论文标题
在$ \ sqrt {χ^2/ν} $缩放处方时出现的好奇偏见首先应用于单个结果的子样本
On a curious bias arising when the $\sqrt{χ^2/ν}$ scaling prescription is first applied to a sub-sample of the individual results
论文作者
论文摘要
众所周知，加权平均值的标准偏差仅取决于单个标准偏差，而不取决于平均值周围值的分散。该属性有时会导致令人尴尬的局势，在这种情况下，结合结果与单独的结果“看起来”。解决问题的一种实用方法是通过$ \ sqrt {χ^2/ν} $缩放扩大产生的标准偏差，这是一种具有任意标准的处方，何时应用于该标准以及在组合中使用哪些个人结果。但是，综合结果与单个结果之间的“明显”差异往往仍然存在。此外，即使单个结果的模式高度偏斜，该规则也不会影响所得的“最佳价值”。除了许多从业人员共享的不满意的原因外，该方法还引起了另一个问题，最近在已发表的被带电的Kaon Mass的测量中指出。实际上，如果将处方应用两次，即首先应用于单个结果的子样本，然后将其施加到整个样本中，则会引入整体组合的结果。原因是该处方不能保证统计充分性，其在本脚本中提醒其重要性，并以教义精神写成，并带有一些历史笔记，并以大多数物理学家习惯的语言。该结论包含有关实验发现有效呈现的一般性评论，附录中提出了相关的难题。
As it is well known, the standard deviation of a weighted average depends only on the individual standard deviations, but not on the dispersion of the values around the mean. This property leads sometimes to the embarrassing situation in which the combined result 'looks' somehow at odds with the individual ones. A practical way to cure the problem is to enlarge the resulting standard deviation by the $\sqrt{χ^2/ν}$ scaling, a prescription employed with arbitrary criteria on when to apply it and which individual results to use in the combination. But the `apparent' discrepancy between the combined result and the individual ones often remains. Moreover this rule does not affect the resulting `best value', even if the pattern of the individual results is highly skewed. In addition to these reasons of dissatisfaction, shared by many practitioners, the method causes another issue, recently noted on the published measurements of the charged kaon mass. It happens in fact that, if the prescription is applied twice, i.e. first to a sub-sample of the individual results and subsequently to the entire sample, then a bias on the result of the overall combination is introduced. The reason is that the prescription does not guaranty statistical sufficiency, whose importance is reminded in this script, written with a didactic spirit, with some historical notes and with a language to which most physicists are accustomed. The conclusion contains general remarks on the effective presentation of the experimental findings and a pertinent puzzle is proposed in the Appendix.
