REVIEW OF NEW STATISTICAL CRITERIA FOR VERIFICATION OF THE HYPOTHESIS OF NORMALITY AND UNIFORMITY OF DISTRIBUTION OF DATA IN SMALL SAMPLES

Abstract

Background. The problem of parallel use of a set of statistical criteria aimed at testing one or another statistical hypothesis is considered. As a rule, on small samples of 16 experiments, statistical tests give a high value of the probabilities of errors of the first and second kind. Materials and methods. However, if we build an equivalent artificial neuron for each of the statistical criteria and combine them into a large network of artificial neurons, then we will get a long code with high redundancy. The reduction of the redundancy of such codes makes it possible to correct the errors of some statistical tests. The paper presents functional dependencies and thresholds used in the software implementation of 11 new criteria and artificial neurons equivalent to them. Several techniques for modifying classical statistical criteria are identified, which allow reducing the values of their probabilities of errors of the first and second kind by up to nine times. Results and conclusions. Presumably, the use of new statistical criteria can make it possible to make decisions with a confidence probability of 0,99 when using 25 artificial neurons equivalent to them.

Keywords

• classical and new statistical criteria
• artificial neurons equivalent to statistical criteria
• parallel statistical analysis of small samples
• error correction of the neural network output code