粗差发现和定位能力与相关系数的关系

Abstract

根据粗差判断方程中的判断矩阵和两个统计检验量之间相关系数的函数式,论证了两种不同的研究方法所确定的粗差不能定位的数学模型实际上是相等的。通过算例,不仅说明两种研究方法对观测量不能定位粗差的判断是一致的,而且使用判断矩阵研究观测量的粗差发现和定位能力会更加方便简单。 On the basis of the judgement matrix of gross errors judgement equation and the function formulation of correlation coefficient between two testing values, this paper proves that both the mathematical models, in fact, are equivalent. The results of a familiar example which gross errors in the observations can not be identified based on judgement matrix are appeared to be exactly the same as that correlation coefficients between their testing values are equal to 1. Furthermore, the gross errors detectability and identifiability of observations analyzed by the judgement matrix would be more convenient and simple than by the method based correlation coefficient.