Skip to main navigation menu Skip to main content Skip to site footer
Logo Revista Latinoamericana de Investigación en Matemática Educativa

Artículos

Vol. 16 No. 2 (2013): Julio

THE CHARACTERISTICS OF COLLEGE STUDENTS ’ STATISTICAL REASONING ON HYPOTHESIS TESTING

DOI
https://doi.org/10.12802/relime.13.1622
Submitted
July 13, 2023
Published
2023-07-13

Abstract

This article shows the results from a research on college students' statistical inference learning process from the major in mathematics. It was specially focused on the students' statistical reasoning on the concepts and processes that involved hypothesis testing. The results were analyzed based on the Structure of Observed Learning Outcomes (SOLO). They showed that students are primarly in the prestructural and unistructural level, which means that they have isolated information about the different concepts involved in hypothesis testing and/or that they take into consideration some relevant aspect of the process without having full awareness of what they are doing. Moreover, it was noticed that there are misguided conceptions on the nature of hypothesis testing and the main concepts involved such as the level of significance, value p and the formulation of the hypothesis.

References

  1. Batanero, C. (2000). Controversies around the role of statistical tests in experimental research. Mathematical Thinking and Learning: An International Journal 2 (1-2), 75-97.
  2. Biggs, J. B.; Collis, K. F. (1982). Evaluating the Quality of Learning: The Solo Taxonomy. New York: Academic Press.
  3. Carver, R. (1978). The case against statistical significance testing. Harvard Educational Review 48 (3), 378-399.
  4. Castro Sotos, A. E., Vanhoof, S., Van den Noortgate, W.; Onghena, P. (2007). Students' misconceptions of statistical inference: A review of the empirical evidence from research on statistics education. Educational Research Review 2 (2), 98-113.
  5. Chance, B., del Mas, R.; Garfield, J. (2004). Reasoning about sampling distributions. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 295-323). Netherlands: Kluwer Academic Publishers.
  6. Cumming, G. (2010). Understanding, teaching and using p values [CD-ROM]. In Ch. Reading (Ed.), Proceedings of the 8th International Conference on Teaching Statistics. Ljubljiana Slovenia: University of Slovenia.
  7. Garfield, J. (2002). The Challenge of Developing Statistical Reasoning. Journal of Statistics Education 10 (3). Recuperado el 08 de octubre de 2010 de http://www.amstat.org/publications/jse/v10n3/garfield.html
  8. Garfield, J.; Ben-Zvi, D. (2008). Developing Students 'Statistical Reasoning. Connecting Research and Teaching Practice. The Netherlands: Springer.
  9. Gigerenzer, G. (1993). The superego, the ego and the id in statistical reasoning. In G. Keren & C. Lewis (Eds.), A handbook for data analysis in the behavioral sciences (Vol. 1, pp. 311-339). Hillsdale: Erlbaum.
  10. Good, P. I. & Hardin, J. W. (2009). Common Errors in Statistics (and how to avoid them). (3th ed.). New Jersey: John Wiley and Sons, Inc.
  11. Grings, R.; Viali, L. (2011). Teste de Hipóteses: uma análise dos erros cometidos por alunos de engenharia. Boletim de Educaqao Matemática 24 (40), 835-854.
  12. Huberty, C. J. (1993). Historical origins of statistical testing practices: The treatment of Fisher versus Neyman-Pearson views in the textbooks. Journal of Experimental Education 61 (4), 317-333.
  13. Inzunsa, S. (2010). Entornos virtuales de aprendizaje: un enfoque alternativo para la enseñanza y aprendizaje de la inferencia estadística. Revista Mexicana de Investigación Educativa 15 (45), 423-452.
  14. Kirk, R. (2001). Promoting good statistical practices: some sugestions. Educational and Psychological Measurement 61 (2), 213-218.
  15. Kline, R. B. (2004). Beyond Significance Testing. Reforming Data Analysis Methods in Behavioral Research. Washington: American Psychological Association.
  16. Levin, J. R. (1998). What If There Were No More Bickering About Statistical Significance Tests? Research in Schools 5 (2), 43-53.
  17. Lipson, K. (2000). The role of the sampling distribution in developing understanding of statistical inference. Doctoral Thesis unpublished, Swinburne University of Technology, Swinburne, Australia.
  18. Lipson, K. (2002). The role of computer based technology in developing understanding of the concept of sampling distribution [CD-ROM]. Proceedings of the 6th International Conference on Teaching of Statistics. Cape Town South Africa: South African Statistical Association.
  19. Liu, Y.; Thompson, P. W. (2005). Teachers' understanding of hypothesis testing [CD-ROM]. In S. Wilson (Ed.), Proceedings of the 27thAnnual Meeting of the International Group for the Psychology of Mathematics Education. Virginia: Virginia Tech University.
  20. McLean, A. (2002). Statistacy: Vocabulary and Hypothesis Testing [CD-ROM]. In B. Phillips (Ed.), Proceedings of the 6th International Conference on Teaching of Statistic. Cape Town South Africa: South African Statistical Association.
  21. McLean, J. E; Ernest, J. M. (1998). The Role of Statistical Significance Testing In Educational Research. Research in Schools 5 (2), 15-22.
  22. Mittag, K. C.; Thompson, B. (2000). A National Survey of AERA Member's Perceptions of Statistical Significance Tests and Other Statistical Issues. Educational Researcher 29(4), 14-20.
  23. Monterrey, P.; Gómez-Restrepo, C. (2007). Aplicación de las pruebas de hipótesis en la investigación en salud: ¿estamos en lo correcto? Universitas Médica 48 (3), 193-206.
  24. Moore, D. S. (1992). ¿What is Statistics? In D. C. Hoaglin & D. S. Moore (Eds.), Perspectives on Contemporary Statistics (pp. 1-17). Washington: Mathematical Association of America.
  25. Morrison, D. E. & Henkel, R. E. (1970). The Significance Test Controversy. New Brunswick: Transactions Publishers.
  26. Pfannkuch, M. (2005). Characterizing year 11 student's evaluation of a statistical process. Statistics Education Research Journal 4 (2), 5-25. Recuperado el 08 de dieciembre de 2010. de http://www.stat.auckland.ac.nz/serj.
  27. Reading, Ch.; Reid, J. (2006). An emerging hierarchy of reasoning about distribution: from a variation perspective. Statistics Education Research Journal 5(2), 46-68. Recuperado el 15 de diciembre de 2010 de http://www.stat.auckland.ac.nz/serj.
  28. Robinson, D. H.; Levin, J.R. (1997). Reflections on statistical and substantive significance with a slice of replication. Educational Researcher 26 (5), 21-26.
  29. Rossman A.; Chance, B. (1999). Teaching the reasoning of statistical inference: A "top ten" list. College Mathematical Journal 30 (4), 297-305. Recuperado el 20 de octubre de 2010 de http://rossmanchance.com/papers/topten.html
  30. Stigler, S. M. (1986). The history of statistics: The measurement of the uncertainty before 1900. Cambridge, MA: Belknap.
  31. Triola, M. F. (2009). Estadística. México: Pearson Educación.
  32. Vallecillos, A. (1996). Inferencia estadística y enseñanza: un análisis didáctico del contraste de hipótesis estadísticas. Granada: Editorial Colmenares.
  33. Vallecillos, A. (1997). El papel de las hipótesis estadísticas en los contrastes: Concepciones y dificultades de aprendizaje. Educación Matemática 9 (2), 5-20.
  34. Vizcarra, F.; Inzunsa, S. (2009). Un estudio sobre la caracterización del razonamiento estadístico de estudiantes de preparatoria: el caso de los promedios y las gráficas [CD-ROM]. Memorias del XXII Congreso Nacional de Enseñanza de las Matemáticas, Tuxtla Gutiérrez Chiapas, México: Asociación Nacional de Profesores de Matemáticas.
  35. Williams, A. M. (1998). Students' understanding of the significance level concept. In L. Pereira Mendoza, L. Seu Kea, T. Wee Kee & W. Wong ( (Eds.), Proceedings of the 5th International Conference on Teaching Statistics. Singapur Korea: University of Korea.
  36. Xitao, F. (2001). Statistical Significance and Effect Size in Education Research: Two Sides of a Coin. The Journal of Educational Research 94 (5), 275-282.
  37. Yañez, G.; Behar, R. (2010). The confidence intervals: a difficult matter, even for experts [CD-ROM]. In Ch. Reading (Ed.), Proceedings of the 8th International Conference on Teaching Statistics. Ljubljiana Slovenia: University of Slovenia.

Downloads

Download data is not yet available.

Similar Articles

1 2 3 4 5 6 7 8 9 10 > >> 

You may also start an advanced similarity search for this article.