Type A evaluation of measurement uncertainty when the sample size is not predetermined

Abstract

The archetypal procedure in Type A evaluation of measurement uncertainty involves making n observations of the same quantity, taking the sample figure s² to be an unbiased estimate of the underlying variance and quoting the figure s / sqrt(n) as the relevant standard uncertainty. Although this procedure is theoretically valid when the sample size n is fixed, it is not necessarily valid when n is chosen in response to the growing dataset. In fact, when the experimenter makes observations until a certain level of uncertainty in the mean is reached, the bias in the estimation of the variance can be as much as -45 %. Likewise, the usual nominal 95 % confidence interval can have a level of confidence as low as 88 %. This issue is discussed and techniques are suggested so that Type A evaluation of uncertainty becomes as accurate as is implied. The 'objective Bayesian' approach to this issue is discussed and an associated unacceptable phenomenon is identified.