A Review on the Statistical Methods and Implementation to Homogeneity Assessment of Certified Reference Materials in Rel
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REVIEW PAPER
A Review on the Statistical Methods and Implementation to Homogeneity Assessment of Certified Reference Materials in Relation to Uncertainty A. Kumar and D. K. Misra* CSIR National Physical Laboratory, Dr. K. S. Krishnan Marg, New Delhi 110012, India Received: 26 October 2019 / Accepted: 16 June 2020 Metrology Society of India 2020
Abstract: An importance of data analysis, methods for homogeneity test and standard uncertainty evaluation associated in any measurement for exact quantification of certified value of any product is vital to be stressed in the scientific community. Herein, we have collectively summarized the detailed discussion on the basics of statistical parameters such as mean, median, mode, standard deviation, variance, range, normal distribution, and central limit theorem. Various statistical analysis methods such as z test, t test, Chi-squared test, and ANOVA including F test have also been discussed in great detail to test the homogeneity of samples for certification of the reference material. The ISO guide 35 (2006) and Guide to Uncertainty in Measurement (GUM) are primarily considered to describe the basic concept of evaluating the associated uncertainty in the light of GUM modelling approach to avoid the error in the measurement which normally occurs in many scientific reports. Keywords: Homogeneity; Certified reference material; Associated uncertainty; Certification; Measurement List of Symbols X Sample mean l Population mean 2 r Variance n Number of data in sample N Number of data in population SSwithin Sum of squares within the samples MSwithin Mean of the square within the samples Xt True value us Standard uncertainty Uexp Expanded uncertainty ubb Between the bottle uncertainty ur Uncertainty due to repeatability k Coverage factor r Standard deviation rx Standard error H0 Null hypothesis Ha Alternative hypothesis X Grand mean SSbetween Sum of squares between the samples MSbetween Mean of the square between the samples Xmeas Measured value
*Corresponding author, E-mail: [email protected]
uc ustab uwithin umeas
Combined uncertainty Uncertainty due to stability Within the bottle uncertainty Measurement uncertainty
1. Introduction Statistical methods play a crucial role in data analysis and interpretation of results and have found great importance in various fields of physical, chemical, biological, agricultural, environmental, and social sciences with more applications in engineering. The inadequate interpretations of statistical analysis may lead to erroneous conclusions of any scientific study. The studies resulting in a large volume of raw data require suitable reduction so that data could be understood in a facile manner and provide information without affecting the result. It is worth mentioning that statistical errors can be found in many procedures such as assumptions-based statistical methods, traditional analysis, and randomly observed experimental data. The International Standard Organization (ISO) has formulated a set of basic guidelines for statistical analys
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