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

Zacca J.J.; Sandoval Jáuregui C.P.; Villafana Bardales F.M.; Remuzgo Yabar J.; Enciso Soria J.E.; Ayala Caro V.D. · Chemometrics and Intelligent Laboratory Systems (2024) · DOI: 10.1016/j.chemolab.2024.105091

Resumen

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.