EMUE-D5-4-MethodComparisonWithCorrelation

Quantifying uncertainty when comparing measurement methods – Haemoglobin concentration as an example of correlation in straight-line regression

In metrology, often two methods measuring the same quantity are to be judged whether or not they are in agreement. For measurements across a whole range of values, this can be done by comparing their straight-line fit to the identity line. Such a comparison is only meaningful, when uncertainties are available. Furthermore, the estimates of the straight-line fit and their uncertainties are only reliable when all sources of uncertainty have been accounted for. In particular, the measurements of both methods in a comparison are usually uncertain, and common instruments or standards cause correlation among or between them.

When fitting a straight-line relation, the weighted total least-squares (WTLS) method accounts for correlation and uncertainties in both variables. This example focuses on WTLS and defines a measurement model from it to propagate all uncertainties and correlations through to the estimate of the slope and intercept, and associate uncertainties with them according to the GUM. Using the example of two high  accuracy methods measuring the total haemoglobin concentration in blood, i.e. the cyanmethaemoglobin and alkaline haematin method, we indicate how correlations can be inferred, demonstrate how they can be accounted for and show their impact on the regression. The results are discussed and recommendations are given.

Files contained in the dataset are:

• Example_A233.pdf: Report “Quantifying uncertainty when comparing measurement methods – Haemoglobin concentration as an example of correlation in straight-line regression”;
• Example_A233.tex: LaTeX file to be compiled in order to produce Example_A233.pdf;
• Compendium_A233.bib: bibliography file;
• Fig1a.pdf: PDF file needed to compile Example_A233.tex;
• Fig1b.pdf: PDF file needed to compile Example_A233.tex;
• Fig2a.pdf: PDF file needed to compile Example_A233.tex;
• Fig2b.pdf: PDF file needed to compile Example_A233.tex;
• data_A233.csv: data file containing the estimates and associated standard uncertainties for the measurements;
• Example_A233.Rmd: R Markdown file for quantifying uncertainty when comparing two measurement methods. As output an HTML file similar to Example_A233.pdf is created with results dynamically produced by underlying R code;
• aps.csl: CSL file needed to cite the reference in example_A233.Rmd according to the American Physical Society style.