Precision and Accuracy in Measurement

Robo's Guide to Precision and Accuracy in Measurement (or how you can be precise without being accurate)

Hey, I know this isn't the most exciting stuff in the world, but it's easier to learn it now before getting too deeply into your lab work. If my creators hadn't worried about accuracy and precision, I'd be just a pile of nuts and bolts.

Most people use the words precision and accuracy interchangeably. It doesn't work that way in science. You can be precise without being accurate.

In science, precision generally characterizes the reproducibility of a set of measurements taken under the same conditions. A measurement is said to have greater precision when it has greater reproducibility. There are numerical methods of quantifying precision; these typically involve calculating something called deviations. At the most fundamental level, the reproducibility of a measurement depends on the resolution of the measuring instrument used. Think of resolution as the fineness of the divisions on the instrument. For example, your centimeter ruler has a resolution of 1 millimeter, although you can read it to a tenth of a millimeter under some conditions. If what you were measuring had sharp, fixed end points like a steel rod and you could lay the ruler parallel to the rod, then you could expect the reproducibility of repeated measurements of the length of the rod to be determined primarily by the resolution of the ruler. If, on the other hand, you were measuring the diameter of the rod with the same ruler, you would have more trouble sighting endpoints that were true diameters. Variability in how you sighted the endpoints from one measurement trial to the next would make this measurement of the diameter less precise than a measurement of the length. You could, however, make the measurement of diameter more precise by using a different measuring instrument. Such an instrument is a vernier calipers. This instrument has expandable jaws that clamp around the object as shown to the right, thus insuring that the distance measured is actually the diameter. So the precision of measurement is, to a certain extent, within your control by your choice of measuring instrument and how you use it.

My creators used very precise instrumentation so that my various parts would fit together. Their manufacturing techniques are so reproducible that they can make clones that look identical to me.

Accuracy is generally taken to mean the degree to which the result of an experiment agrees with an accepted value, if there is one. There's more to accuracy than that, though. You could get close to the accepted value by luck. That doesn't mean you had an accurate experiment. You need to be able to show that you had a good method. If you repeated the experiment several times and the result was always close to the accepted value, then you would have a foundation for a claim of accuracy. Scientists don't always have the resources (time and money) to be able to repeat an experiment many times and they don't always know an accepted value, so they use other ways to assess accuracy. They examine their experimental methods closely and estimate the uncertainties that their methods may introduce. They use statistical methods to come up with a single value for the uncertainty of the final result.

One problem with assessing uncertainties in a method is that sometimes a source of uncertainty can be overlooked and can create what's called a systematic error. This is something that puts the result in error by the same amount every time. It can seem like you're doing a very good experiment, but your results are always wrong. An example might be a calibration error in an instrument. Such errors can be very difficult to detect. Sometimes they're discovered by accident. They can also be discovered by trying techniques that use different measuring instruments.

One time a new engineer was put to work creating some scaled up versions of me. He used very precise instrumentation and techniques, but when he scaled my legs, he didn't take into account that weight and strength obey different scaling laws. When the first clone was assembled, all the parts went together beautifully. It was a very precise job. But when the clone tried to stand up, it crumpled under his own weight. It was very sad.

I hope that helps you understand the difference between precision and accuracy. Having said all that, people probably aren't going to jump on you if you use the terms precision and accuracy interchangeably. What's important is that you know how to express measurements to appropriate precision and how to assess reproducibility and uncertainty in measurements. The latter is something that you'll learn as you progress through your lab work.