Correlation coefficient distribution and its application in the comparison of chemical data sets.

This paper presents a comprehensive statistical framework in order to rigorously derive the correlation coefficient distribution between two independent chemical data sets. The novel approach not only allows for unequivocal interpretation of distribution parameters and confidence intervals but also the generalization of previous results for fixed size comparisons into the new and experimentally important case of variable dimension data assessments. Original theoretical results include an objective criterion ("number of nines") for the coefficient of multiple determination in mathematical model fitting (e.g. calibration curve acceptance in validation protocols) and the requirement of a minimum correlation coefficient match of approximately 70% in variable size evaluations. Significance tests have been applied to the drug profile linkage of 532 real case cocaine samples seized by the National Police of Peru between the years of 2021 and 2022. • A novel and comprehensive mathematical framework to rigorously derive the correlation coefficient distribution between independent data sets. • Generalization of fixed dimension comparisons into the new and experimentally important case of variable size assessments. • Explicit derivation of critical correlation coefficient values in terms of Excel® statistical functions. • Minimum correlation coefficient value of approximately 70% for variable size data evaluations. • Coefficient of multiple determination criterion for calibration curve acceptance in validation protocols. [ABSTRACT FROM AUTHOR]