Journal für Mathematik-Didaktik

, Volume 21, Issue 2, pp 101–123 | Cite as

Understanding of the Logic of Hypothesis Testing Amongst University Students

  • Augustias Vallecillos


The Significance testing is one of the most controversial subjects in research work (Morrison & Henkel, 1970) and also one of the most misunderstood topics in statistics learning (Brewer, 1986). In this paper, we present the whole results of a theoretical and experimental study concerning University students’ understanding about the logic of statistical testing. The theoretical study discusses epistemological issues concerning Fisher’s and Neyman-Pearson’s approaches to hypotheses testing and their reiationship with the problem of induction in experimental sciences.


Inductive Inference Mathematical Demonstration Mathematic Education Research Journal Probabilistic Proof Correct Argument 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Signifikanztests sind sowohl ein umstrittener Bereich in der Forschung (Morrison & Henkel, 1970) als auch der von den Lernenden am häufigsten missverstandene Gegenstand in der Stochastik (Brewer, 1986). In dieser Arbeit stellen wir die Ergebnisse einer theoretischen und experimentellen Studie vor, in der es um das Verständnis von Universitätsstudentinnen und -Studenten für die Logik statistischer Tests geht. In der theoretischen Studie werden epistemologische Fragen, die die Entscheidungstheorie beim Testen von Hypothesen nach Fisher und Neyman/Pearson betreffen, und deren Beziehung zum induktiven Schließen in experimentellen Wissenschaften diskutiert.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Altman, D. G. & Martin, B. J. (1991). Improving Doctors’ Understanding of Statistics. Journal of the Royal Statistical Society, Ser. A, 154(2), 223–267.CrossRefGoogle Scholar
  2. Artigue, M. (1990). Épistémologie et Didactique. Recherches en Didactique des Mathématiques, 10(2–3), 241–286Google Scholar
  3. Batanero, C; Godino, J. D; Vallecillos, A; Green, D. & Holmes, P. (1994). Errors and difficulties in understanding elementary statistical concepts. International Journal of Mathematics Education in Science and Technology, 25(4), 527–547.CrossRefGoogle Scholar
  4. Birnbaum I. (1982). Interpreting statistical significance. Teaching Statistics, 4, 24–27.CrossRefGoogle Scholar
  5. Black, M. (1979). Inducción y probabilidad. Madrid: Cátedra, S. A.Google Scholar
  6. Brewer, J. K (1986). Behavioral statistics textbooks source of myths and misconceptions?. In R. Davidson and J Swift (Ed.): Proceedings of the ICOTS II, pp. 127–131. University of Victoria.Google Scholar
  7. Brousseau, G. (1983). Les obstacles épistémologiques et les problèmes en mathématiques. Recherches en Didactique des Mathématiques, 4(2), 164–198.Google Scholar
  8. Burks, A W. (1977). Chance, Cause, Reason. An Inquiry into the Nature of Scientific Evidence. Chicago: The Chicago University Press.Google Scholar
  9. Canavos, G. C. (1986). Probabilidad y Estadística. Aplicaciones y Métodos. Mexico: McGraw-Hill.Google Scholar
  10. Carver, R. P. (1978). The case against statistical significance testing. Harvard Educational Review, 48, 378–399.Google Scholar
  11. Dawes, R. M. (1988). Rational choice in an uncertain world. San Diego: Harcourt Brace Jovanovich.Google Scholar
  12. DeGroot, M. H. (1988). Probabilidad y Estadística. Mexico: AddisonWesley Iberoamericana, S. A.Google Scholar
  13. Falk, R. (1986). Misconceptions of Statistical Significance. Journal of Structural Learning. 9, 83–96.Google Scholar
  14. Falk, R. & Greenbaum, C. W. (1995). Significance tests die hard. Theory and Psychology, 5(1), 75–98.CrossRefGoogle Scholar
  15. Fine, T. L. (1973). Theories of probability: An examination of foundations. New York: Academic Press.Google Scholar
  16. Fisher, R. A. (1935). The logic of inductive inference. Journal of the Royal Statistical Society, 98, 39–54.CrossRefGoogle Scholar
  17. Gephart R. P. (1988). Ethnostatistics: Qualitative foundations for quantitative research. Sage University Paper Series on Qualitative Research Methods, Vol. 2. Beverly Hills, CA: Sage.Google Scholar
  18. Gingerenzer, G. (1989). The Superego, the Ego, and the Id in statistical reasoning. En G. Keren and C. Lewis (Eds.): A handbook for data analysis in the behavioural sciences Methodological issues, pp. 311–339. Hillsdale, NJ: Erlbaum.Google Scholar
  19. Godino, J. D.; Batanero, C. & Cañizares, Ma J. (1987). Azar y Probabilidad. Madrid: Síntesis.Google Scholar
  20. Godino J. D. & Batanero, C. (1994). Significado institucional y personal de los objetos matemáticos. Recherches en Didactique des Mathématiques, 14(3), 325–355.Google Scholar
  21. Lehmann, E. L. (1993). The Neyman-Pearson theories of testing hypotheses: one theory or two? Journal of the American Statistical Association, 88, 424, 1242–1249.CrossRefGoogle Scholar
  22. Lindley, D. (1993). The Analysis of Experimental Data. The appreciation of Tea and Wine. Teaching Statistics, 15(1), 22–25.CrossRefGoogle Scholar
  23. Lindsay, R. M. (1988). The use of tests of significance in accounting research. a methodological, philosophical and empirical inquiry. Ph. D. Thesis University of Lancaster. U. K.: UMI.Google Scholar
  24. Menon, R. (1993). Statistical Significance Testing Should be Discontinued in Mathematics Education Research. Mathematics Education Research Journal, 5(1), 4–18.CrossRefGoogle Scholar
  25. Morrison, D. E. & Henkel, R. E. (Eds.). (1970). The Significance Tests Controversy -A Reader. Chicago. Aldine.Google Scholar
  26. Oakes, M. (1986). Statistical inference A commentary for the social and behavioural sciences. Chichester: Wiley.Google Scholar
  27. Pollard, P. & Richardson, J. T. E. (1987). On the probability of making Type I errors. Psychological bulletin, 10, 159–163.CrossRefGoogle Scholar
  28. Popper, K. (1967). La lógica de la investigación científica. Madrid: Tecnos.Google Scholar
  29. Reeves, C. A. & Brewer, J. K. (1980). Hypothesis Testing and Proof by contradiction: An Analogy. Teaching Statistics, Band 1/2, 57–59.Google Scholar
  30. Rivadulla, A. (1991). Probabilidad e Inferencia Científica. Barcelona: Anthropos.Google Scholar
  31. Rowley. G. (1993). Response to Menon. Mathematics Education Research Journal, 5(1), 28–29.CrossRefGoogle Scholar
  32. Sierra, R. (1985). Técnicas de investigación social Teoría y ejercicios. Madrid: Paraninfo.Google Scholar
  33. Smith, T. M. E. (1993). Population and Selection. Limitation of Statistics. Journal of the Royal Statistical Society, 156, Part. 2, 145–166.Google Scholar
  34. Taylor, S. J. & Bogdan, R. (1986). Introducción a los Métodos Cualitativos de Investigación. Buenos Aires: Paidos.Google Scholar
  35. Vallecillos, A. (1994). Estudio teórico-experimental de errores y concepciones sobre el contraste estadístico de hipótesis en estudiantes universitarios. Ph. D. Granada: Universidad de Granada.Google Scholar
  36. Vallecillos, A. (1995a). Comprensión de la lógica del contraste de hipótesis en estudiantes universitarios. Recherches en Didactique des Mathématiques, 15(3), 53–81.Google Scholar
  37. Vallecillos, A. (1995b). Consideraciones epistemológicas sobre la inferencia estadística: implicaciones para la práctica docente. UNO, 80–90.Google Scholar
  38. Vallecillos, A. (1996a). Inferencia estadística y enseñanza: un análisis didáctico del contraste de hipótesis estadísticas. Granada: Comares.Google Scholar
  39. Vallecillos, A. (1996b). Student’ conceptions of the logic of the logic of hypothesis testing. Hiroshima Journal of Mathematics Education, 4, 43–61.Google Scholar
  40. Vallecillos, A. (1997). El papel de las hipótesis estadísticas en los contrastes: concepciones y dificultades de aprendizaje. Educación Matemática, 9(2), 5–20.Google Scholar
  41. Vallecillos, A. (1998). Experimental study on the learning of the significance level concept. Proceedings of the ICOTS 5, Vol. 3, 1475–1476. Singapore.Google Scholar
  42. Vallecillos, A. (1999). Some empirical evidences on learning difficulties about testing hypotheses. Invited paper. Proceedingof the 52nd Session of the International Statistical Institute, Vol. 2, pp. 201–204. The Netherland: ISI.Google Scholar
  43. Vallecillos, A. & Batanero, C. (1995). La inferencia estadística en la investigación experimental en el campo educativo. Revista de Educación de la Universidad de Granada, 8, 5–16.Google Scholar
  44. Vallecillos, A. & Batanero, C. (1996). Conditional probability and the level of significance in the tests of hypotheses. Proceedings of the 20 PME, Vol. 4, 371–378.Google Scholar
  45. Valencia (Spain). Vallecillos, A. & Batanero, C. (1997). Comprensión de la lógica del contraste de hipótesis en estudiantes universitarios. Recherches en Didactique des Mathématiques, 17(1), 29–48.Google Scholar
  46. Vallecillos, A. & Holmes, P. (1994). Student’s understanding of the logic of hypotheses testing. Proceedings of the ICOTS 4, Vol. 2, 477. Marrakech (Morocco).Google Scholar
  47. White, A. L (1980). Avoiding Errors in Educational Research. In R. J. Shumway (Ed.) Research in Mathematics Education, pp. 47–65. Reston, Va: NCTM.Google Scholar
  48. Zacks, S. (1981). Parametric Statistical Inference. Basic Theory and Modern Approaches. Oxford: Pergamon Press.Google Scholar

Copyright information

© GDM - Gesellschaft für Didaktik der Mathematik 2000

Authors and Affiliations

  1. 1.Didáctica de la Matemática Facultad de Ciencias de la Educación. Campus de CartujaUniversidad de GranadaEspaña

Personalised recommendations