A tutorial review of some elementary concepts in the statistical evaluation of trace element measurements

Abstract This tutorial review discusses the concepts of limit of detection, C L , limit of identification (=limit of guarantee for purity), C I , and limit of determination, C D , from an elementary, statistical point of view. The interrelation between the limit of detection and the limit of identification is treated in terms of α and β errors. It is emphasized that limits of detection, though they are useful figures of merit of a complete analytical procedure, represent safeguards only to not mistaking random fluctuations of the blank for true analyte signals (“α error”). Customers of analytical chemists, however, intuitively want to be informed about the maximum concentrations present in their samples that might escape attention (“β error”), and therefore they are inclined to interpret the limits of detection stated in reports of analytical chemists as if they were limits of identification. The paper further elaborates the dependence of C L and C I on two distinct numbers of measurements, viz. the number (N) that underlies the determination of standard deviations ( s ) and the number ( n ) that underlies the determination of means. It is illustrated that limits of identification are at least a factor of 3 to 4 above the “2σ limits of detection” commonly reported in the literature. The author concludes that, in spite of the fact that the basic concepts concerning the definition, determination and interpretation of detection limits are well established, psychological barriers remain to be removed before these concepts can be fully implemented in analytical chemistry.