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Central Limit Theorem–An illustration based on simulated data using R

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Author Affiliations

  • 1Division of Biostatistics, MOSC Medical College, Ernakulam, 682311, Kerala, India
  • 2Department of Biostatistics, Jawaharlal Institute of Postgraduate Medical Education & Research, Puducherry, 605006, India

Res. J. Mathematical & Statistical Sci., Volume 12, Issue (2), Pages 4-7, September,12 (2024)

Abstract

The central limit theorem is the most fundamental theory in modern statistics and quite an important concept in biostatistics, and data science. The central limit theorem states that the sampling distribution of the mean for a variable will approximate a normal distribution regardless of that variable’s distribution in the population, when the sample size is large. In real life we cannot repeat studies (resampling) many times to estimate the sampling distribution of the mean. Hence only a simulation-based illustration is possible to understand the concept of central limit theorem. Present study aims to provide a clear understanding of the concept of central limit theorem with the help of simulated data using R codes.

References

  1. Gerald, B., & Patson, T. F. (2021)., Parametric and nonparametric tests: A brief review., Int J Stat Distrib Appl, 7(3), 78-82.
  2. Habibzadeh, F. (2024)., Data distribution: normal or abnormal?., Journal of Korean medical science, 39(3).
  3. Razali, N. M., & Wah, Y. B. (2011)., Power comparisons of shapiro-wilk, kolmogorov-smirnov, lilliefors and anderson-darling tests., Journal of statistical modeling and analytics, 2(1), 21-33.
  4. Rostampour, M., & Azarmi-Atajan, F. (2023)., Comparison of normality test methods for some soil properties in the arid land of South Khorasan., Desert, 28(2), 381-402.
  5. Kwak, S. G., & Kim, J. H. (2017)., Central limit theorem: the cornerstone of modern statistics., Korean journal of anesthesiology, 70(2), 144-156.
  6. Dunbar, S. R. (2011)., The de moivre-laplace central limit theorem., Topics in Probability Theory and Stochastic Processes.
  7. Glencross, M. J. (1988)., A practical approach to the Central Limit Theorem., In Proceedings of the second international conference on teaching statistics (pp. 91-95).
  8. Adams, W. J. (2009)., The life and times of the central limit theorem (Vol. 35)., American Mathematical Soc..
  9. Rathore, G. S. (2023)., Biostatistics And Research Methodology., Academic Guru Publishing House.
  10. Pitman, J. (2012)., Probability., Springer Science & Business Media.
  11. Gerber, S. B., & Finn, K. V. (2005)., Basic Ideas of Probability., Using SPSS For Windows: Data Analysis and Graphics, 91-94.
  12. Moscarelli, M. (2023)., Biostatistics With, Springer.