纵谈标准差(分期连载)

On standard deviation (serial)

在误差理论、数理统计理论、计量质量保证方案的制定和测量不确定度的表达中 ,标准差是最重要的参数之一。但对于部分科技人员来说 ,很难对标准差的概念作全面准确的理解 ,因此 ,对上述理论和方法的理解和应用也受到不同程度的影响。针对这种情况 ,用比较浅显的文字介绍了标准差的来源 ,并着重介绍了标准差的物理意义、几何意义和统计意义 ,以及其估算方法和应用方法。与此同时 ,还对分组测量中常用的各种标准差的定义、计算方法和应用范围作了具体介绍。此外 ,2 0世纪末 ,为了评估测量不确定度的B类分量 ,国际标准化组织 (ISO)、国际计量局 (BIPM )等还提出了与传统意义上的标准差的定义完全不同的等价标准差的概念。虽然在学术界对此还存在一定异议 ,但是 ,这种方法已在ISO导则和我国的计量技术规范 (JJF)中正式采用 ,因此 ,对这一类标准差也作了比较详细的介绍 ,以供参考。

Standard deviation (SD) is one of the most important parameters in the error theory, mathematical statistics theory, the drafting of metrological quality assurance program as well as the expression of measurement uncertainty. However, it is difficult for some scientific personnel to achieve a comprehensive and accurate understanding of it, which adversely influences the understanding and applications of the above mentioned theories and methods. Therefore, the author describes in simple terms the origin of SD, emphatically its physical, geometrical, statistical significance and its estimation and application methodologies. Meanwhile, a detailed exposition is also given on the definitions, algorithms and application scopes of various SDs frequently used in group measurement. In addition, with a view to evaluating the component type B of measurement uncertainty, ISO, BIPM, etc. presented in the end of the 20th century the concept of equivalent SD, which is totally different from the SD defined conventionally. This method, although being contentious, has been formally adopted in the related ISO Guide and Chinas codes for metrological technology (JJF). Consequently, SD of this type is also described in detail for reference.