Chapter 1: Introduction
1.3 Accuracy and Precision
Authors: William Moebs, Samuel Ling, Jeff Sanny
Adapted by: Rob Pryce, Alix Blacklin
Learning Objectives
By the end of this section, you will be able to:
- Determine the correct number of significant figures for the result of a computation.
- Describe the relationship between the concepts of accuracy, precision, uncertainty, and discrepancy.
- Calculate the percent uncertainty of a measurement, given its value and its uncertainty.
- Determine the uncertainty of the result of a computation involving quantities with given uncertainties.
Figure 1.11 shows two instruments used to measure the mass of an object. The digital scale has mostly replaced the double-pan balance in most labs because it gives more accurate and precise measurements. But what exactly do we mean by accurate and precise? Aren’t they the same thing? In this section we examine in detail the process of making and reporting a measurement.
Accuracy and Precision of a Measurement
Biomechanics is based on observation and experiment—that is, on measurements. There are specific parameters used to describe measurements:
Accuracy is how close a measurement is to the correct value for that measurement. For example, let us say that you are measuring the distance of a running tack. The international standard for running track length provided by the IAAF specifies the inside lane of the track should be 400m (measured 20-30 centimetres from the inside border) Assuming the track is known to be exactly 400.0m, you measure the length of the track three times and obtain the following measurements: 401.4m, 400.9m and 399.4m. These measurements are quite accurate because they are very close to the correct value of 400.0m. In contrast, if you had obtained measurements of 385.1, 415.3, and 430.2m, your measurements would not be very accurate. Notice that the number of decimal places used doesn’t necessarily relate to accuracy – you could have obtained a measurement of 430.23156m, which would have been similarly inaccurate .
The precision of a measurement system refers to how close the agreement is between repeated measurements (which are repeated under the same conditions). For the measurements of the running track above the precision of the measurements refers to the spread of the measured values. One way to analyze the precision of the measurements would be to determine the range, or difference, between the lowest and the highest measured values. In that case, the lowest value was 399.4m and the highest value was 401.4m. Therefore the range is 401.4m – 399.4m = 2.0m, indicating the measured values deviated from each other by at most 2.0m
Regardless of which method is used, they all show that the measurements were relatively precise because they did not vary too much in value. However, if the measured values had been 401.4m, 399.4m and 430.2m, then the measurements would not be very precise because there would be significant variation from one measureme