ACCURACY AND PRECISION
There is no such thing as an absolutely accurate measurement. All measurements are approximations of the “true” value. Thus, when the accuracy of a measurement or set of measurements is stated, it is always stated in terms of inaccuracy or a range around the true measurement in which the given measurement may be found. Accuracy, precision, and resolution are terms associated with measurement. Many other terms are used to describe measurement conditions, but these three are components of every measurement, even simple measurements. As an example, consider the measurement of a simple line segment, as in Figure.
Accuracy is how closely you approximate the true value. The measurement shown in falls between 2″ and 2 ¼”. If the desired accuracy was “to the nearest inch,” then this would be an accurate estimate. However, if you wanted accuracy to 1/16″ then the ruler shown in Figure would not have the scale accuracy to measure to that degree of accuracy. You can approximate to ¼” with the given scale, but not much better than that. Trying to guess any closer to the true value would be just that, guessing.
ACCURACY AND PRECISION
Precision, particularly in instrumentation, means repeatability. You cannot have accuracy without precision. Repeatability means that each time you measure the same real value, you arrive within a given range around the same reading. Each time you measure Line A with the ruler in Figure, you interpolate (make an educated guess) that line A is 2 ¼” in length. Each time you make the measurement you arrive at the same conclusion (assuming you are consistent). Therefore, the precision of the scale in Figure is ¼”, that being the closest approximation you can realistically
make for this measurement.
Resolution is the smallest change (or interval) that can be measured by a particular measurement reading scale. For the ruler in Figure 2–2, the resolution depends upon the viewer’s ability to approximate a change in the two measured lines. Line A is 2 ¼”; Line B is 2 1/8″. As you can see, the difference in length is hard to determine, particularly if only one line was visible. If you add ¼” scaling marks, however, as in Figure 2–3, it is far easier to detect the small change and measure it.
By adding the ¼” scale you have improved the accuracy by making possible closer approximations of the real value. You have also improved the precision because you have improved the likelihood that the observer can make the same, more accurate reading each time. This really is a direct result of increasing the resolution of the scale.
Question: Can you have accuracy without precision?
Answer: No. Accuracy refers to how close the measurement value is to the actual value. To be accurate, each measurement of the same quantity should fall within the stated accuracy range around the true value. Since precision means the ability to obtain the same reading when measuring the same value, you must have the necessary precision (repeatability) for the accuracy of the instrument.
Question: Can you have precision without accuracy?
Answer: Yes, you may be precisely wrong. If you obtain the same measurement value each time a real value is measured, then you have a high degree of precision. Using the rule in Figure 2–3, if, for example, the scale 0 is offset from the line by ½”, then your readings may be precise, but reading the wrong value will give the wrong value each time.
