相对误差对相关系数影响的统计特性  

Statistical Properties of Influence of Relative Error on Correlation Coefficient

作　　者：丁勇 Ding Yong(School of Science,Kangda College of Nanjing Medical University,Lianyungang Jiangsu 222000,China)

机构地区：[1]南京医科大学康达学院理学部

出　　处：《统计与决策》2018年第18期78-81,共4页Statistics & Decision

摘　　要：在两个变量之一有相对误差的情况下,文章研究了相对误差对相关系数的影响。推导了有误差数据的相关系数的总体均数和相对总体均数的近似公式,计算机模拟研究表明,近似公式有较高的精度。从统计特性来看,受相对误差影响,相关系数的绝对值会变小;相对误差越小,相关系数受到的影响也越小;有误差数据的二阶原点矩与二阶中心矩比值越小,相关系数受到的影响也越小。This paper studies the influence of relative error on correlation coefficient under the condition that one of the two variables has a relative error. The paper also derives an approximate formula for the population mean of the correlation coefficient of error data and the relative population mean. Computer simulation shows that the approximate formula has a relatively higher precision. From the perspective of statistical characteristics, the absolute value of the correlation coefficient decreases under the influence of relative error; the smaller the relative error, the smaller influence the correlation coefficient is affected; the smaller the ratio of second order origin moment to second order center moment of error data, the smaller the influence of correlation coefficient.

关 键 词：相对误差 相关系数 计算机模拟 二阶矩 

分 类 号：O212.1[理学—概率论与数理统计]