In this chapter we present four case studies based on typical undergraduate experiments, involving the determination of best estimates of measurands, standard uncertainties, expanded uncertainties and coverage intervals. For completeness, we include a brief description of each experiment. The equipment required is inexpensive or can usually be found in an undergraduate science laboratory. The account of each experiment contains data obtained in an actual experiment.

We have not included a detailed introduction to each experiment, nor have we indicated how each might be improved or ‘finessed’. The account of each experiment is biased towards giving details of the data analysis such as the calculations of standard uncertainties and coverage intervals. A more detailed analysis would normally require consideration of the uncertainty in the calibration of instruments used. For many undergraduate experiments such information is not available, and therefore we have not included the contribution of the calibration uncertainty to the combined standard uncertainty. At the end of the account of each experiment we suggest practically based exercises related to the experiment.

Reporting measurement results

An account of an experiment, as presented in a formal report, may contain many sections with headings such as introduction, materials and methods, results, analysis and conclusion. With respect to the analysis of data, best estimates of particular quantities obtained through experiment and by other means should be communicated clearly, concisely, and in a manner that is useful to others.