Factors Considered by Secondary Students When Judging the Validity of a Given Statistical Generalization

Hanan Ayoub Innabi

doi:10.29333/iejme/182

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Hanan Ayoub Innabi

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Abstract

This study investigated the factors that 12th grade students in the United Arab Emirates take into consideration when judging the validity of a given statistical generalization, particularly, in terms of the sample size and sample selection bias. The sample consisted of 360 students who had not studied sampling yet. Results show that a small percentage of the students take the sample size and selection bias into consideration properly. Many students based their judgment on their personal beliefs regardless of the properties of the selected sample. This study identified some pre-teaching misconceptions that students have with regard to sampling. Such misconceptions include ‘any sample represents the population’, and, ‘any sample does not represent the population’.

Keywords

Statistical Thinking
Sampling
Judging Generalizations
Secondary School Students

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 2, Issue 3, October 2007, 168-186

https://doi.org/10.29333/iejme/182

Publication date: 12 Dec 2007

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References

Bar-Hillel, M. (1979). The role of sample size in sample evaluation. Organizational Behavior and Human Performance, 24, 245-257.
Bar-Hillel, M. (1982). Studies of representativeness. In D. Kahneman, P. Slovic, & A. Tversky (Eds.), Judgment under uncertainty: Heuristics and biases (pp 69-83). Cambridge: Cambridge University Press.
Cosmides, L., & Toody, J. (1996). Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty. Cognition, 58, 1-73.
Ennis, R. (1985). A logical basis for measuring critical thinking. Educational Leadership, 43 (2), 44-48.
Evans, J. (1989). Bias in human reasoning: causes and consequences. London: Lawrence Erlbaum.
Evans, J., & Dusoir, A. (1977). Proportionality and sample size as factors in statistical judgments. Acta Psychologica, 41, 129-137.
Falk, R. (1989). Judgment of coincidences: Mine versus yours. American Journal of Psychology, 102, 477-493.
Fong, G., Krantz, D., & Nisbett, R. (1993). The effects of statistical training on thinking about everyday problems. In R. Nisbett (Ed.), Rules for reasoning (pp 91- 139). London: Lawrence Erlbaum
Innabi, H. (1999). Students’ understanding of the relationship between sample and population. Unpublished Ph.D. University of Nottingham, England.
Kahneman, D., & Tversky, A. (1972). Subjective probability: A judgment of representativeness. Cognitive Psychology, 3, 430-454.
Kahneman, D., & Tversky, A. (1973). On the psychology of prediction. Psychological Review, 80, 237-251.
Kahneman, D., Tversky, A. (1979). The simulation heuristic. In D. Kahneman, P. Slovic, & A. Tversky (Eds.), Judgment under uncertainty: Heuristics and biases (pp 201-208). Cambridge: Cambridge University Press.
Konold, C. (1989). Informal conceptions of probability. Cognition and Instruction, 6, 59-98.
Konold, C. (1991). Understanding students' beliefs about probability. In E. von Glasersfeld (Ed.), Radical Constructivism in Mathematics education (pp. 139-156). Dordrecht: Kluwer.
Kuhn, D. (1991). The skills of argument. Cambridge: Cambridge University Press.
Lawson, T. J., Schwiers, M., Doellman, M., Grady, G., & Kelnhofer, R. (2003). Enhancing students' ability to use statistical reasoning with everyday problems. Teaching of Psychology, 30 (2), 107-110.
Lehman, D., & Nisbett, R. (1990). A Longitudinal study of the effects of undergraduate training on reasoning. Developmental Psychology, 26 (6), 952-960.
Lewis, C. P. (1999). Understanding the sampling distribution and the central limit theorem. Paper presented at the Annual Meeting of the Southwest Educational Research Association, San Antonio, TX.
Lovett, M. C., & Greenhouse, J. B. (2000). Applying cognitive theory to statistics instruction. American Statistician, 54 (3), 196-206.
MOEU. (2001). National document on mathematics curriculum. United Arab Emirates: Ministry of Education and Youth.
Nisbett, R. (1993). Reasoning, abstraction, and the prejudices of 20th century psychology. In R. Nisbett (Ed.), Rules For Reasoning (pp. 1-12). London: Lawrence Erlbaum.
Nisbett, R., & Borgida, E. (1975). Attribution and the psychology of prediction. Journal of Personality and Social Psychology, 32, 932-943.
Nisbett, R., Krantz, D., & Jepson, C. (1993). The use of statistical heuristics in everyday inductive reasoning. In R. Nisbett (Ed.), Rules for reasoning (pp 15- 54). London: Lawrence Erlbaum
Nisbett, R., & Ross, L. (1980). Human inference: Strategies and shortcomings of social judgement. Prentice-Hall, Inc, Englewood cliffs, NJ.
Olson, C. (1976). Some apparent violations of the representativeness heuristic in human judgement. Journal of Experimental Psychology: Human Perception and Performance, 2, 599-608.
Phung, N. (2005). Public opinion polls, chicken soup and sample size. Teaching Statistics, 27 (3), 89-92.
Reading, C., & Reid, J. (2006). Listen to the students: Understanding and supporting students' reasoning about variation. In A. Rossman & B. Chance (Eds.), Proceedings of the Seventh International Conference on Teaching Statistics, Salvador, Brazil: International Statistical Institute and International Association for Statistical Education. Online: http://www.stat.auckland.ac.nz/~iase.
Rubin, A., Bruce, B., & Tenney, Y. (1991). Learning about sampling: Trouble at the core of statistics. In D. Vere-Jones (Ed.), Proceedings of the Third International Conference on Teaching Statistics (Vol. 1, pp. 314-319). Voorburg: International Statistical Institute.
Rubin, A., Hammerman, J., & Konold, C. (2006). Exploring informal inference with interactive visualization software. In A. Rossman & B. Chance (Eds.), Proceedings of the Seventh International Conference on Teaching Statistics, Salvador, Brazil: International Statistical Institute and International Association for Statistical Education. Online: http://www.stat.auckland.ac.nz/~iase.
Saldanha, L., & Thompson, P. (2002). Students' scheme-based conceptions of sampling and its relationship to statistical inference. Proceedings of the Annual meetings of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1305-1316) Athens, GA: PME-NA
Saldanha, L., & Thompson, P. (2006). Investigating statistical unusualness in the context of a resampling activity: Students exploring connections between sampling distributions and statistical inference. In A. Rossman & B. Chance (Eds.), Proceedings of the Seventh International Conference on Teaching Statistics, Salvador, Brazil: International Statistical Institute and International Association for Statistical Education. Online: http://www.stat.auckland.ac.nz/~iase.
Salmon, M. (2002). Introduction to logic and critical thinking, 4th ed. Belmont, CA: Wadsworth.
Shaughnessy, J. (1981). Misconceptions of probability: From systematic errors to systematic experiments and decisions. In A. Schulte (Ed.), Teaching Statistics and Probability. Yearbook of the National Council of Teachers of Mathematics (NCTM). (pp. 90-100). Reston, VA: NCTM.
Shaughnessy, J. (1992). Research in probability and statistics: reflections and directions. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 465-494). New York: National Council of Teachers of Mathematics and MacMillan.
Shaughnessy, J. (1993). Probability and statistics. The Mathematics Teacher, 86 (3), 244-248.
Tversky, A., & Kahneman, D. (1973). Availability: A heuristic for judging frequency and probability. Cognitive Psychology, 5, 207-232.
Tversky, A., & Kahneman, D. (1974). Judgement under uncertainty: Heuristics and biases. In D. Kahneman, P. Slovic, & A. Tversky (Eds.), Judgment under uncertainty: Heuristics and biases (pp 3-22). Cambridge: Cambridge University Press.
Watson, J. (2000). Preservice mathematics teachers' understanding of sampling: intuition or mathematics. Mathematics Teacher Education and Development, 2, 121-135.
Well, A., Pollatsek, A., Boyce, S. (1990). Understanding the effects of sample size on the variability of the mean. Organizational Behavior and Human Decision Processes, 47, 289-312.

How to cite this article

APA

Innabi, H. A. (2007). Factors Considered by Secondary Students When Judging the Validity of a Given Statistical Generalization. International Electronic Journal of Mathematics Education, 2(3), 168-186. https://doi.org/10.29333/iejme/182

Vancouver

Innabi HA. Factors Considered by Secondary Students When Judging the Validity of a Given Statistical Generalization. INT ELECT J MATH ED. 2007;2(3):168-86. https://doi.org/10.29333/iejme/182

AMA

Innabi HA. Factors Considered by Secondary Students When Judging the Validity of a Given Statistical Generalization. INT ELECT J MATH ED. 2007;2(3), 168-186. https://doi.org/10.29333/iejme/182

Chicago

Innabi, Hanan Ayoub. "Factors Considered by Secondary Students When Judging the Validity of a Given Statistical Generalization". International Electronic Journal of Mathematics Education 2007 2 no. 3 (2007): 168-186. https://doi.org/10.29333/iejme/182

Harvard

Innabi, H. A. (2007). Factors Considered by Secondary Students When Judging the Validity of a Given Statistical Generalization. International Electronic Journal of Mathematics Education, 2(3), pp. 168-186. https://doi.org/10.29333/iejme/182

MLA

Innabi, Hanan Ayoub "Factors Considered by Secondary Students When Judging the Validity of a Given Statistical Generalization". International Electronic Journal of Mathematics Education, vol. 2, no. 3, 2007, pp. 168-186. https://doi.org/10.29333/iejme/182