# What is the difference between precision and accuracy

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scoopposted 6 years ago

What is the difference between precision and accuracy

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DreamerMegposted 6 years ago

I don't think there is any difference. The online dictionaries show them as synonyms of each other.

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Farmer Rachelposted 6 years ago

In chemistry classes in college, I learned that there is a difference. Accuracy is about measurements, and how close one or more measurements is to the true value of something, i.e. can you measure 1 gram of water on your scale to be 1 gram of water exactly? Precision deals with being able to reproduce the same measurements time and again. I think I explained it correctly!!
http://en.wikipedia.org/wiki/Accuracy_and_precision

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AlexK2009posted 6 years ago

A watch with a second hand is precise to one second. If it gains a minute a week its accuracy diminishes by one minute each week.

So precision tells you how closely you can measure something, accuracy telly you how close the measurement is to reality.

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I have answered this question "accurately" from a layman's point of view. But within the fields of engineering, industry, science, and statistics, this answer is not precisely accurate!  Farmer Rachel has it right.

There is some overlap in meaning. One of the dictionary definitions of "accurate" is "precise" - but not vice versa.

The focus of the two words is different. The word "accurate" tends to answer an either-or question (is something correct or is it not?) and the word "precise" answers "to what degree is it correct or not?"

As examples, (1) in the context of my family budget, I could accurately say I spent "about \$10" at McDonald's. To be precise, I would say I spent \$9.88.  (2) In the context of statistics related to demographics, someone could accurately say [at least, at one point in American history] that the average American family had "2 or 3" children. With numerical precision, the figure was 2.54 - as an average. But would that be "accurate"? Who has 54/100 of a child? - no, the statisticians were not talking about the unborn.

(3) In archery, it would be accurate to say that someone hit the bull's-eye, if the arrow pierces any point within the inner ring. If the announcer or coach wants to be precise, they might say the arrow hit "dead center"; or, in another situation, they might use an exact (precise) measurement and say that the arrow hit 1.68" inside the boundary of the innermost ring.

In mathematics, precision depends upon the degree of exactness which is being measured. Is pi more accurate taken to 100 decimal places than to 20? It is certainly more precise. But I would argue that the term accuracy would depend on the use of pi. If the answer would be rounded to the nearest 5 decimal places, then pi to 100 decimal places is no more accurate than pi to 20 decimal places.  If the calculation for some reason requires 50 decimal places, then in that situation pi to 100 places would provide the accurate answer, but pi to 20 decimal places would not.

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SidKempposted 6 years ago

In statistics. science, and engineering, there is a difference, and it is not explained completely clearly by any other answer. My brother and I, in writing Business Statistics Demystified (McGraw-Hill, 2004) spent two weeks writing four pages to make this clear. That's longer than we spent on some other chapters!

What physics and engineering call precision, statisticians call reliability.
What physics and engineering call accuracy, statisticians call validity.

Imagine 4 archers each shooting 10 arrows at a target, aiming for the bulls-eye.

One of them shoots all 10 arrows very close to one another, in a two-inch circle. Unfortunately, all the arrows are about 2 feet away from the bulls-eye, say, to the left. This shooter is very precise - he does the same thing every time. But he is not very accurate. He has a bias of 2 feet to the left.

The second archer shoots all around the bulls eye - everything is in the yellow or blue, but none is in the red. Some are above the bulls-eye, others below. Some are to the right, others to the left. He is very precise - the center of all of his shooting is the center of the bulls-eye. But he is not precise enough. He needs to become more steady and reduce variability from the center.

The third archer sends all ten arrows low, to the bottom of the target, and scattered around. He is neither precise nor accurate. He needs to become more precise by eliminating his bias (too low) and also become more accurate.

The fourth archer lands all the arrows closely grouped in the bulls-eye, centered right at the center. He is both accurate and precise.

In physics and engineering, we know where the target is. In statistics, we can't see the target. That's why statisticians use a different term.

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It is great to see this clear and complete technical explanation, but I do have a question about the sixth paragraph (the 2nd archer).  You wrote "He is very precise....But he is not precise enough."  Was that worded right or is there a slip in it?

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Farmer Rachelposted 6 years agoin reply to this

I am confused about the second archer, too. Is he really precise at all for having missed the bullseye?

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SidKempposted 6 years agoin reply to this

Oops! It should have been "he is very *accurate* . . . But he is not precise enough." Thanks for catching the error.

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