Synthesis of four new neuro-statistical tests for testing the hypothesis of independence of small samples of biometric data

Abstract

The paper considers the analysis of small samples according to several statistical criteria to test the hypothesis of independence, since the direct calculation of the correlation coefficients using the Pearson formula gives an unacceptably high error on small biometric samples. Each of the classical statistical criteria for testing the hypothesis of independence can be replaced with an equivalent artificial neuron. Neuron training is performed based on the condition of obtaining equal probabilities of errors of the first and second kind. To improve the quality of decisions made, it is necessary to use a variety of statistical criteria, both known and new. It is necessary to form networks of artificial neurons, generalizing the number of artificial neurons that is necessary for practical use. It is shown that the classical formula for calculating the correlation coefficients can be modified with four options. This allows you to create a network of 5 artificial neurons, which is not yet able to reduce the probability of errors in comparison with the classical formula. A gain in the confidence level in the future can only be obtained when using a network of more than 23 artificial neurons, if we apply the simplest code to detect and correct errors.