A Study on the Treatment of Uncertainty in Linear Regression Method for Chemical Analysis

회귀식 사용에 따른 화학 분석 과정의 불확도 처리 연구

  • Woo, Jin-Chun (Division of Chemical Metrology and Materials Evaluation, Korea Research Institute of Standards and Science(KRISS)) ;
  • Suh, JungKee (Division of Chemical Metrology and Materials Evaluation, Korea Research Institute of Standards and Science(KRISS)) ;
  • Lim, MyungChul (Division of Chemical Metrology and Materials Evaluation, Korea Research Institute of Standards and Science(KRISS)) ;
  • Park, MinSu (Department of Environmental Engineering, Daejeon University)
  • 우진춘 (한국표준과학연구원, 물질량표준부) ;
  • 서정기 (한국표준과학연구원, 물질량표준부) ;
  • 임명철 (한국표준과학연구원, 물질량표준부) ;
  • 박민수 (대전대학교, 환경공학과)
  • Received : 2002.10.11
  • Accepted : 2003.04.09
  • Published : 2003.06.25

Abstract

We applied modified least square method (MLS) and ordinary least square method (OLS) to 1st order equation for the comparison of the uncertainties calculated by these methods. The uncertainty calculated by OLS covered statistically safe interval because it was over-estimated in many cases of measurement and concentration level. But, if the uncertainty of the concentration as a reference value was comparably large (about 5% of the relative standard deviation of random scattering from the regression line and about 7% of relative standard uncertainty of reference values), then uncertainty calculated by OLS was seriously under-estimated at high concentration level. It was revealed that the calculated uncertainty didn't cover statistically safe interval at the stated confidence level. It was found that the method, MLS, described in the previously article would be valid for this calculation of uncertainty.

Keywords

uncertainty;linear regression;calibration curve

References

  1. NIST, Techincal Note 1297 Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results NIST
  2. Statistics and Experimental Design in Engineer and Physical Science(2nd. Ed.) v.Ⅰ N. L. Johnson;F. C. Leone
  3. Bull. Korean Chem. Soc. v.22 Jumg-Ki Suh;Jin-Chun Woo;Dong-Min Moon;Minsoo Park
  4. Quantifying Uncertainty in Analytical Measurements EURACHEM
  5. 불확도 계산 컴퓨터 보조 프로그램(Version 2) PUMA
  6. DIN 1319-7 Grundlagan der Messtechnik
  7. KRISS-99-070-SP 측정불확도 표현 지침 한국표준과학연구원
  8. Guide to the Expression of Uncertainty in Measurements ISO