Journal of Pedagogical Sociology and Psychology
Undergraduate students’ proficiencies in solving bivariate normal distribution problems
Bosire Nyambane Onyancha 1 * , Ugorji I. Ogbonnaya 2
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1 University of South Africa, South Africa
2 University of Pretoria, South Africa
* Corresponding Author
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Journal of Pedagogical Sociology and Psychology, 2022 - Volume 4 Issue 1, pp. 20-34
https://doi.org/10.33902/JPSP.202212259

Article Type: Research Article

Published Online: 17 May 2022

Views: 1437 | Downloads: 1466

ABSTRACT
This study explored undergraduate students’ proficiencies in solving bivariate normal distribution (BND) problems in a Kenyan university. The study followed a case study design and qualitative research approach. One hundred and seventy-five undergraduate statistics students in a Kenyan university participated in the study. Data was collected using an achievement test. Content analysis of the students’ solutions to test questions revealed that majority of the students were not proficient in solving BND problems with respect to calculating; (i) the probability of a normal distribution given the mean and variance of a variable, (ii) the mean of a normal distribution given the variance and the probability of a variable, (iii) the mean and variance of the joint distribution, and hence the probability of the variable given the conditional distribution of a variable, and (iv) the mean and standard deviation of two random variables given a bivariate random density function. It is recommended that the basic statistical concepts relevant to learning the BND be thoroughly revised before formally teaching BND.
KEYWORDS
bivariate normal distribution joint distribution probability random variables statistics
In-text citation: (Onyancha & Ogbonnaya, 2022)
Reference: Onyancha, B. N., & Ogbonnaya, U. I. (2022). Undergraduate students’ proficiencies in solving bivariate normal distribution problems. Journal of Pedagogical Sociology and Psychology, 4(1), 20-34. https://doi.org/10.33902/JPSP.202212259
In-text citation: (1), (2), (3), etc.
Reference: Onyancha BN, Ogbonnaya UI. Undergraduate students’ proficiencies in solving bivariate normal distribution problems. Journal of Pedagogical Sociology and Psychology. 2022;4(1), 20-34. https://doi.org/10.33902/JPSP.202212259
In-text citation: (1), (2), (3), etc.
Reference: Onyancha BN, Ogbonnaya UI. Undergraduate students’ proficiencies in solving bivariate normal distribution problems. Journal of Pedagogical Sociology and Psychology. 2022;4(1):20-34. https://doi.org/10.33902/JPSP.202212259
In-text citation: (Onyancha and Ogbonnaya, 2022)
Reference: Onyancha, Bosire Nyambane, and Ugorji I. Ogbonnaya. "Undergraduate students’ proficiencies in solving bivariate normal distribution problems". Journal of Pedagogical Sociology and Psychology 2022 4 no. 1 (2022): 20-34. https://doi.org/10.33902/JPSP.202212259
In-text citation: (Onyancha and Ogbonnaya, 2022)
Reference: Onyancha, B. N., and Ogbonnaya, U. I. (2022). Undergraduate students’ proficiencies in solving bivariate normal distribution problems. Journal of Pedagogical Sociology and Psychology, 4(1), pp. 20-34. https://doi.org/10.33902/JPSP.202212259
In-text citation: (Onyancha and Ogbonnaya, 2022)
Reference: Onyancha, Bosire Nyambane et al. "Undergraduate students’ proficiencies in solving bivariate normal distribution problems". Journal of Pedagogical Sociology and Psychology, vol. 4, no. 1, 2022, pp. 20-34. https://doi.org/10.33902/JPSP.202212259
REFERENCES
  • Arum D. P., Kusmayadi T. A., & Pramudya I. (2018). Students’ difficulties in probabilistic problem-solving. Journal of Physics. Conference series. IOP publishing. https://doi.org/10.1088/1742-6596/983/1/012098
  • Batanero C., Tauber L. M., & Sanchez V. (2004). Students’ reasoning about the normal distribution. In Ben-Zvi D., Garfield J. (Eds). The challenge of developing statistical literacy, reasoning and thinking (pp. 257-276). Springer. https://doi.org/10.1007/1-4020-2278-6_11
  • Bengtsson, M. (2016). How to plan and perform a qualitative study using content analysis. NursingPlus Open, 2, 8-14. https://doi.org/10.1016/j.npls.2016.01.001
  • Bhandari, P. (2021). Understanding normal distributions. Retrived May 11, 2021, from https://www.scribbr.com/statistics/normal-distribution/
  • Cain, M. K., Zhang, Z., & Yuan, K. H. (2017). Univariate and multivariate skewness and kurtosis for measuring nonnormality: Prevalence, influence and estimation. Behavior Research Methods, 49, 1716–1735. https://doi.org/10.3758/s13428-016-0814-1
  • Creswell, J. W. (2014). Research design: Qualitative, quantitative and mixed methods approaches. (4th ed.). Sage.
  • Flury, B. (2013). A first Course in Multivariate Statistics. Springer texts in Statistics. Springer Science+Business Media, LLC
  • Garfield, J. B, & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. New York, NY: Springer.
  • Gauvrit, N., & Morsanyi, K. (2014). The equiprobability bias from a mathematical and psychological perspective. Advances in cognitive psychology, 10(4), 119–130. https://doi.org/10.5709/acp-0163-9
  • Gloves S., (2012). Developing mathematical proficiency. Journal of Science and Mathematics Education. 35(2), 119-145. Retrieved on 18th November, 2021, from, http://www.recsam.edu.my/sub_JSMESEA/images/journals/YEAR2012/dec2012vol-2/119-145.pdf
  • Gordon, S. (2006). The normal distribution. Mathematics learning centre, University of Sydney. Retrieved May 16, 2021, from https://www.sydney.edu.au/content/dam/students /documents/mathematics-learning-centre/normal-distribution.pdf
  • Grover,G., Sabharwal, A. & Mittal, J. (2014). Application of Multivariate and Bivariate Normal Distributions to Estimate Duration of Diabetes, International Journal of Statistics and Applications, 4 (1), 46-57. doi: 10.5923/j.statistics.20140401.05
  • Harradine, A., Batanero, C., & Rossman, A. (2011). Students and teachers’ knowledge of sampling and inference. In Teaching Statistics in school mathematics-challenges for teaching and teacher education. Springer. Dordrecht. 235-246
  • Kachapova, F., & Kachapov, I. (2012). Students’ misconceptions about random variables. International Journal of Mathematical Education, 43 (7), 963-971. https://doi.org/10.1080/0020739X.2011.644332
  • Khazanov, L. & Prado, L. (2010). Correcting students’ misconceptions about probability in an introductory college statistics course: ALM International Journal, 5(1), 23-35.
  • Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn Mathematics. National Research Council. ISBN: 0-309-50524-0, 480. Retrieved on 16th November, 2021, from, http://www.nap.edu/catalog/9822.html
  • Koparan, T. (2015). Difficulties in learning and teaching statistics: Teacher views. International Journal of Mathematical Education in Science and Technology, 46(1), 94-104. https://doi.org/10.1080/0020739X.2014.941425
  • Krippendorff, K. (2018). Content analysis: An introduction to its methodology (4th ed.). California: Sage.
  • Lin, G.D., Dou, X., Kuriki, S. & Huang, J. (2014). Recent developments on the construction of bivariate distributions with fixed marginals. Journal of Statistical Distributions and Applications, 1(14), 1-23. https://doi.org/10.1186/2195-5832-1-14
  • Lugo-Armenta, J. G., & Pino-Fan, L. R. (2021). Inferential Statistical Reasoning of Math Teachers: Experiences in Virtual Contexts Generated by the COVID-19 Pandemic. Education Sciences, 11(7), 363. https://doi.org/10.3390/educsci11070363
  • McLeod, S. A. (2019). What is a normal distribution in statistics? Retrieved September 16, 2019, from https://www.simplypsychology.org/normal-distribution.html.
  • Memnun D. S., Ozbilen O., & Dinc E. (2019). A qualitative research on the difficulties and failures about probability concepts of high school students. Journal of Educational Issues, 5(1), 1-19. https://doi.org/10.5296/jei.v5i1/14146
  • Rouaud M. (2017). Probability, Statistics and Estimation: Propagation of uncertainties in experimental measurement. Retrieved April 28, 2021, from http://www.incertitudes.fr/book.pdf
  • Schoenfeld, A. H., & Kilpatrick, J. (2008). Towards a theory of proficiency in teaching mathematics. In D. Tirosh & T. Wood (Eds.), The international handbook of mathematics teacher education: Tools and processes in mathematics teacher education. 2, 321–354. Rotterdam, The Netherlands: Sense Publishers.
  • Shojaie, S. R. H., Aminghafari, M., & Mahammadpour, A. (2012). On the expected absolute value of a bivariate normal distribution. Journal of Statistics Theory and Applications, 11(4), 371-377.
  • 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. https://doi.org/10.1016/j.edurev.2007.04.001
  • Tacq, J. (2010). Multivariate normal distributions. Elseiver.
  • Weisstein, E. W. (2002). Bivariate normal distribution. From MathWorld-- A wolfram web resource. Retrieved October 25, 2019, from, http://mathworld.wolfram.com/BivariateNormalDistribution.html
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