FEASIBILITY STUDY OF USING BOOTSTRAP TO COMPUTE THE UNCERTAINTY CONTRIBUTION FROM FEW REPEATED MEASUREMENTS

Information on possible values of a quantity can be gained in various ways and be expressed by a probability density function (PDF) for this quantity. Its expectation value is then taken as the best estimate of the value and its standard deviation as the uncertainty associated with that value. A coverage interval can also be computed from that PDF. Information given by a small number n of values obtained from repeated measurements requires special treatment. The Guide to the Expression of Uncertainty in Measurement recommends in this case the t-distribution approach that is justified if one knows that the PDF for the measured quantity is a Gaussian. The bootstrap approach could be an alternative. It does not require any information on the PDF and -based on the plugin principle- can be used to estimate the reliability of any estimator. This paper studies the feasibility of the bootstrap approach for a small number of repeated measurements. Emphasis is laid on methods for a systematic comparison of t-distribution and bootstrap approach. To support this comparison, a fast algorithm has been developed for computing the total bootstrap and total median.