The Normal, Chi-squared and Student’s T Distributions in the Teaching of Biostatistics for Students of Medical Sciences

Rafael Mauro Avila Avila; Maria del Carmen Exposito Gallardo; Julio Cesar Pino Tarrago

doi:doi:10.11648/j.sjams.20221002.11

| Peer-Reviewed

The Normal, Chi-squared and Student’s T Distributions in the Teaching of Biostatistics for Students of Medical Sciences

Rafael Mauro Avila Avila, Maria del Carmen Exposito Gallardo, Julio Cesar Pino Tarrago

Published in Science Journal of Applied Mathematics and Statistics (Volume 10, Issue 2)

Received: 21 December 2021 Accepted: 14 January 2022 Published: 8 April 2022

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

The normal, Chi-Squared and Student’s t distribution are three of the most important in the teaching learning process of Biostatistics for the specialty of Medicine. However, the absence of a deductive approach in the introduction to the topics, makes difficult to understand its origin. From the starting point of the systems of continue distributions of probability, it is proposed an alternative way to introduce the normal distribution in general and standard form, as well as the analytic expressions for the Chi-Squared and Student’s T distributions. Some epistemic gaps in the treatment of the thematic are identified by means of the analytic synthetic and documentary review methods. The essential objectives consist of the deduction the mathematical expression of such distribution as well as to value the possibility to introduce the basic elements of the used procedure, in the program of Biostatistics, emphasizing the notions of Differential Calculus developed in previous stage to the Integral Calculus. The essential conclusion is associated to the contribution of the suggested approach to the rigor and harmony of mathematical statistic knowledge in the discipline, although some concepts of Mathematical Analysis are necessary in order to facilitate the understanding of the practical applications in the career of Medicine and in other branches of the research in biomedical sciences.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 10, Issue 2)
DOI	10.11648/j.sjams.20221002.11
Page(s)	15-21
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Biostatistics, Normal Distribution, Pearson’s Distributions, Teaching Learning Process

References

[1]	Torres Delgado, J. A., Rubén Quesada, M., Bayarre Vea, H., Garriga Sarría, E. P., Pría Borras, M. C., & Gran Álvarez, M. et al. (2004). Informática Médica, tomo II Bioestadística. Centro de Cibernética Aplicada a la Medicina (CECAM). Editorial Ciencias Médicas: La Habana, 2004.
[2]	Koroliuk, V. V. (1986). Manual de la teoría de las probabilidades y estadística matemática. Moscú: Mir.
[3]	Gnedenko, B. V. (1997). The theory of probability. Overseas Publishers Association: Netherlands.
[4]	Whittle, P. (1982). Probability. Moscow: Nauka (in Russian Languaje).
[5]	Guerra Bustillo, C. W., Menéndez Acuña, E., Barrera Morera, R., & Egaña Morales, E. (1991). Estadística. La Habana: Pueblo y Educación.
[6]	Freund, J. E., Perles, B. M. (2007). Modern Elementary Statistics (12th International Editions). Pearson Prentice Hall: New Jersey.
[7]	Chistiakov, B. P. (1982). Course on Probability Theory. Moscow: Nauka (in Russian Languaje).
[8]	Ander-Egg, E. (1995). Métodos y Técnicas de investigación social. Vol. III: Cómo organizar el trabajo de investigación. Lumen: Buenos Aires.
[9]	Giacosa, N., Vergara, M. L., Zang, C., López, J., Galeano, R., Godoy, N. & et al. (2015). Libros de texto y Programas Analíticos de Física en carreras de Ingeniería de la UNaM. Revista de Enseñanza de la Física, 199-207, 27 (no extra).
[10]	Van Belle, G.; Fisher, L. D.; Heagerty, P. J., & Lumley, T. (2004). Biostatistics. A Methodology for the Health Sciences. New Jersey: John Wiley & Sons.
[11]	Herrerías Pleguezuelo, R., & Callejón Céspedes, J. (2017). Los sistemas de Pearson como generadores de distribuciones de probabilidad. Aplicaciones estadísticas y económicas. http://www. ugr. es/~callejon/lossistemas. pdf
[12]	Weisstein, Eric W. (2017) Pearson System. MathWorld, A Wolfram. http://mathworld.wolfram.com/PearsonSystem.html.
[13]	Ávila, Ávila, R. M, Pino Tarragó, J. M., Expósito Gallardo, M. C., & Domínguez Gálvez, D. L. (2020). La distribución normal en ciencias biomédicas: un enfoque a partir de las distribuciones de Pearson. Revista Sinapsis; Vol 1, No 16.
[14]	Cherniick, M. R., & Riss, R. H. (2003). Introductory Biostatistics for the Health Sciences. Modern Applications Including Bootstrap. New Jersey: John Wiley & Sons.
[15]	Valdés Castro, C., & Sánchez Fernández, C. (2011). Introducción al Análisis Matemático. La Habana: Félix Varela.
[16]	Escalona Fernández, L. A. (2020). Alternativa didáctica para desarrollar el proceso de enseñanza-aprendizaje de la Bioestadística en la carrera de Medicina. Acta Latinoamericana de Matemática. Vol. 33, Número 1.
[17]	Elgoltz, L. E. (2010). Ecuaciones diferenciales y cálculo variacional. Félix Varela: La Habana.
[18]	Robinson, J. C. (2004). An introduction to Ordinary Differential Equation. University Press: Cambridge.
[19]	Escalona Fernández, L. A., & Velázquez, J. R. (2012). Resolución de problemas de optimización sin el uso de límites y derivadas. Interpretaciones médicas”. En: Flores, R. (ed.). Acta Latinoamericana de Matemática Educativa 25, 365-374.
[20]	Escalona Fernández, L. A. (2013). Resolución de problemas matemáticos aplicados a la medicina y su impacto en la formación del médico general”. Correo Científico Médico Holguín; volumen: vol. 17, No. 24.
[21]	Bowman, W. C., & Raud, M. J. (1984). Farmacología. Bases bioquímicas y patológicas. Aplicaciones clínicas. Interamericana: México D. F.
[22]	Oliva González, L., & O’Farril Mons, E. (1988). Bioestadística y computación: guía de estudio. La Habana: Pueblo y Educación.
[23]	D’Agostino, R. B., Sullivan, L. M., & Beiser, A. S. (2006). Introductory applied biostatistics. Thomson, Brooks/Cole: Toronto.
[24]	Bluman, A. G. (2009). Elementary Statistics: A Step by Step Approach. McGraw-Hill Companies, Inc.: New York.
[25]	Lancaster, H. O. (2011). Quantitative Methods in Biological and Medical Sciences: A Historical Essay. Springer: New York.
[26]	Anderson, S. J. (2012). Biostatistics. A Computing Approach. Boca Raton: CRC Press.
[27]	Indrayan, A., & Kumar Malhotra, R. (2018). Medical Biostatistics. Boca Raton: CRC Press.

Cite This Article

Plain Text BibTeX RIS

APA Style

Rafael Mauro Avila Avila, Maria del Carmen Exposito Gallardo, Julio Cesar Pino Tarrago. (2022). The Normal, Chi-squared and Student’s T Distributions in the Teaching of Biostatistics for Students of Medical Sciences. Science Journal of Applied Mathematics and Statistics, 10(2), 15-21. https://doi.org/10.11648/j.sjams.20221002.11

Copy | Download

ACS Style

Rafael Mauro Avila Avila; Maria del Carmen Exposito Gallardo; Julio Cesar Pino Tarrago. The Normal, Chi-squared and Student’s T Distributions in the Teaching of Biostatistics for Students of Medical Sciences. Sci. J. Appl. Math. Stat. 2022, 10(2), 15-21. doi: 10.11648/j.sjams.20221002.11

Copy | Download

AMA Style

Rafael Mauro Avila Avila, Maria del Carmen Exposito Gallardo, Julio Cesar Pino Tarrago. The Normal, Chi-squared and Student’s T Distributions in the Teaching of Biostatistics for Students of Medical Sciences. Sci J Appl Math Stat. 2022;10(2):15-21. doi: 10.11648/j.sjams.20221002.11

Copy | Download

@article{10.11648/j.sjams.20221002.11,
  author = {Rafael Mauro Avila Avila and Maria del Carmen Exposito Gallardo and Julio Cesar Pino Tarrago},
  title = {The Normal, Chi-squared and Student’s T Distributions in the Teaching of Biostatistics for Students of Medical Sciences},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {10},
  number = {2},
  pages = {15-21},
  doi = {10.11648/j.sjams.20221002.11},
  url = {https://doi.org/10.11648/j.sjams.20221002.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20221002.11},
  abstract = {The normal, Chi-Squared and Student’s t distribution are three of the most important in the teaching learning process of Biostatistics for the specialty of Medicine. However, the absence of a deductive approach in the introduction to the topics, makes difficult to understand its origin. From the starting point of the systems of continue distributions of probability, it is proposed an alternative way to introduce the normal distribution in general and standard form, as well as the analytic expressions for the Chi-Squared and Student’s T distributions. Some epistemic gaps in the treatment of the thematic are identified by means of the analytic synthetic and documentary review methods. The essential objectives consist of the deduction the mathematical expression of such distribution as well as to value the possibility to introduce the basic elements of the used procedure, in the program of Biostatistics, emphasizing the notions of Differential Calculus developed in previous stage to the Integral Calculus. The essential conclusion is associated to the contribution of the suggested approach to the rigor and harmony of mathematical statistic knowledge in the discipline, although some concepts of Mathematical Analysis are necessary in order to facilitate the understanding of the practical applications in the career of Medicine and in other branches of the research in biomedical sciences.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - The Normal, Chi-squared and Student’s T Distributions in the Teaching of Biostatistics for Students of Medical Sciences
AU  - Rafael Mauro Avila Avila
AU  - Maria del Carmen Exposito Gallardo
AU  - Julio Cesar Pino Tarrago
Y1  - 2022/04/08
PY  - 2022
N1  - https://doi.org/10.11648/j.sjams.20221002.11
DO  - 10.11648/j.sjams.20221002.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 15
EP  - 21
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20221002.11
AB  - The normal, Chi-Squared and Student’s t distribution are three of the most important in the teaching learning process of Biostatistics for the specialty of Medicine. However, the absence of a deductive approach in the introduction to the topics, makes difficult to understand its origin. From the starting point of the systems of continue distributions of probability, it is proposed an alternative way to introduce the normal distribution in general and standard form, as well as the analytic expressions for the Chi-Squared and Student’s T distributions. Some epistemic gaps in the treatment of the thematic are identified by means of the analytic synthetic and documentary review methods. The essential objectives consist of the deduction the mathematical expression of such distribution as well as to value the possibility to introduce the basic elements of the used procedure, in the program of Biostatistics, emphasizing the notions of Differential Calculus developed in previous stage to the Integral Calculus. The essential conclusion is associated to the contribution of the suggested approach to the rigor and harmony of mathematical statistic knowledge in the discipline, although some concepts of Mathematical Analysis are necessary in order to facilitate the understanding of the practical applications in the career of Medicine and in other branches of the research in biomedical sciences.
VL  - 10
IS  - 2
ER  -

Copy | Download

Author Information

Rafael Mauro Avila Avila

Department of Mathematics, Faculty of Informatics and Mathematics, Holguin University, Holguin, Cuba
Maria del Carmen Exposito Gallardo

Department of Informatics, University of Medical Sciences, Holguin, Cuba
Julio Cesar Pino Tarrago

Civil Engineering, Manabi South State University, Manabí, Ecuador

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Rafael Mauro Avila Avila, Maria del Carmen Exposito Gallardo, Julio Cesar Pino Tarrago. (2022). The Normal, Chi-squared and Student’s T Distributions in the Teaching of Biostatistics for Students of Medical Sciences. Science Journal of Applied Mathematics and Statistics, 10(2), 15-21. https://doi.org/10.11648/j.sjams.20221002.11

Copy | Download

ACS Style

Rafael Mauro Avila Avila; Maria del Carmen Exposito Gallardo; Julio Cesar Pino Tarrago. The Normal, Chi-squared and Student’s T Distributions in the Teaching of Biostatistics for Students of Medical Sciences. Sci. J. Appl. Math. Stat. 2022, 10(2), 15-21. doi: 10.11648/j.sjams.20221002.11

Copy | Download

AMA Style

Rafael Mauro Avila Avila, Maria del Carmen Exposito Gallardo, Julio Cesar Pino Tarrago. The Normal, Chi-squared and Student’s T Distributions in the Teaching of Biostatistics for Students of Medical Sciences. Sci J Appl Math Stat. 2022;10(2):15-21. doi: 10.11648/j.sjams.20221002.11

Copy | Download

@article{10.11648/j.sjams.20221002.11,
  author = {Rafael Mauro Avila Avila and Maria del Carmen Exposito Gallardo and Julio Cesar Pino Tarrago},
  title = {The Normal, Chi-squared and Student’s T Distributions in the Teaching of Biostatistics for Students of Medical Sciences},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {10},
  number = {2},
  pages = {15-21},
  doi = {10.11648/j.sjams.20221002.11},
  url = {https://doi.org/10.11648/j.sjams.20221002.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20221002.11},
  abstract = {The normal, Chi-Squared and Student’s t distribution are three of the most important in the teaching learning process of Biostatistics for the specialty of Medicine. However, the absence of a deductive approach in the introduction to the topics, makes difficult to understand its origin. From the starting point of the systems of continue distributions of probability, it is proposed an alternative way to introduce the normal distribution in general and standard form, as well as the analytic expressions for the Chi-Squared and Student’s T distributions. Some epistemic gaps in the treatment of the thematic are identified by means of the analytic synthetic and documentary review methods. The essential objectives consist of the deduction the mathematical expression of such distribution as well as to value the possibility to introduce the basic elements of the used procedure, in the program of Biostatistics, emphasizing the notions of Differential Calculus developed in previous stage to the Integral Calculus. The essential conclusion is associated to the contribution of the suggested approach to the rigor and harmony of mathematical statistic knowledge in the discipline, although some concepts of Mathematical Analysis are necessary in order to facilitate the understanding of the practical applications in the career of Medicine and in other branches of the research in biomedical sciences.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - The Normal, Chi-squared and Student’s T Distributions in the Teaching of Biostatistics for Students of Medical Sciences
AU  - Rafael Mauro Avila Avila
AU  - Maria del Carmen Exposito Gallardo
AU  - Julio Cesar Pino Tarrago
Y1  - 2022/04/08
PY  - 2022
N1  - https://doi.org/10.11648/j.sjams.20221002.11
DO  - 10.11648/j.sjams.20221002.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 15
EP  - 21
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20221002.11
AB  - The normal, Chi-Squared and Student’s t distribution are three of the most important in the teaching learning process of Biostatistics for the specialty of Medicine. However, the absence of a deductive approach in the introduction to the topics, makes difficult to understand its origin. From the starting point of the systems of continue distributions of probability, it is proposed an alternative way to introduce the normal distribution in general and standard form, as well as the analytic expressions for the Chi-Squared and Student’s T distributions. Some epistemic gaps in the treatment of the thematic are identified by means of the analytic synthetic and documentary review methods. The essential objectives consist of the deduction the mathematical expression of such distribution as well as to value the possibility to introduce the basic elements of the used procedure, in the program of Biostatistics, emphasizing the notions of Differential Calculus developed in previous stage to the Integral Calculus. The essential conclusion is associated to the contribution of the suggested approach to the rigor and harmony of mathematical statistic knowledge in the discipline, although some concepts of Mathematical Analysis are necessary in order to facilitate the understanding of the practical applications in the career of Medicine and in other branches of the research in biomedical sciences.
VL  - 10
IS  - 2
ER  -

Copy | Download