Systematic Errors: Facts and Fictions

The treatment of systematic errors is often mishandled. This is due to lack of understanding and education, based on a fundamental ambiguity as to what is meant by the term. This note addresses the problems and offers guidance to good practice. 1 RIVAL DEFINITIONS: UNCERTAINTY AND MISTAKE 1.1 Random Uncertainties and Mistakes The word error is used in several ways. The everyday dictionary definition is a synonym for mistake. In statistics this usage continues (as in ‘Type I error’ for the rejection of a true hypothesis and ‘Type II error’ for the acceptance of a false one) but it is also used in the sense of discrepancy: the statistician writes the equation of a straight line fit as where is the ‘error term’, the difference between the measured and the ideal value. A physicist does not use this language; their interest is concentrated not on the actual discrepancy of a single measurement, but on the overall uncertainty. They write a straight line as where the equals sign signifies agreement to some uncertainty (or resolution) , and they will call this the ‘error’. (In early texts this was called the ‘probable error’ but the ‘probable’ got dropped.) This use of ‘error’ to mean ‘uncertainty’ rather than ‘mistake’ or ‘discrepancy’ is common in the language, for example ‘error bar’, ‘error analysis’, and ‘quoted error on the result.’ Suppose a set of measurements have been made of the same quantity, and the values are