• Journal of the Korean Statistical Society
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• v.16 no.2
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• pp.117-127
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• 1987

The Simpson's paradox is a paradoxical phenomenon which might occur when analyzing $2 \times 2$ contingency table. This paper considers the role of probability assignment of the experimental units in reducing the chances of Simpson's paradox. Numerical results are given to illustrate how the chance of Simpson's paradox behaves.

• Journal of the Korean Statistical Society
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• v.16 no.2
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• pp.113-116
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• 1987

The role of randomization is examined with regard to the Simpson's paradox. When the sample size n is large, it is known that the randomization is powerful in preventing the Simpson's paradox. In the present study, the question is whether is performs well for small n.

• Journal of Educational Research in Mathematics
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• v.20 no.3
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• pp.203-219
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• 2010

Several studies have reported on how and what mathematically gifted students develop superior ability or creativity in geometry and algebra. However, there are lack of studies in probability area, though there are a few trials of probability education for mathematically gifted students. Moreover, less attention has paid to the strategies to develop gifted students' creativity. This study has drawn three teaching strategies for creativity development based on literature review embedding: cognitive conflict, multiple representations, and social interaction. We designed a series of tasks via reconstructing, so called Simpson's paradox to meet these strategies. The findings showed that the gifted students made Quite a bit of improvement in creativity while participating in reflective thinking and active discussion, doing internal and external connection, translating representations, and investigating basic assumption.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.311-321
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• 2008

Mathematical paradoxes may arise when computations give unexpected results. We use three paradoxes to illustrate how they work in the basic probability theory. In the process of resolving the paradoxes, we expect that student-teachers can pedagogically gain valuable experience in regards to sharpening their mathematical knowledge and critical reasoning.

• Asia-pacific Journal of Multimedia Services Convergent with Art, Humanities, and Sociology
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• v.8 no.8
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• pp.845-852
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• 2018

Mayer-Schönberger and Cukier(2013) explain why big data is important for our life, while showing many cases in which analysis of big data has great significance for our life and raising intriguing issues on the analysis of big data. The two authors claim that correlation is in many ways practically far more efficient and versatile in the analysis of big data than causality. Moreover, they claim that causality could be abandoned since analysis and prediction founded on correlation must prevail. I critically examine the two authors' accounts of causality and correlation. First, I criticize that corelation is sufficient for our analysis of data and our prediction founded on the analysis. I point out their misunderstanding of the distinction between correlation and causality. I show that spurious correlation misleads our decision while analyzing Simpson paradox. Second, I criticize not only that causality is more inefficient in the analysis of big data than correlation, but also that there is no mathematical theory for causality. I introduce the mathematical theories of causality founded on structural equation theory, and show that causality has great significance for the analysis of big data.