Reporting uncertainties in measurement: what approach should be followed?

Abstract

Much of the work of a scientist or engineer involves taking measurements. For example, a radiation oncology medical physicist measures the absorbed dose in a water phantom. However any measurement has some limit in the accuracy of the final value you obtain. This is due to limits in the accuracy of the measuring equipment, any bias in the measurements, calibration issues or simple mistakes you make. All of these contribute to an uncertainty in the value of the parameter you are measuring. For example, the absorbed dose of radiation from a linear accelerator can be measured in a water phantom using a well characterised ionisation chamber. In this particular case of radiation dose measurement, there will be uncertainties due to the equipment consisting of an ionisation chamber, electrometer and the water phantom. There will also be uncertainties in the setup of the equipment, the linear accelerator. Traditionally these uncertainties are characterised as random errors or systematic errors. Random errors can be minimised by taking multiple measurements while the reduction of systematic uncertainties requires a good understanding of the equipment. Systematic errors are often ‘‘fixed’’ by application of some calibration factor or may be even missed. The method used to determine the uncertainty of a measurement is widely varied. For example, you can repeat the measurements a number of times usually between 3 and 5, and from this calculate the standard deviation. A more systematic approach is to determine random and systematic errors and summate these together to give the final uncertainty in your parameter. This takes a bit more time and requires that you have a good understanding of your equipment. Finally, you can ignore your errors, assume your equipment is working correctly and just quote your results. A review of published papers in any medical physics or biomedical engineering journal will show a similar variation in reporting of uncertainties. This can give the impression of a much lower uncertainty in your measurements. For example, the IAEA TRS 398 dosimetry protocol reports that the estimated relative uncertainty in the dose calibration of megavoltage X-ray beams is ±1.5 % [1]. Therefore any absolute dose measurements using these X-ray beams must have an uncertainty larger than this. There is a more uniform approach for uncertainty analysis as prescribed by the International Organization for Standardization (ISO). The ISO has published a document called the ‘‘Guide to the expression of uncertainties in R. Hill (&) Department of Radiation Oncology, Royal Prince Alfred Hospital, Missenden Road, Camperdown, NSW 2050, Australia e-mail: robin.hill@email.cs.nsw.gov.au