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Vol. 13 No. 5 (2026)
International Multidisciplinary Journal for Research & Development

Articles

MATHEMATICAL MODELS AND STATISTICAL METHODS FOR ANALYZING EXPERIMENTAL DATA

Published 2026-05-17

  • Umidjon Goyipov Gulonjonovich
    • ,
  • Khakimova Nafisa Omonjon qizi

Umidjon Goyipov Gulonjonovich
PhD, Namangan State Technical University

Khakimova Nafisa Omonjon qizi
Master’s Student, Namangan State Technical University

Abstract

The analysis of experimental data occupies an important place in modern scientific research. The reliability, accuracy, and practical significance of scientific conclusions directly depend on the correct application of mathematical models and statistical methods. Mathematical modeling allows researchers to describe natural, technical, economic, and social processes quantitatively, while statistical methods help evaluate the reliability and significance of obtained results. This article examines the theoretical foundations and practical importance of mathematical models and statistical methods used in the analysis of experimental data. Particular attention is paid to regression analysis, correlation analysis, dispersion analysis, probability theory, hypothesis testing, and optimization models. The article also discusses the stages of data processing, methods of assessing statistical reliability, and approaches to eliminating errors in experimental studies. The presented information is based on internationally recognized scientific literature and methodological sources.

Keywords

experimental data, mathematical model, statistical analysis, regression analysis, correlation, dispersion analysis, hypothesis testing, probability theory, statistical reliability, data processing

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References

  1. Montgomery D. C. Design and Analysis of Experiments. New York: Wiley, 2017. pp. 15–48.
  2. Ross S. Introduction to Probability and Statistics for Engineers and Scientists. Academic Press, 2014. pp. 32–76.
  3. Freedman D., Pisani R., Purves R. Statistics. W.W. Norton & Company, 2007. pp. 101–145.
  4. James G., Witten D., Hastie T., Tibshirani R. An Introduction to Statistical Learning. Springer, 2021. pp. 67–120.
  5. Creswell J. Research Design: Qualitative, Quantitative, and Mixed Methods Approaches. Sage Publications, 2018. pp. 50–91.
  6. Boccara N. Modeling Complex Systems. Springer, 2010. pp. 22–59.
  7. Draper N., Smith H. Applied Regression Analysis. Wiley, 1998. pp. 75–138.
  8. Cohen J., Cohen P., West S., Aiken L. Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences. Routledge, 2003. pp. 84–117.
  9. Fisher R. A. Statistical Methods for Research Workers. Oliver and Boyd, 1954. pp. 132–170.
  10. Student. “The Probable Error of a Mean.” Biometrika, 1908. Vol. 6, No. 1, pp. 1–25.
  11. Spiegel M., Stephens L. Theory and Problems of Statistics. McGraw-Hill, 2017. pp. 41–96.
  12. Taylor J. An Introduction to Error Analysis. University Science Books, 1997. pp. 11–58.
  13. Taha H. Operations Research: An Introduction. Pearson, 2016. pp. 201–289.
  14. Popper K. The Logic of Scientific Discovery. Routledge, 2002. pp. 33–78.
  15. Bishop C. Pattern Recognition and Machine Learning. Springer, 2006. pp. 145–221.

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