Experiment!: Planning, Implementing and Interpreting

11.2 Measurement Uncertainty

When you step onto the bathroom scales in the morning, it translates the gravitational force, F, that you exert on it into a readout, which is your weight, W. The relation between them can be expressed as:

(11.1)

where a represents an offset, b is a proportionality constant (or slope), and ε is the random measurement error. If the scales are well calibrated the readout should be very close to zero when there is no weight on the scales, allowing for some random error. This means that a should be zero. The slope b should also be tuned so that correct readouts are produced when different weights are put on the scales. If either of these two parameters is off we say that there is bias in the readout. If ε is large we say that the readout suffers from noise.

This equation is quite a simplified description of the measurement chain, as the force is not directly translated into readout. In mechanical scales, the force of your body acts on levers, which extend a spring that turns a dial through a rack and pinion arrangement. Each of these components contributes both to the bias and the noise in the readout, and adds to the overall measurement uncertainty. If you want to improve the quality of your data, you must identify the components that contribute the most to the uncertainty and focus your efforts there.

Measurement uncertainty generally comes from a range ...