Introduction

Chemists, physicists and other physical scientists are proud of the quantitative nature of their disciplines. By subjecting nature to ever closer examination, new relationships between quantities are discovered, and established relationships are pushed to the limits of their applicability. When ‘numbers’ emerge from an experiment, they can be subjected to quantitative analysis, compared to the ‘numbers’ obtained by other experimenters and be expressed in a clear and concise manner using tables and graphs. If an unfamiliar experiment is planned, an experimenter will often carry out a pilot experiment. The purpose of such an experiment might be to assess the effectiveness of the experimental methods being used, or to offer a preliminary evaluation of a theoretical prediction. It is also possible that the experimenter is acting on instinct or intuition. If the results of the pilot experiment are promising, the experimenter typically moves to the next stage in which a more thorough investigation is undertaken and where there is increased emphasis on the quality of the data gathered. The analysis of these data often provides crucial and defensible evidence sought by the experimenter to support (or refute) a particular theory or idea.

The goal of an experiment might be to determine an accurate value for a particular quantity such as the electrical charge carried by an electron. Experimenters are aware that influences exist, some controllable and others less so, that conspire to adversely affect the values they obtain. Despite an experimenter’s best efforts, some uncertainty in an experimentally determined value remains. In the case of the charge on the electron, its value is recognised to be of such importance that considerable effort has gone into establishing an accurate value for it. Currently (2011) the best value for the charge on the electron is (1.602176487 ± 0.000000040) × 10−19 C. A very important part of the expression for the charge is the number following the ± sign. This is the uncertainty in the value for the electronic charge and, though the uncertainty is rather small compared to the size of the charge, it is not zero. In general, every value obtained through measurement has some uncertainty and though the uncertainty may be reduced by thorough planning, prudent choice of measuring instrument and careful execution of the experiment, it cannot be eliminated entirely.