基于数理统计方法的水质总氮校准曲线残差值检验

Residual Value Test of Determination Calibration Curve of Total Nitrogen in Water Based on Mathematical Statistics Method

(目的)探讨水质总氮校准曲线残差值的正态性、独立性、同方差性。(方法)一年内对不同浓度的硝酸盐氮标准使用液进行了6次测定,对测定结果进行校准曲线拟合,计算残差值。通过QQ图及Anderson—Darling(AD)法检验残差值的正态性;通过图示法及DW法检验残差值的独立性;通过残差图及等级相关系数法检验残差值的同方差性。结果表明,该曲线残差值满足正态性,不满足独立性和同方差性。(结论)使用普通最小二乘法对数据进行曲线拟合需建立在一系列假定条件上,因此实际工作中不能盲目默认相关假定条件成立,应将数理统计理论与化验检测实际相结合,保障曲线拟合的可靠性。

Objective Exploring the normality,independence,and homoscedasticity of residual values in the determination calibration curve of total nitrogen in water.Methods Six measurements of nitrate nitrogen standard solutions with different concentrations were conducted within a year,and the calibration curve was fitted using the measurement results to calculate the residual value.Test the normality of residual values through QQ diagrams and Anderson Darling(AD)method;Test the independence of residual values through graphical and DW methods;Test the homoscedasticity of residual values through Residual Plots and Rank Correlation Coefficient methods.Results The residual value of this sample satisfies normality,but does not satisfy independence and homoscedasticity.Conclusion The curve fitting of data using Ordinary Least Squares method needs to be based on a series of assumptions.In actual work,we cannot blindly default the establishment of relevant assumptions,and should combine mathematical statistics theory with laboratory testing to ensure the reliability of curve fitting.