Systematic Errors: facts and fictions

摘要: The treatment of systematic errors is often mishandled. This due to lack understanding and education, based on a fundamental ambiguity as what meant by the term. note addresses problems offers guidance good practice. 1 RIVAL DEFINITIONS: UNCERTAINTY AND MISTAKE 1.1 Random Uncertainties Mistakes word error used in several ways. everyday dictionary definition synonym for mistake. In statistics this usage continues (as ‘Type I error’ rejection true hypothesis II acceptance false one) but it also sense discrepancy: statistician writes equation straight line fit where ‘error term’, difference between measured ideal value. A physicist does not use language; their interest concentrated actual discrepancy single measurement, overall uncertainty. They write equals sign signifies agreement some uncertainty (or resolution) , they will call ‘error’. (In early texts was called ‘probable ‘probable’ got dropped.) ‘error’ mean ‘uncertainty’ rather than ‘mistake’ or ‘discrepancy’ common language, example bar’, analysis’, ‘quoted result.’ Suppose set measurements have been made same quantity, values are ! " $# These exhibit 3rd decimal place, mistake that one clearly belong with others. Statistics provides tools identify It can be estimated from rms deviation about mean, then specifying accuracy number would needed achieve desired accuracy, so on. mistake, it. We see value 1.52 wrong or, more correctly, probability being produced measurement consistent others small we reject cannot tell us do next. Perhaps transcription 1.25. taken while apparatus still warming up. an unforeseen Nobel-prize-winning effect. right wrong. What next has experience sense, prescribe 1.2 Systematic For consistency physicists must way random error: denote But consider following two definitions ‘Systematic effects general category which includes such background, selection bias, scanning efficiency, energy resolution, angle variation counter efficiency beam