Accuracy and precision

We want to measure things well.

One way is to be close to the real size. This is being right. Another way is to get the same answer every time. This is being steady.

You can be right but not steady. You can also be steady but not right. To be truly good, you must be both. A great tool is both right and steady. It gives the same answer and that answer is true. This helps us understand our world.

When we measure things, we want to be correct. Scientists use two main words to talk about this. These words are accuracy and precision.

Accuracy means how close a measurement is to the true value. If you measure a stick, accuracy tells you how close you are to its real length. Scientists also use the word trueness. This describes how close the average of many tests is to the true value.

Precision is different. Precision is how close measurements are to each other. If you measure the same stick many times, precision tells you if you get the same result every time.

You can have one without the other. A tool might be precise but not accurate. This means it gives the same answer every time, but the answer is wrong. This often happens because of a systematic error. A systematic error is a mistake that happens the same way every time.

A measurement system is valid if it is both accurate and precise. This means the results are close to the truth and close to each other.

In science, measuring things correctly is very important. Scientists use two special words to describe how good a measurement is: accuracy and precision.

Accuracy tells us how close a measurement is to the true value. If you weigh an apple, accuracy shows if your scale shows its real weight. Precision is about how consistent your results are. It shows how close your measurements are to each other when you repeat them.

A system is considered valid only if it is both accurate and precise.

These two ideas work in different ways. Accuracy is often linked to systematic error, which is a mistake that happens the same way every time. If a scale always adds one gram, it has a systematic error. Precision is linked to random error, which is just natural variability.

To be accurate, the average of many tests must be close to the true value. This part is sometimes called trueness. To be precise, the results must be tightly clustered together. You can have a precise tool that is not accurate if it repeats the same wrong answer.

Rules for these words have changed over time. In 1994, a series of standards called ISO 5725 was published. These standards helped define how accuracy and precision should be used. Later, in 2008, the International Vocabulary of Metrology, or VIM, included these ideas too. Before these rules, some people used the word "bias" to talk about inaccuracy. Now, scientists prefer to use terms like trueness and precision to be more clear. These rules help everyone in science speak the same language.

Scientists use many numbers to show how much they trust a measurement. They often use significant figures to show the margin of error. For example, a measurement of 843.6 meters implies a margin of error of 0.05 meters. This is because the last digit is in the tenths place. If a scientist writes 8,000 meters, it can be hard to tell the precision. They might use scientific notation, like 8.0 x 10^3 meters, to make it clear. This tells the reader exactly how much error to expect.

You can see these ideas in many parts of life. In the military, accuracy refers to how close shots are to the center of a target. In math, accuracy is how close a calculation is to the real answer. Even computers use these ideas to classify things. A computer might try to identify a picture, and its accuracy is how many it gets right. Whether measuring a tiny atom or a huge planet, these tools help us understand our world.

In the scientific method, measuring the world requires more than just reading a number. Scientists must understand the quality of their data using two distinct concepts: accuracy and precision. While people often use these words as synonyms in daily life, they mean very different things in science and engineering.

Accuracy describes how close a measurement is to the true or accepted value. Precision describes how close repeated measurements are to one another under unchanged conditions. A measurement system is only considered valid if it achieves both high accuracy and high precision.

To understand how these work, we must look at the types of errors involved. Accuracy is closely linked to systematic error, which is a consistent, directed effect caused by a specific factor. If a scale is broken and always adds five grams, it has a systematic error. Precision is linked to random error, which refers to natural statistical variability.

If you measure the same object ten times, random errors might cause the results to scatter slightly. Precision is a measure of how small that scatter is. You can have a precise system that is inaccurate if a systematic error pulls all the results away from the true value.

International standards have provided specific ways to define these terms. According to the ISO 5725-1 standard, accuracy is actually a combination of two things: trueness and precision. Trueness is the closeness of the arithmetic mean of a large number of test results to the true value. This addresses the systematic error. Precision refers to the closeness of agreement between the results themselves, addressing the random error.

The International Vocabulary of Metrology (VIM) also supports these definitions. This standardization ensures that scientists across the globe interpret data in the same way.

History shows that these definitions have evolved to become more precise. Before the ISO 5725 series was published in 1994, some scientific guides used the term "bias" to describe inaccuracy. However, modern standards like ISO 5725-1 and the 2008 VIM often avoid "bias." This is because "bias" can have different meanings in other fields, such as law or medicine. By using trueness and precision, scientists avoid confusion. This helps maintain clear communication when discussing the reliability of experimental results.

Scientists use specific mathematical tools to express these concepts. One common method is using significant figures to imply a margin of error. For example, a measurement of 843.6 meters implies a margin of error of 0.05 meters because the last digit is in the tenths place. To avoid ambiguity with large numbers, scientists use scientific notation. A recording of 8.0 x 10^3 meters clearly shows a margin of 50 meters. This level of detail allows other researchers to know exactly how much uncertainty exists in the data.

Precision can also be broken down into two specific types: repeatability and reproducibility. Repeatability is the variation seen when the same operator uses the same instrument over a short time. Reproducibility is the variation seen when different operators use different instruments over longer periods. In engineering, precision is often calculated as three times the standard deviation. This calculation represents the range where 99.73% of all measurements are expected to fall. This provides a statistical way to guarantee the consistency of a tool.

These concepts apply to many different fields beyond basic measurement. In military terms, accuracy refers to the closeness of a grouping of shots to the center of a target. In computer science, accuracy is used in binary classification. This measures the proportion of correct predictions, such as how well a test identifies a specific condition. In multiclass classification, accuracy is the fraction of correct classifications out of the total. Whether in a lab or a computer program, these principles help us define truth and consistency.