Stochastic process computational modeling for learning research

Authors

DOI:

https://doi.org/10.31812/educdim.4498

Keywords:

computational modeling, computer-based simulation, statistical hypothesis significance testing, education, learning research

Abstract

The goal of our research was to compare and systematize several approaches to non-parametric null hypothesis significance testing using computer-based statistical modeling. For teaching purposes, a statistical model for simulation of null hypothesis significance testing was created. The results were analyzed using Fisher's angular transformation, Chi-square, Mann-Whitney, and Fisher's exact tests. Appropriate software was created, allowing us to recommend new illustrative materials for expressing the limitations of the tests that were examined. Learning investigations as a technique of comprehending inductive statistics has been proposed, based on the fact that modern personal computers can run simulations in a reasonable amount of time with great precision. The collected results revealed that the most often used non-parametric tests for small samples have low power. Traditional null hypothesis significance testing does not allow students to analyze test power because the true differences between samples are unknown. As a result, in Ukrainian statistical education, including PhD studies, the emphasis must shift away from null hypothesis significance testing and toward statistical modeling as a modern and practical approach of establishing scientific hypotheses. This finding is supported by scientific papers and the American Statistical Association's recommendation.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

References

Berkson, J.: In dispraise of the exact test: Do the marginal totals of the 2x2 table contain relevant information respecting the table proportions? Journal of Statistical Planning and Inference 2(1), 27–42 (1978). https://doi.org/10.1016/0378-3758(78)90019-8 DOI: https://doi.org/10.1016/0378-3758(78)90019-8

Billiet, P.: The Mann-Whitney U-test – analysis of 2-between-group data with a quantitative response variable (2003), https://psych.unl.edu/psycrs/handcomp/hcmann.PDF

Bilousova, L.I., Kolgatin, O.H., Kolgatina, L.S., Kuzminska, O.H.: Introspection as a condition of students’ self-management in programming training. In: Proceedings of the 1st Symposium on Advances in Educational Technology - Volume 1: AET. pp. 142–153. INSTICC, SciTePress (2022). https://doi.org/10.5220/0010922000003364Educational Dimension (2022) https://doi.org/10.31812/educdim.4498 DOI: https://doi.org/10.31812/educdim.4498

Bilousova, L.I., Kolgatina, L.S., Kolgatin, O.H.: Computer simulation as a method of learning research in computational mathematics. CEUR Workshop Proceedings 2393, 880–894 (2019)

Bradley, D.R., Hemstreet, R.L., Ziegenhagen, S.T.: A simulation laboratory for statistics. Behavior Research Methods, Instruments, and Computers 24(2), 190–204 (1992). https://doi.org/10.3758/BF03203496, https://link.springer.com/content/pdf/10.3758/BF03203496.pdf DOI: https://doi.org/10.3758/BF03203496

Castro Sotos, A.E., Vanhoof, S., Van den Noortgate, W., Onghena, P.: How confident are students in their misconceptions about hypothesis tests? Journal of Statistics Education 17(2) (2009). https://doi.org/10.1080/10691898.2009.11889514 DOI: https://doi.org/10.1080/10691898.2009.11889514

D’Agostino, R.B., Chase, W., Belanger, A.: The appropriateness of some common procedures for testing the equality of two independent binomial populations. The American Statistician 42(3), 198–202 (1988), http://www.jstor.org/stable/2685002 DOI: https://doi.org/10.1080/00031305.1988.10475563

Fay, M.P., Proschan, M.A.: Wilcoxon-Mann-Whitney or t-test? On assumptions for hypothesis tests and multiple interpretations of decision rules. Statistics Surveys 4, 1–39 (2010). https://doi.org/10.1214/09-SS051 DOI: https://doi.org/10.1214/09-SS051

Flusser, P., Hanna, D.: Computer simulation of the testing of a statistical hypothesis. Mathematics and Computer Education 25(2), 158 (1991), https://www.learntechlib.org/p/144840

Fong, Y., Huang, Y.: Modified Wilcoxon-Mann-Whitney test and power against strong null. The American Statistician 73(1), 43–49 (2019). https://doi.org/10.1080/00031305.2017.1328375 DOI: https://doi.org/10.1080/00031305.2017.1328375

Gubler, Y.V., Genkin, A.A.: Primeneniye Neparametricheskikh Metodov Statistiki v Mediko-Biologicheskikh Issledovaniyakh (Application of Nonparametric Methods of Statistics in Biomedical Research). Meditsina, Leningradskoye otdeleniye, Leningrad (1973)

Jamie, D.M.: Using computer simulation methods to teach statistics: A review of the literature. Journal of Statistics Education 10(1) (2002). https://doi.org/10.1080/10691898.2002.11910548 DOI: https://doi.org/10.1080/10691898.2002.11910548

Kanji, G.K.: 100 Statistical Tests. SAGE Publications, London - Thousand Oaks - New Delhi (2006)

Khazina, S.A., Ramskyi, Y.S., Eylon, B.S.: Computer modeling as a scientific means of training prospective physics teachers. In: EDULEARN16 Proceedings. pp. 7699–7709. 8th International Conference on Education and New Learning Technologies, IATED (4-6 July 2016). https://doi.org/10.21125/edulearn.2016.0694 DOI: https://doi.org/10.21125/edulearn.2016.0694

Kolgatin, O.: Computer-based simulation of stochastic process for investigation of efficiency of statistical hypothesis testing in pedagogical research. Journal of Information Technologies in Education (ITE) (27), 007–014 (Oct 2016). https://doi.org/10.14308/ite000582, http://ite.kspu.edu/index.php/ite/article/view/101 DOI: https://doi.org/10.14308/ite000582

Kolgatin, O.H.: Informatsionnyye tekhnologii v nauchno-pedagogicheskikh issledovaniyakh (Information technologies in educational researches). Upravlyayushchiye Sistemy i Mashiny (Control Systems and Machines) 255(1), 66–72 (2015)

Kolgatin, O.H., Kolgatina, L.S., Ponomareva, N.S., Shmeltser, E.O., Uchitel, A.D.: Systematicity of students’ independent work in cloud learning environment of the course "educational electronic resources for primary school" for the future teachers of primary schools. In: Proceedings of the 1st Symposium on Advances in Educational Technology - Volume 1: AET. pp. 538–549. INSTICC, SciTePress (2022). https://doi.org/10.5220/0010926000003364 DOI: https://doi.org/10.5220/0010926000003364

Kravtsov, H.M.: Methods and technologies for the quality monitoring of electronic educational resources. CEUR Workshop Proceedings 1356, 311–325 (2015)

Lang, K.M., Sweet, S.J., Grandfield, E.M.: Getting beyond the Null: Statistical Modeling as an Alternative Framework for Inference in Developmental Science. Research in Human Development 14(4), 287–304 (2017). https://doi.org/10.1080/15427609.2017.1371567 DOI: https://doi.org/10.1080/15427609.2017.1371567

Liddell, D.: Practical tests of 2 × 2 contingency tables. Journal of the Royal Statistical Society. Series D (The Statistician) 25(4), 295–304 (1976). https://doi.org/10.2307/2988087 DOI: https://doi.org/10.2307/2988087

Markova, O., Semerikov, S., Popel, M.: CoCalc as a learning tool for neural network simulation in the special course “Foundations of mathematic informatics”. CEUR Workshop Proceedings 2104, 388–403 (2018) DOI: https://doi.org/10.31812/0564/2250

Marx, A., Backes, C., Meese, E., Lenhof, H.P., Keller, A.: EDISON-WMW: Exact dynamic programing solution of the Wilcoxon-Mann-Whitney test. Genomics, Proteomics and Bioinformatics 14(1), 55–61 (2016). https://doi.org/10.1016/j.gpb.2015.11.004 DOI: https://doi.org/10.1016/j.gpb.2015.11.004

McShane, B.B., Gal, D., Gelman, A., Robert, C., Tackett, J.L.: Abandon Statistical Significance. The American Statistician 73(sup1), 235–245 (2019). https://doi.org/10.1080/00031305.2018.1527253 DOI: https://doi.org/10.1080/00031305.2018.1527253

Modlo, Y.O., Semerikov, S.O.: Xcos on Web as a promising learning tool for Bachelor’s of Electromechanics modeling of technical objects. CEUR Workshop Proceedings 2168, 34–41 (2018)

Preacher, K.J.: Calculation for Fisher’s exact test (2021), http://quantpsy.org/fisher/fisher.html

Ricketts, C., Berry, J.: Teaching statistics through resampling. Teaching Statistics 16(2), 41–44 (1994). https://doi.org/10.1111/j.1467-9639.1994.tb00685.x DOI: https://doi.org/10.1111/j.1467-9639.1994.tb00685.x

Semerikov, S.O., Teplytskyi, I.O., Yechkalo, Y.V., Kiv, A.E.: Computer Simulation of Neural Networks Using Spreadsheets: The Dawn of the Age of Camelot. CEUR Workshop Proceedings 2257, 122–147 (2018) DOI: https://doi.org/10.31812/123456789/2648

Semerikov, S.O., Teplytskyi, I.O., Yechkalo, Y.V., Markova, O.M., Soloviev, V.N.: Computer Simulation of Neural Networks Using Spreadsheets: Dr. Anderson, Welcome Back. CEUR Workshop Proceedings 2393, 833–848 (2019) DOI: https://doi.org/10.31812/123456789/3178

Sidorenko, Y.V.: Metody Matematicheskoy Obrabotki v Psikhologii (Methods of Mathematical Processing in Psychology). Rech, St. Petersburg (2002), https://www.sgu.ru/sites/default/files/textdocsfiles/2014/02/19/sidorenko.pdf

Taylor, D.W., Bosch, E.G.: CTS: A clinical trials simulator. Statistics in Medicine 9(7), 787–801 (1990). https://doi.org/10.1002/sim.4780090708 DOI: https://doi.org/10.1002/sim.4780090708

Verma, J.P.: Data Analysis in Management with SPSS Software. Springer, India (2013). https://doi.org/10.1007/978-81-322-0786-3 DOI: https://doi.org/10.1007/978-81-322-0786-3

Wasserstein, R.L., Lazar, N.A.: The ASA Statement on p-Values: Context, Process, and Purpose. The American Statistician 70(2), 129–133 (2016). https://doi.org/10.1080/00031305.2016.1154108 DOI: https://doi.org/10.1080/00031305.2016.1154108

Wasserstein, R.L., Schirm, A.L., Lazar, N.A.: Moving to a World Beyond “p < 0.05”. The American Statistician 73(sup1), 1–19 (2019). https://doi.org/10.1080/00031305.2019.1583913 DOI: https://doi.org/10.1080/00031305.2019.1583913

Downloads

Published

14-06-2022

How to Cite

Kolgatin, O., Kolgatina, L., & Ponomareva, N. (2022). Stochastic process computational modeling for learning research. Educational Dimension, 58, 68–83. https://doi.org/10.31812/educdim.4498

Issue

Section

Theories of Learning, Education and Training