Measurement Uncertainty in One-of-a-kind Experiments
A golden standard in science is to repeat an experimental measurement multiple times and calculate the measured value with experimental uncertainty by following well developed statistical procedures. For various reasons – cost, technical difficulty, international treaties, ethics of dealing with human or animal subjects, ecology - many important experiments and observations can not be repeated. Astronomy, earthquakes, hurricanes produce data from one-of-a-kind events. When information is not available in any other way, it should not be dismissed as qualitative, anecdotal evidence only. Analyzed in a mathematically rigorous way, it produces quantitative experimental data. Analysis of data from one-of-a-kind event differs from analysis of repeated experiments’ data. For repeated experiments, the experimental error includes a range of true values generated by repetitions of the experiment, and measurement uncertainty caused by detectors. They are independent. Repetitions of any experiment, as similar as achievable, always have built-in differences resulting in a range of the true values rather than in a single value. Measurement uncertainty depends on the measurement system only. Digital measurements have very small uncertainty, frequently smaller than the range of true experimental values resulting from built-in differences in the experiment repetitions. When data from one–of–a kind experiment are analyzed, only the measurement uncertainty can be reported.