Reducing sample size requirements for neural network combining the classical Edgeworth-Edleton-Pearson test and its two-fractal counterparts when testing the data independence hypothesis

Abstract

Background. At the end of the 19th century, statisticians began to actively use the Edgeworth-Edleton-Pearson formula, which gives significant errors in the calculation of correlation coefficients on small samples. The purpose of the work is to improve the accuracy of calculations by combining the neural network of three statistical criteria. Materials and methods. In addition to the Edgeworth-Edleton-Pearson formula, it is proposed to use two new versions of fractal statistical criteria synthesized in 2017. Each of the three criteria is represented by an equivalent artificial neuron. Results and conclusions. It is shown that the neural network combination of three statistical criteria makes it possible to reduce the requirements for the size of the test sample by 1.87 times when testing the hypothesis of independence of the analyzed data. A small sample of 16 trials becomes equivalent to using a larger sample of 30 trials. Sharing 4, 5 or more statistical criteria should lead to a monotonous increase in confidence in the neural network decisions. When using 4 statistical tests, a confidence level of 0.9 is expected. Approximately 230 statistical tests would be required to achieve a confidence level of 0.99.

Keywords

• statistical criteria for testing the hypothesis of independence
• artificial neuron equivalent to a statistical criterion
• single-layer neural network
• self-correcting codes capable of detecting and correcting errors