was taught you can be precise and not accurate but not vice versa. The best analogy is the target one. If you cluster a bunch of shots in the same location you are precise. The cluster doesn't necessarily have to hit the bullseye. But if it is then you're accurate. I learned this in High school chemistry class and was taught to use it in regards to taking measurements.

EDIT: The link shoottx provided gives a better explanation.

[pelligrini]

According to the dictionary definitions it looks like you can have precision without accuracy.

I think it would really depend on the context of the arguement. Take his example, 3.23675 is a more precise number than 3.14 in pure mathmatical terms, but in refrence to the specificity of PI, it is not percise, nor accurate.

[jussi]

I think if a person who didn't know the value of PI was trying to find it by taking measurements of different circles and he was getting say 3.4234, 3.4294, 3.2254 he would be precise but inaccurate. If he got closer to 3.1415 he would be accurate.

[Bigbit]

The Wiki entry captures the principle very well. Accuracy describes how close, on average, the measurement output of a device matches the actual value. Precision is a measure of how repeatable a device is. If a device gives out a very consistent readout, but the reading does not agree with a well-accepted reference, it is described as precise but not accurate. On the other hand, if a device's readout is averaged over many readings, and on average, has a value very close to a well-accepted reference, but each reading varies widely, one to another, it is decribed as accurate but not precise.

[maxparot]

According to the dictionary definitions it looks like you can have precision without accuracy.

I think it would really depend on the context of the arguement. Take his example, 3.23675 is a more precise number than 3.14 in pure mathmatical terms, but in refrence to the specificity of PI, it is not percise, nor accurate.

Agreed and as referenced to PI to express it both accurately and precisely as a mathmatical term I was taught to use 22/7

[crokett]

Looks like I owe him lunch. I'm not really upset, mostly I wanted to argue.

Still, it doesn't matter how precise you are if you are wrong.

[pelligrini]

hehe, from the OED on my pocket PC;
accuracy- exactness or careful precision

precision- 1. accuracy 2. marked by or adapted for precision

[jussi]

On the other hand, if a device's readout is averaged over many readings, and on average, has a value very close to a well-accepted reference, but each reading varies widely, one to another, it is decribed as accurate but not precise.

I don't think this would be either precise or accurate.

[Bigbit]

I don't think this would be either precise or accurate.

To be clearer, the average of the readings would be considered accurate, but an individual reading would not be. To achieve desired accuracy, you would need to increase the sample quantity or time to the square of the desired improvement in accuracy, as noise is directly related to sample time /size as a square root function. See http://tf.nist.gov/general/glossary.htm which also has a good description of accuracy versus stability (precision).

[LCHIEN]

To be clearer, the average of the readings would be considered accurate, but an individual reading would not be. To achieve desired accuracy, you would need to increase the sample quantity or time to the square of the desired improvement in accuracy, as noise is directly related to sample time /size as a square root function. See http://tf.nist.gov/general/glossary.htm which also has a good description of accuracy versus stability (precision).

Jussi and Bigbit:
I agree with Bigbit that a value can be of limited precision yet highly accurate. One prime example of this is provided by the single-bit converters used to reproduce audio and other measurements. Its precision is only 1 bit (e.g. +/-50%) but when sampled repeated and at high speeds the filterered or averaged answer can be accurate to measures well beyond that of 16 bit converters. A single measurement would be accurate to the level of the precision of that one measurement.

And as an instrument engineer my take on accuracy vs precision agrees wth most of the others. Accuracy represents the ability to give or express an measure close to and with little error from the correct answer. Precision is the resolution, comparable to the number of digits used.

It is possible to have precision without accuracy (for example Pi=3.4567389076) but Pi = 3.14 is more accurate.
Pi=3.1415926535 is both accurate and precise.

[Kristofor]

Still, it doesn't matter how precise you are if you are wrong.

Well, it's seems that way, but in many cases it's better to start out precise than to start out accurate. Anywhere a correction factor can be used adjusting accuracy is an option, but eliminating the imprecision may be much harder.

For Example, many people are either near-sighted or far-sighted due to a defect in the shape of their eye. The photons going through their eye will all be focused on a target other than the intended location (it's in 3D, but think of them all being to the left of the bullseye).

When the defect is uniform, a simple corrective lense can be added to the system (glasses/contacts) that adjusts the location to hit the correct portion of the retina in focus. If the eye was randomly distorted so that on average the photons were focused in the right place but with a very low degree of precision (scattered all around) it would be much harder to correct this problem as you would need to account for and correct every little distortion.

These types of examples happen all the time. Take you're table saw fence. If you want to cut a 6" slice of plywood. Would you be more concerned about having to move the fence from the 8" position (correction of poor accuracy), or that once positioned at 6" it might lockdown eratically or slide 1/4" off of that mark (correction of precision)

Kristofor.

[LinuxRandal]

I am going to take a different aproach, due to the nature of this forum.


You can make precise cuts on your board/plywood, measure them and can't believe you actually took into account the blade kerf, only to find out, you didn't accurately measure the dimensions to begin with.

[leehljp]

I make precision cuts on my BT all the time that are not accurate!