Sample distribution of observations of the falling number of corn flour

Abstract

The sample distribution of observations is studied in order to study the variational feature, while the measured value is considered as random. For practical purposes, the empirical distribution of a random variable is estimated by proximity to the theoretical law. The statistical hypothesis of the sample data belonging to the general population is tested using the consent criteria. The object of this study was the observation of the falling number of corn flour, which is a prescription component of bakery products. In world practice, the falling number method for raw materials from corn is used as a reference for establishing reference interval values, detecting a variation of the studied trait. The purpose of this work was to study the sample distribution of observations of the falling number of corn flour to determine the representativeness of the sample of experimental data. Relying on Glivenko's theorem on the expediency of grouping sample data into a variation series in order to replace the distribution function of the general population with a sample distribution function, at the beginning of the research, the sample data were converted into a statistical series. The research material was an industrial sample of fine-ground corn flour that meets the requirements of GOST 14176-69 "Corn flour. Technical conditions". The falling number was studied when implementing the standard method on the PPP-99 device according to GOST ISO 2093-2016 "Grain and its processed products. Determination of the number of falls by the Hagberg-Perten method". The interval variation series was studied according to a wide list of characteristics: distribution center indicators (sample mean, mode, median, quartiles, deciles), variation indicators (span, average linear deviation, variance, unbiased variance estimate, mean square deviation, coefficient of variation, linear coefficient of variation, oscillation coefficient), distribution form indicators (relative quartile variation index, asymmetry coefficient, Pearson structural asymmetry coefficient, kurtosis index), indicators of interval estimation of the center of the general population (confidence intervals for the general average, interval estimation of the general share, i.e. the probability of an event). For the studied random variable of the falling number of corn flour, the hypothesis of a normal distribution was proved using the indicators of asymmetry and kurtosis, as well as using the 3σ sigma rule. As a result of the calculations, the representativeness of the sample data with respect to the variation of the studied trait in the general population was established