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Accuracy vs precision: what's the difference?

Highlighted from a real textbook passage. Explained by Clicked.

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University Course Reader · STEM

The readings agreed with each other, but the accuracy check against a certified weight showed the scale 20 grams high.

The reader highlighted one word in a textbook passage. Clicked broke down the measurement term “accuracy” into plain English:

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Overview

Accuracy is how close a measurement comes to the true value. Precision is how close repeated measurements come to each other. They are separate questions. A kitchen scale that shows 520 grams for a 500 gram bag of flour, every time, is precise and not accurate. One that shows 480, 515, 490 and 512 is not precise, though its readings average to 499, so it is accurate on average. Accurate is near the truth; precise is near each other.
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Overview

Accuracy is how near a measurement is to the truth. Precision is how near your repeat measurements are to one another. A thermometer that reads 38.2, 38.2 and 38.2 on someone who is really 36.7 is consistent and wrong every time: consistent is not the same as correct. Its opposite reads 36.4, 37.0 and 36.7, readings that average to the truth while each one alone misses it a little. Neither is the thermometer you want, and only the first is easy to fix. 😎

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Detail

Accuracy is how close a measurement comes to the true value, and precision is how close repeated measurements come to each other. The two are separate questions. Weigh a 500 gram bag of flour four times on a kitchen scale. Readings of 520, 520, 521 and 520 are precise and inaccurate: the scale agrees with itself and is 20 grams high every time. Readings of 480, 515, 490 and 512 are imprecise, and their average is 499, so the scale is accurate on average though any one reading can miss by 20. The two faults have different fixes. A reading that is always 20 grams high has a bias, a fixed offset. One adjustment removes it, and that adjustment is calibration. Scatter has no fixed offset to remove; adjust the scattered scale and you only move the scatter. The remedy is to take more readings and average them. Precision shows in the readings alone; accuracy shows only against the truth, so a scale is checked against a weight whose mass is already certified. The flour scale reads to the nearest gram, and people call that precise too. Reading to the gram did not stop it being 20 grams high, so how finely an instrument reads is a third property, resolution. And psychology, where the instrument is often a questionnaire, calls the same agreement between repeats reliability.
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Detail

Accuracy is how near a measurement is to the truth, and precision is how near your repeat measurements are to one another. Take a thermometer on someone who is really 36.7 degrees. One reads 38.2, 38.2, 38.2: it agrees with itself to the decimal and is a degree and a half high every time. Precise, and wrong. Another reads 36.4, 37.0, 36.7. Those average out on 36.7, so this one is accurate on average, but accurate means each reading lands close to the truth, and here 36.4 and 37.0 both miss it. The steady-and-wrong thermometer is the dangerous one, because it looks trustworthy, and it is also the easy one to fix. Its error is the same every time, so one adjustment brings every reading down by a degree and a half. The scattered one has no single error to adjust; the only cure is more readings and an average. How finely it reads is a separate matter again, and its name is resolution. A display that shows 38.24 rather than 38.2 has finer resolution, which people also call precise, but the extra decimal is no help while it is still a degree and a half high. And when psychology talks about a questionnaire giving the same answer twice, it calls that reliability, which is precision under another name. Precise means the readings agree. Accurate means they are right. 😎

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Analogy

Accuracy and precision are the two questions you can ask about a handful of darts: how close to the bullseye did they land, and how close to each other. The first is accuracy, the second precision. Four darts in a tight cluster off to one side are precise and not accurate: every one is off by the same amount. Four darts spread all round the bullseye are imprecise: their centre is on it, and no single dart is. The tight cluster is the one to remember, because it looks like skill and is a fixed fault. Shift your aim once and every dart moves with it. The spread darts have no single fault to shift, so no one change fixes them; only more throws, and a look at where they centre.
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Analogy

A watch that runs exactly five minutes fast, and has done for years, is precise and inaccurate. Check it against the station clock and it is five minutes ahead. Never four, never six. It agrees with itself perfectly and is wrong every time. Because the error is fixed you can live with it: you subtract five minutes in your head, which is calibration done by a person, and you are never late. A watch that is two minutes fast on Monday, three slow on Tuesday and one fast on Wednesday is closer to right on average and useless in the moment, because there is no right thing to subtract. Wrong the same way every time is fixable. Wrong a different way every time is not. 😎
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AI explanations may contain errors · Not professional advice

Formal definition — The same term, explained the usual way

Accuracy is the closeness of agreement between a measured value and the true value of the quantity being measured; low accuracy is associated with systematic error, or bias. Precision is the closeness of agreement between independent measured values obtained under stipulated conditions; low precision is associated with random error, and it is expressed as a standard deviation. The two are independent, so a measurement may be precise without being accurate and accurate on average without being precise. In the ISO 5725 vocabulary, accuracy is the combination of trueness (closeness of the mean to the reference value) and precision. Precision is distinct from resolution, the smallest change in a quantity that an instrument can display, and corresponds to what psychology calls reliability.

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