Accuracy and Precision: Measuring Instruments

Measuring is essential to understanding the world. Measurements are made using tools that allow us to correctly quantify quantities. Although measurements are a good way of giving value to the world, it is important to recognise that the results have uncertainty. This uncertainty is known as error. The error in a measurement is the difference between the measured value and the true value of a quantity. The error represents the uncertainty of measurement in its value. This error is understood as the amount of the measurement that may be greater or less than the true value. 

This error can be understood more clearly from other relevant terms. Two terms that are relevant to understanding measurements and their error are accuracy and precision. 

The closeness of an instrument’s measurement to its actual result is called accuracy. On the other hand, by taking the same reading of measurement several times, differences between each measurement can be found. This is called precision and is classified into three types:

Types of Accuracy

1. Point accuracy: this is the accuracy of an instrument at a single measurement point. This information does not reveal the accuracy of the instrument itself.
2. Accuracy as a percentage of the range of the scale: this is defined as a range of the accuracy scale. An example of this is the accuracy of a thermometer. When we measure a temperature by using a thermometer it can be 0.5°C higher or lower than the indicated value. In other words, the accuracy range is 0.5°C.
3. Accuracy as a percentage of the actual value: this is a percentage given by comparing the measured value against the actual value. Normally this accuracy is 5%. 

Precision

The distance between two or more measurements from each other. A measurement can be precise and not accurate or vice versa. Precision is divided into different factors:

1. Repeatability: the variation between measurements taken identically over a short period.
2. Reproducibility: the variation between measurements made under the same conditions, but with longer periods with different instruments.

Examples of Accuracy and Precision

There are several analogies for understanding accuracy or precision. For example, in a basketball game, if a player shoots several times at the backboard without making a basket but hitting the same spot, he would be said to make accurate shots. However, because he has not made a basket, he cannot be said to be precise. An accurate and precise player will not only hit the same point several times but will also make a basket. 

Examples With Length

Suppose a person is 170 cm tall. This person can make several visits to the doctor, where he or she will be measured with a tape measure or a laser beam.  The first measurement gives a result of 169.99 cm. The second measurement gives a result of 187 cm. The first measurement is more accurate, as it is much closer to the real one. On the other hand, the measurements are not precise as the two values are different from each other.

Examples of Temperature

Normally the human body is at 37 °C. If you measure your temperature for several days and get values of 17, 18, 17, 17, 18.5, 17, and 18, would it be accurate or precise? In this case, it is precise because the values are very close, but it is not accurate because it is far from the real value (37 °C). If, on the other hand, your measurements are 34, 40, 35, 38, 41, and 35, the measurements would be less precise because the difference in values from one to the next is greater. These measurements on the other hand would be more accurate, as they are closer to the real value.  

One Last Example

Imagine you have a target shooting board. Two people are throwing darts trying to score points. Person A fails to throw his dart in the centre, but his shots are all very close to each other. All his shots are in the top centre of the second closest circle to the centre. Person B on the other hand did manage to throw 1 dart in the centre. The other darts are distributed in different parts of the board. In this case, person A is very precise but not very accurate. For person B, it can be concluded that he had one accurate throw, but all the other throws were neither accurate nor precise.

Difference Between Accuracy and Precision

To make these concepts clearer, let’s review the differences: