Application of Mathematical Statistics Methods in Assessing the Reliability of Forensic Testing Techniques

Quantitative assessment of reliability of forensic testing techniques (FTT) is not given sufficient attention. In this article, we use the metrological parameter of validation—“reliability,” which is understood as the reproducibility of test results, with multiple repetitions of tests for samples with known characteristics/properties under varying conditions: different operators, use of different equipment, different time. The quantitative characteristic of FTT reliability is the level of false positive and false negative results in the total number of tests. The specificity of control samples for the experiment and the need to take into account the variability of features in them are emphasized, the use of samples with a distinct manifestation of controlled features for validation is recommended. Statistical assessment of test results consists in calculating the indicators (experimental probability) of errors according to the given formulas. Formulas for calculating various indicators related to true positive and negative results are also given. A binary classification table is provided to present the results of the validation experiment. As an example, the correspondence of the indicators (experimental probabilities) to the true probabilities of events is given for the case of a comparative study of the situation with a pair of samples: “the same source of origin (coincidence)” and “different sources of origin (mismatch).” Formulas are given for the approximate calculation of the confidence limits for the binomial distribution, which most of the binary response methods considered in the work obey. A practical example of calculating the confidence interval in the validation of a specific FTT technique is considered. It is shown that, based on the experimentally established indicators of the true results of “sensitivity” and “specificity” and in the presence of a priori data on the prevalence of samples by a set of controlled characteristics, using the Bayesian formula, it is possible to calculate the proportions of false positive/negative analytical calls (FPC and FNC). Low values of the FPS and FNS indicators indicate the trueness of testing or the trueness of the decision made and the suitability of the technique for its intended purposes.