Small datasets comprising observations made under conditions of repeatability or of reproducibility pervade the practice of measurement science. Many laboratories typically will make only one determination, occasionally they will make two, and only rarely will they make three or more replicate determinations of the same measurand. Interlaboratory comparisons, including key comparisons, and meta-analyses, often involve only a handful of participants. These limitations pose considerable challenges to the production of reliable uncertainty evaluations. This contribution, intended for metrologists, describes techniques that may be employed to address this challenge either when the only information in hand is what those few observations provide, or when there also is preexisting knowledge about the measurement procedure or about the measurand. Although the technical details vary, the key message is persistently the same: that there is no universal solution to the challenges raised by small datasets, and that if a measurand is worth measuring, then the observations deserve a customized treatment responsive to the peculiarities of the case, and a level of effort sufficient to render the final result fit for its intended purpose. The focus is on the measurement of scalar measurands, similarly to the Guide to the Expression of Uncertainty in Measurement (GUM), but the range of measurement models considered is much wider than the GUM entertains. We review the advantages of the Hodges–Lehmann estimator, as a general purpose replacement for the arithmetic average, in all cases where the replicated observations are approximately symmetrically distributed around a central, typical value. We illustrate the application of empirical Bayes methods to uncertainty evaluations, in particular in the context of data reductions of small data sets. Metrologists who are skeptical about the use of subjective prior distributions may derive some value from this novel application, and thereby develop an appreciation for how Bayesian procedures can help address the challenges posed by small datasets. The estimates of the measurand that different approaches produce often agree, at least approximately, but the corresponding uncertainty quantifications may differ markedly. In one example, involving three observations, a Bayesian approach yields a coverage interval appreciably narrower than the GUM’s approach. In another example, involving only two observations, an approach involving far less restrictive assumptions than those made in the GUM, produces a confidence interval that is almost as narrow as the conventional interval.

包含在可重复性或可再现性条件下进行的观察的小型数据集遍布测量科学的实践。许多实验室通常只会做出一个决定，偶尔会做出两个决定，而很少会做出三个或更多个相同测量对象的重复决定。实验室间的比较，包括关键比较和荟萃分析，通常只涉及少数参与者。这些局限性给可靠的不确定性评估产生了很大的挑战。本专为计量学家设计的文稿描述了可用于应对这一挑战的技术，既可以在掌握的唯一信息就是很少的观测结果所提供的信息时，也可以在已有关于测量程序或被测量者的知识的情况下使用。尽管技术细节各不相同，但关键信息始终如一：没有统一的解决方案来解决小型数据集所带来的挑战，并且如果要衡量的是值得衡量的指标，那么观察结果就应根据客户的特殊性进行定制化处理。案例，以及足以使最终结果适合其预期目的的工作水平。重点是标量被测量物的测量，类似于测量不确定度表示指南（GUM），但考虑的度量模型范围比GUM的娱乐范围要广得多。我们回顾了在所有重复观测值围绕中心典型值对称对称分布的所有情况下，Hodges-Lehmann估计器的优点，它可以代替算术平均值。我们说明了经验贝叶斯方法在不确定性评估中的应用，特别是在小数据集的数据缩减的情况下。对主观先验分布的使用持怀疑态度的计量学家可能会从这种新颖的应用程序中获得一些价值，从而对贝叶斯方法如何帮助解决小型数据集所带来的挑战产生了赞赏。对不同方法产生的被测量值的估算通常至少一致，但是相应的不确定性量化可能会明显不同。在涉及三个观察结果的一个示例中，贝叶斯方法产生的覆盖间隔比GUM方法要窄得多。在仅涉及两个观察结果的另一个示例中，这种方法所包含的限制性假设远少于GUM中的限制性假设，所产生的置信区间几乎与常规区间一样窄。