Methods for nonparametric statistics in scientific research. Overview. Part 2

The use of nonparametric methods in scientific research provides a number of advantages. The most important of these advantages are versatility and a wide range of such methods. There are no strong assumptions associated with nonparametric tests, which means that there is little chance of assumptions being violated, i. e. the result is reliable and valid. Nonparametric tests are widely used because they may be applied to experiments for which it is not possible to obtain quantitative indicators (descriptive studies) and to small samples. The second part of the article describes nonparametric goodness-of-fit tests, i. e. Pearson’s test, Kolmogorov test, as well as tests for homogeneity, i. e. chi-squared test and Kolmogorov-Smirnov test. Chi-squared test is based on a comparison between the empirical (experimental) frequencies of the indicator under study and the theoretical frequencies of the normal distribution. Kolmogorov-Smirnov test is based on the same principle as Pearson’s chi-squared test, but involves comparing the accumulated frequencies of the experimental and theoretical distributions. Pearson’s chi-squared test and Kolmogorov test may also be used to compare two empirical distributions for the significance of differences between them. Kolmogorov test based on the accumulation of empirical frequencies is more sensitive to differences and captures those subtle nuances that are not available in Pearson’s chi-squared test. Typical errors in the application of these tests are analyzed. Examples are given, and step-by-step application of each test is described. With nonparametric methods, researcher receives a working tool for statistical analysis of the results.The use of nonparametric methods in scientific research provides a number of advantages. The most important of these advantages are versatility and a wide range of such methods. There are no strong assumptions associated with nonparametric tests, which means that there is little chance of assumptions being violated, i. e. the result is reliable and valid. Nonparametric tests are widely used because they may be applied to experiments for which it is not possible to obtain quantitative indicators (descriptive studies) and to small samples. The second part of the article describes nonparametric goodness-of-fit tests, i. e. Pearson’s test, Kolmogorov test, as well as tests for homogeneity, i. e. chi-squared test and Kolmogorov-Smirnov test. Chi-squared test is based on a comparison between the empirical (experimental) frequencies of the indicator under study and the theoretical frequencies of the normal distribution. Kolmogorov-Smirnov test is based on the same principle as Pearson’s chi-squared test, but involves comparing the accumulated frequencies of the experimental and theoretical distributions. Pearson’s chi-squared test and Kolmogorov test may also be used to compare two empirical distributions for the significance of differences between them. Kolmogorov test based on the accumulation of empirical frequencies is more sensitive to differences and captures those subtle nuances that are not available in Pearson’s chi-squared test. Typical errors in the application of these tests are analyzed. Examples are given, and step-by-step application of each test is described. With nonparametric methods, researcher receives a working tool for statistical analysis of the results

Methods for nonparametric statistics in scientific research. Overview. Part 1.

Daily, researcher faces the need to compare two or more observation groups obtained under different conditions in order to confirm or argue against a scientific hypothesis. At this stage, it is necessary to choose the right method for statistical analysis. If the statistical prerequisites are not met, it is advisable to choose nonparametric analysis. Statistical analysis consists of two stages: estimating model parameters and testing statistical hypotheses. After that, the interpretation of the mathematical processing results in the context of the research object is mandatory. The article provides an overview of two groups of nonparametric tests: 1) to identify differences in indicator distribution; 2) to assess shift reliability in the values of the studied indicator. The first group includes: 1) Rosenbaum Q-test, which is used to assess the differences by the level of any quantified indicator between two unrelated samplings; 2) Mann-Whitney U-test, which is required to test the statistical homogeneity hypothesis of two unrelated samplings, i. e. to assess the differences by the level of any quantified indicator between two samplings. The second group includes sign G-test and Wilcoxon T-test intended to determine the shift reliability of the related samplings, for example, when measuring the indicator in the same group of subjects before and after some exposure. Examples are given; step-by-step application of each test is described. The first part of the article describes simple nonparametric methods. The second part describes nonparametric tests for testing hypotheses of distribution type (Pearson’s chi-squared test, Kolmogorov test) and nonparametric tests for testing hypotheses of sampling homogeneity (Pearson’s chi-squared test for testing sampling homogeneity, Kolmogorov-Smirnov test)

Cyber-physical systems in food production chain

The article reviews the state-of-the-science in the field of cyber-physical systems (CPSs). CPSs are intelligent systems that include physical, biological and computational components using engineering networks. CPSs are able to integrate into production processes, improve the exchange of information between industrial equipment, qualitatively transform production chains, and effectively manage business and customers. This is possible due to the ability of CPSs to manage ongoing processes through automatic monitoring and controlling the entire production process and adjusting the production to meet customer preferences. A comprehensive review identified key technology trends underlying CPSs. These are artificial intelligence, machine learning, big data analytics, augmented reality, Internet of things, quantum computing, fog computing, 3D printing, modeling and simulators, automatic object identifiers (RFID tags). CPSs will help to improve the control and traceability of production operations: they can collect information about raw materials, temperature and technological conditions, the degree of food product readiness, thereby increasing the quality of food products. Based on the results, terms and definitions, and potential application of cyber-physical systems in general and their application in food systems in particular were identified and discussed with an emphasis on food production (including meat products).The article reviews the state-of-the-science in the field of cyber-physical systems (CPSs). CPSs are intelligent systems that include physical, biological and computational components using engineering networks. CPSs are able to integrate into production processes, improve the exchange of information between industrial equipment, qualitatively transform production chains, and effectively manage business and customers. This is possible due to the ability of CPSs to manage ongoing processes through automatic monitoring and controlling the entire production process and adjusting the production to meet customer preferences. A comprehensive review identified key technology trends underlying CPSs. These are artificial intelligence, machine learning, big data analytics, augmented reality, Internet of things, quantum computing, fog computing, 3D printing, modeling and simulators, automatic object identifiers (RFID tags). CPSs will help to improve the control and traceability of production operations: they can collect information about raw materials, temperature and technological conditions, the degree of food product readiness, thereby increasing the quality of food products. Based on the results, terms and definitions, and potential application of cyber-physical systems in general and their application in food systems in particular were identified and discussed with an emphasis on food production (including meat products)

Nonparametric statistics. Part 3. Correlation coefficients

A measure of correlation or strength of association between random variables is the correlation coefficient. In scientific research, correlation analysis is most often carried out using various correlation coefficients without explaining why this particular coefficient was chosen and what the resulting value of this coefficient means. The article discusses Spearman correlation coefficient, Kendall correlation coefficient, phi (Yule) correlation coefficient, Cramér’s correlation coefficient, Matthews correlation coefficient, Fechner correlation coefficient, Tschuprow correlation coefficient, rank-biserial correlation coefficient, point-biserial correlation coefficient, as well as association coefficient and contingency coefficient. The criteria for applying each of the coefficients are given. It is shown how to establish the significance (insignificance) of the resulting correlation coefficient. The scales in which the correlated variables should be located for the coefficients under consideration are presented. Spearman rank correlation coefficient and other nonparametric indicators are independent of the distribution law, and that is why they are very useful. They make it possible to measure the contingency between such attributes that cannot be directly measured, but can be expressed by points or other conventional units that allow ranking the sample. The benefit of rank correlation coefficient also lies in the fact that it allows to quickly assess the relationship between attributes regardless of the distribution law. Examples are given and step-by-step application of each coefficient is described. When analyzing scientific research and evaluating the results obtained, the strength of association is most commonly assessed by the correlation coefficient. In this regard, a number of scales are given (Chaddock scale, Cohen scale, Rosenthal scale, Hinkle scale, Evans scale) grading the strength of association for correlation coefficient, both widely recognized and not so well known