Examining the factors affecting students' science success with Bayesian networks

Abstract

Bayesian Networks (BNs) are probabilistic graphical statistical models that have been widely used in many fields over the last decade. This method, which can also be used for educational data mining (EDM) purposes, is a fairly new method in education literature. This study models students' science success using the BN approach. Science is one of the core areas in the PISA exam. To this end, we used the data set including the most successful 25% and the least successful 25% students from Turkey based on their scores from Program for International Student Assessment (PISA) survey. We also made the feature selection to determine the most effective variables on success. The accuracy value of the BN model created with the variables determined by the feature selection is 86.2%. We classified effective variables on success into three categories; individual, family-related and school-related. Based on the analysis, we found that family-related variables are very effective in science success, and gender is not a discriminant variable in this success. In addition, this is the first study in the literature on the evaluation of complex data made with the BN model. In this respect, it serves as a guide in the evaluation of international exams and in the use of the data obtained.

Keywords

• Bayesian Networks
• Educational Data Mining
• PISA
• Science Success

References

1. Almond, R.G., DiBello, L.V., Moulder, B., & Zapata‐Rivera, J.-D. (2007). Modeling Diagnostic Assessments with Bayesian Networks. Journal of Educational Measurement, 44(4), 341–359. https://doi.org/10.1111/j.1745-3984.2007.00043.x
2. Almond, R.G., & Mislevy, R.J. (1999). Graphical Models and Computerized Adaptive Testing. Applied Psychological Measurement, 23(3), 223 237. https://doi.org/10.1177/01466219922031347
3. Almond, R.G., Mislevy, R.J., Steinberg, L.S., Yan, D., & Williamson, D.M. (2015). Bayesian Networks in Educational Assessment. Springer.
4. Altun, A., & Kalkan, Ö.K. (2019). Cross-national study on students and school factors affecting science literacy. Educational Studies, 1 19. https://doi.org/10.1080/03055698.2019.1702511
5. Archibald, S. (2006). Narrowing in on Educational Resources That Do Affect Student Achievement. Peabody Journal of Education, 81(4), 23 42. https://doi.org/10.1207/s15327930pje8104_2
6. Aşkın, Ö.E., & Öz, E. (2020). Cross-National Comparisons of Students’ Science Success Based on Gender Variability: Evidence From TIMSS. Journal of Baltic Science Education, 19(2), 186–200. https://doi.org/10.33225/jbse/20.19.186
7. Augustyniak, R.A., Ables, A.Z., Guilford, P., Lujan, H.L., Cortright, R.N., & DiCarlo, S.E. (2016). Intrinsic motivation: An overlooked component for student success. Advances in Physiology Education, 40(4), 465–466. https://doi.org/10.1152/advan.00072.2016
8. Baker, R.S.J.d, & Yacef, K. (2009). The State of Educational Data Mining in 2009: A Review and Future Visions. Journal of Educational Data Mining, 1(1), Article 1. https://doi.org/10.5281/zenodo.3554657

9. BayesFusion, L. (2017). GeNIe modeler user manual. BayesFusion, LLC, Pittsburgh, PA.
10. Bayrak, B.K., & Bayram, H. (2010). The effect of computer aided teaching method on the students’ academic achievement in the science and technology course. Procedia - Social and Behavioral Sciences, 9, 235–238. https://doi.org/10.1016/j.sbspro.2010.12.142
11. Beese, J., & Liang, X. (2010). Do resources matter? PISA science achievement comparisons between students in the United States, Canada and Finland. Improving Schools, 13(3), 266–279. https://doi.org/10.1177/1365480210390554
12. Bingimlas, K.A. (2009). Barriers to the Successful Integration of ICT in Teaching and Learning Environments: A Review of the Literature. Eurasia Journal of Mathematics, Science & Technology Education, 5(3), 235–245.
13. Borland, M.V., Howsen, R.M., & Trawick, M.W. (2005). An investigation of the effect of class size on student academic achievement. Education Economics, 13(1), 73–83. https://doi.org/10.1080/0964529042000325216
14. Cansiz, N., & Cansiz, M. (2019). Evaluating Turkish science curriculum with PISA scientific literacy framework. Turkish Journal of Education, 8(3), Article 3. https://doi.org/10.19128/turje.545798
15. Carnoy, M., Khavenson, T., & Ivanova, A. (2015). Using TIMSS and PISA results to inform educational policy: A study of Russia and its neighbours. Compare: A Journal of Comparative and International Education, 45(2), 248 271. https://doi.org/10.1080/03057925.2013.855002
16. Chang, C.-Y. (2002). Does Computer-Assisted Instruction + Problem Solving = Improved Science Outcomes? A Pioneer Study. The Journal of Educational Research, 95(3), 143–150. https://doi.org/10.1080/00220670209596584
17. Chen, J., Zhang, Y., Wei, Y., & Hu, J. (2019). Discrimination of the Contextual Features of Top Performers in Scientific Literacy Using a Machine Learning Approach. Research in Science Education. https://doi.org/10.1007/s11165-019-9835-y
18. Clarke, E.A., & Kiselica, M.S. (1997). A systemic counseling approach to the problem of bullying. Elementary School Guidance & Counseling, 31(4), 310–325.
19. Culbertson, M.J. (2016). Bayesian Networks in Educational Assessment: The State of the Field. Applied Psychological Measurement, 40(1), 3 21. https://doi.org/10.1177/0146621615590401
20. Deng, Z., & Gopinathan, S. (2016). PISA and high-performing education systems: Explaining Singapore’s education success. Comparative Education, 52(4), 449 472. https://doi.org/10.1080/03050068.2016.1219535
21. Desmarais, M.C., & Baker, R.S.J.d. (2012). A review of recent advances in learner and skill modeling in intelligent learning environments. User Modeling and User-Adapted Interaction, 22(1), 9–38. https://doi.org/10.1007/s11257-011-9106-8
22. Ehrenberg, R.G., Brewer, D.J., Gamoran, A., & Willms, J.D. (2001). Class Size and Student Achievement. Psychological Science in The Public Interest, 2(1), 30.
23. Ertem, H.Y. (2021). Examination of Turkey’s PISA 2018 reading literacy scores within student-level and school-level variables. Participatory Educational Research, 8(1), 248–264. https://doi.org/10.17275/per.21.14.8.1
24. Ferri, C., Hernández-Orallo, J., & Modroiu, R. (2009). An experimental comparison of performance measures for classification. Pattern Recognition Letters, 30(1), 27–38. https://doi.org/10.1016/j.patrec.2008.08.010
25. Fry, D., Fang, X., Elliott, S., Casey, T., Zheng, X., Li, J., Florian, L., & McCluskey, G. (2018). The relationships between violence in childhood and educational outcomes: A global systematic review and meta-analysis. Child Abuse & Neglect, 75, 6–28. https://doi.org/10.1016/j.chiabu.2017.06.021
26. Gamazo, A., & Martínez-Abad, F. (2020). An Exploration of Factors Linked to Academic Performance in PISA 2018 Through Data Mining Techniques. Frontiers in Psychology, 11. https://doi.org/10.3389/fpsyg.2020.575167
27. Gilbert, J.K., Boulter, C.J., & Elmer, R. (2000). Positioning Models in Science Education and in Design and Technology Education. In J.K. Gilbert & C.J. Boulter (Eds.), Developing Models in Science Education (pp. 3 17). Springer Netherlands. https://doi.org/10.1007/978-94-010-0876-1_1
28. Hall, M.A. (1999a). Correlation-based Feature Selection for Machine Learning [PhD Thesis]. The University of Waikato.
29. Hall, M.A. (1999b). Feature selection for discrete and numeric class machine learning [Working Paper]. Computer Science, University of Waikato. https://researchcommons.waikato.ac.nz/handle/10289/1033
30. Hall, M.A. (2000). Correlation-based feature selection of discrete and numeric class machine learning [Working Paper]. University of Waikato, Department of Computer Science. https://researchcommons.waikato.ac.nz/handle/10289/1024
31. Hanushek, E.A., & Woessmann, L. (2017). School Resources and Student Achievement: A Review of Cross-Country Economic Research. In M. Rosén, K. Yang Hansen, & U. Wolff (Eds.), Cognitive Abilities and Educational Outcomes (pp. 149–171). Springer International Publishing. https://doi.org/10.1007/978-3-319-43473-5_8
32. Harker, R. (2000). Achievement, Gender and the Single-Sex/Coed Debate. British Journal of Sociology of Education, 21(2), 203–218. https://doi.org/10.1080/713655349
33. Hattie, J. (2005). The paradox of reducing class size and improving learning outcomes. International Journal of Educational Research, 43(6), 387 425. https://doi.org/10.1016/j.ijer.2006.07.002
34. Hossin, M., & Sulaiman, M.N. (2015). A Review on Evaluation Metrics for Data Classification Evaluations. International Journal of Data Mining & Knowledge Management Process, 5(2), 01–11. https://doi.org/10.5121/ijdkp.2015.5201
35. Jan, A. (2015). Bullying in Elementary Schools: Its Causes and Effects on Students. Journal of Education and Practice, 15.
36. Karaboga, H.A., Gunel, A., Korkut, S.V., Demir, I., & Celik, R. (2021). Bayesian Network as a Decision Tool for Predicting ALS Disease. Brain Sciences, 11(2), Article 2. https://doi.org/10.3390/brainsci11020150
37. Karakoç Alatlı, B. (2020). Investigation of Factors Associated with Science Literacy Performance of Students by Hierarchical Linear Modeling: PISA 2015 Comparison of Turkey and Singapore. TED Education and Science Magazine. https://doi.org/10.15390/EB.2020.8188
38. Karataş, H., & Ergi̇n, A. (2018). Üniversite Öğrencilerinin Başarı Odaklı Motivasyon Düzeyleri [Achievement-Oriented Motivation Levels of University Students]. Hacettepe University Journal of Education, 1–20. https://doi.org/10.16986/HUJE.2018036646
39. Kenekayoro, P. (2018). An Exploratory Study on the Use of Machine Learning to Predict Student Academic Performance: International Journal of Knowledge-Based Organizations, 8(4), 67–79. https://doi.org/10.4018/IJKBO.2018100104
40. Kilic Depren, S. (2018). Prediction of Students’ Science Achievement: An Application of Multivariate Adaptive Regression Splines and Regression Trees. Journal of Baltic Science Education, 17(5), 887–903. https://doi.org/10.33225/jbse/18.17.887
41. Kilic Depren, S. (2020). Determination of the Factors Affecting Students’ Science Achievement Level in Turkey and Singapore: An Application of Quantile Regression Mixture Model. Journal of Baltic Science Education, 19(2), 247 260. https://doi.org/10.33225/jbse/20.19.247
42. Kiray, S.A., Gok, B., & Bozkir, A.S. (2015). Identifying the Factors Affecting Science and Mathematics Achievement Using Data Mining Methods. Journal of Education in Science, Environment and Health, 1(1), 28. https://doi.org/10.21891/jeseh.41216
43. Kjærnsli, M., & Lie, S. (2004). PISA and scientific literacy: Similarities and differences between the nordic countries. Scandinavian Journal of Educational Research, 48(3), 271–286. https://doi.org/10.1080/00313830410001695736
44. Korb, K.B., & Nicholson, A.E. (2010). Bayesian Artificial Intelligence. CRC Press.
45. Kustitskaya, T.A., Kytmanov, A.A., & Noskov, M.V. (2020). Student-at-risk detection by current learning performance indicators using Bayesian networks. ArXiv:2004.09774 [Stat]. http://arxiv.org/abs/2004.09774
46. Lee, J., & Shute, V.J. (2010). Personal and Social-Contextual Factors in K–12 Academic Performance: An Integrative Perspective on Student Learning. Educational Psychologist, 45(3), 185–202. https://doi.org/10.1080/00461520.2010.493471
47. Levy, R. (2016). Advances in Bayesian Modeling in Educational Research. Educational Psychologist, 51(3–4), 368–380. https://doi.org/10.1080/00461520.2016.1207540
48. Lima. (2014). Heuristic Discretization Method for Bayesian Networks. Journal of Computer Science, 10(5), 869–878. https://doi.org/10.3844/jcssp.2014.869.878
49. Lytvynenko, V., Savina, N., Voronenko, M., Doroschuk, N., Smailova, S., Boskin, O., & Kravchenko, T. (2019). Development, Validation and Testing of the Bayesian Network of Educational Institutions Financing. 2019 10th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS), 1, 412–417. https://doi.org/10.1109/IDAACS.2019.8924307
50. Margolis, E. (2001). The Hidden Curriculum in Higher Education. Psychology Press.
51. Marsland, S. (2015). Machine Learning: An Algorithmic Perspective (Second Edition). CRC press.
52. Martínez Abad, F., & Chaparro Caso López, A.A. (2017). Data-mining techniques in detecting factors linked to academic achievement. School Effectiveness and School Improvement, 28(1), 39–55. https://doi.org/10.1080/09243453.2016.1235591
53. MEB. (2018). Fen Bilimleri Dersi Öğretim Programı [Science Course Curriculum].. Talim ve Terbiye Kurulu Başkanlığı, Ankara. https://mufredat.meb.gov.tr/Dosyalar/201812312311937 FEN%20B%C4%B0L%C4%B0MLER%C4%B0%20%C3%96%C4%9ERET%C4%B0M%20PROGRAMI2018.pdf
54. MEB. (2019). PISA 2018 Turkiye Ön Raporu [PISA 2018 Turkey Preliminary Report]. Milli Eğitim Bakanlığı. http://www.meb.gov.tr/meb_iys_dosyalar/2019_12/03105347_PISA_2018_Turkiye_On_Raporu.pdf
55. Millán, E., Descalço, L., Castillo, G., Oliveira, P., & Diogo, S. (2013). Using Bayesian networks to improve knowledge assessment. Computers & Education, 60(1), 436–447. https://doi.org/10.1016/j.compedu.2012.06.012
56. Muñoz-Merino, P.J., Molina, M.F., Muñoz-Organero, M., & Kloos, C.D. (2014). Motivation and Emotions in Competition Systems for Education: An Empirical Study. IEEE Transactions on Education, 57(3), 182–187. https://doi.org/10.1109/TE.2013.2297318
57. Neapolitan, R.E. (2009). Probabilistic methods for bioinformatics: With an introduction to Bayesian networks. Morgan Kaufmann/Elsevier.
58. Nguyen, L., & Do, P. (2009). Combination of Bayesian Network and Overlay Model in User Modeling. In G. Allen, J. Nabrzyski, E. Seidel, G.D. van Albada, J. Dongarra, & P.M.A. Sloot (Eds.), Computational Science – ICCS 2009 (pp. 5–14). Springer. https://doi.org/10.1007/978-3-642-01973-9_2
59. Nielsen, T.D., & Jensen, F.V. (2009). Bayesian Networks and Decision Graphs. Springer Science & Business Media.
60. Nojavan A., F., Qian, S.S., & Stow, C.A. (2017). Comparative analysis of discretization methods in Bayesian networks. Environmental Modelling & Software, 87, 64–71. https://doi.org/10.1016/j.envsoft.2016.10.007
61. O’Connell, M. (2019). Is the impact of SES on educational performance overestimated? Evidence from the PISA survey. Intelligence, 75, 41 47. https://doi.org/10.1016/j.intell.2019.04.005
62. Odell, B., Galovan, A.M., & Cutumisu, M. (2020). The Relation Between ICT and Science in PISA 2015 for Bulgarian and Finnish Students. EURASIA Journal of Mathematics, Science and Technology Education, 16(6). https://doi.org/10.29333/ejmste/7805
63. OECD. (2019a). PISA 2018 Assessment and Analytical Framework. OECD. https://doi.org/10.1787/b25efab8-en
64. OECD. (2019b). PISA 2018 Results (Volume I): What Students Know and Can Do. OECD. https://doi.org/10.1787/5f07c754-en
65. OECD. (2019c). PISA 2018 Results (Volume II): Where All Students Can Succeed. OECD. https://doi.org/10.1787/b5fd1b8f-en
66. OECD. (2020). Do boys and girls have similar attitudes towards competition and failure? (PISA in Focus 105; PISA in Focus, Vol. 105). https://doi.org/10.1787/a8898906-en
67. Özdemi̇r, E., Cansiz, M., Cansiz, N., & Üstün, U. (2019). Türkiye deki Öğrencilerin Fen Okuryazarlığını Etkileyen Faktörler Nelerdir PISA 2015 Verisine Dayalı Bir Hiyerarşik Doğrusal Modelleme Çalışması. Hacettepe University Journal of Education, 1–16. https://doi.org/10.16986/HUJE.2019050786
68. Pearl, J. (2014). Probabilistic reasoning in intelligent systems: Networks of plausible inference (Revised Second Printing). Morgan Kaufmann. https://doi.org/10.1016/B978-0-08-051489-5.50002-3
69. Peña-Ayala, A. (2014). Educational data mining: A survey and a data mining-based analysis of recent works. Expert Systems with Applications, 41(4), 1432 1462. https://doi.org/10.1016/j.eswa.2013.08.042
70. Ramírez-Noriega, A., Juárez-Ramírez, R., Leyva-López, J.C., Jiménez, S., & Figueroa-Pérez, J.F. (2021). A Method for Building the Quantitative and Qualitative Part of Bayesian Networks for Intelligent Tutoring Systems. The Computer Journal, bxab124. https://doi.org/10.1093/comjnl/bxab124
71. Rastrollo-Guerrero, J.L., Gómez-Pulido, J.A., & Durán-Domínguez, A. (2020). Analyzing and Predicting Students’ Performance by Means of Machine Learning: A Review. Applied Sciences, 10(3), 1042. https://doi.org/10.3390/app10031042
72. Reichenberg, R. (2018). Dynamic Bayesian Networks in Educational Measurement: Reviewing and Advancing the State of the Field. Applied Measurement in Education, 31(4), 335–350. https://doi.org/10.1080/08957347.2018.1495217
73. Reilly, D., Neumann, D.L., & Andrews, G. (2019). Investigating Gender Differences in Mathematics and Science: Results from the 2011 Trends in Mathematics and Science Survey. Research in Science Education, 49(1), 25–50. https://doi.org/10.1007/s11165-017-9630-6
74. Romero, C., & Ventura, S. (2010). Educational Data Mining: A Review of the State of the Art. IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 40(6), 601–618. https://doi.org/10.1109/TSMCC.2010.2053532
75. Ropero, R.F., Renooij, S., & van der Gaag, L.C. (2018). Discretizing environmental data for learning Bayesian-network classifiers. Ecological Modelling, 368, 391–403. https://doi.org/10.1016/j.ecolmodel.2017.12.015
76. Sağlam, A.Ç., & Aydoğmuş, M. (2016). Gelişmiş ve Gelişmekte Olan Ülkelerin Eğitim Sistemlerinin Denetim Yapıları Karşılaştırıldığında Türkiye Eğitim Sisteminin Denetimi Ne Durumdadır? [When the Supervision Structures of the Education Systems of Developed and Developing Countries are Compared, How is the Supervision of the Turkish Education System?]. Uşak Üniversitesi Sosyal Bilimler Dergisi, 9(1), Article 1. https://doi.org/10.12780/uusbd.50788
77. Saini, M.K., & Goel, N. (2019). How Smart Are Smart Classrooms? A Review of Smart Classroom Technologies. ACM Computing Surveys, 52(6), 130:1-130:28. https://doi.org/10.1145/3365757
78. Schleicher, A. (2019). PISA 2018: Insights and Interpretations. In OECD Publishing. OECD Publishing.
79. Sebastian, J., Moon, J.-M., & Cunningham, M. (2017). The relationship of school-based parental involvement with student achievement: A comparison of principal and parent survey reports from PISA 2012. Educational Studies, 43(2), 123–146. https://doi.org/10.1080/03055698.2016.1248900
80. Sener, E., Karaboga, H.A., & Demir, I. (2019). Bayesian Network Model of Turkish Financial Market from Year-to-September 30th of 2016. Sigma: Journal of Engineering & Natural Sciences / Mühendislik ve Fen Bilimleri Dergisi, 37(4), 1493–1507.
81. Sheldrake, R., Mujtaba, T., & Reiss, M.J. (2017). Science teaching and students’ attitudes and aspirations: The importance of conveying the applications and relevance of science. International Journal of Educational Research, 85, 167 183. https://doi.org/10.1016/j.ijer.2017.08.002
82. Shin, D., & Shim, J. (2021). A Systematic Review on Data Mining for Mathematics and Science Education. International Journal of Science and Mathematics Education, 19(4), 639–659. https://doi.org/10.1007/s10763-020-10085-7
83. Sing, T., Sander, O., Beerenwinkel, N., & Lengauer, T. (2005). ROCR: Visualizing classifier performance in R. Bioinformatics, 21(20), 3940 3941. https://doi.org/10.1093/bioinformatics/bti623
84. Sinharay, S. (2006). Model Diagnostics for Bayesian Networks. Journal of Educational and Behavioral Statistics, 31(1), 1–33.
85. Sinharay, S. (2016). An NCME Instructional Module on Data Mining Methods for Classification and Regression. Educational Measurement: Issues and Practice, 35(3), 38–54. https://doi.org/10.1111/emip.12115
86. Sirin, S.R. (2005). Socioeconomic Status and Academic Achievement: A Meta-Analytic Review of Research. Review of Educational Research, 75(3), 417–453. https://doi.org/10.3102/00346543075003417
87. Sjøberg, S. (2019). The PISA-syndrome – How the OECD has hijacked the way we perceive pupils, schools and education. Confero: Essays on Education, Philosophy and Politics, 7(1), 12–65.
88. Stearns, E., & Glennie, E.J. (2010). Opportunities to participate: Extracurricular activities’ distribution across and academic correlates in high schools. Social Science Research, 39(2), 296–309. https://doi.org/10.1016/j.ssresearch.2009.08.001
89. Sudrajad, K., Soemanto, Rb., & Prasetya, H. (2020). The Effect of Bullying on Depression, Academic Activity, and Communication in Adolescents in Surakarta: A Multilevel Logistic Regression. Journal of Health Promotion and Behavior, 5(2), 79–86. https://doi.org/10.26911/thejhpb.2020.05.02.02
90. Suna, H.E., Tanberkan, H., & Özer, M. (2020). Changes in Literacy of Students in Turkey by Years and School Types: Performance of Students in PISA Applications. Eğitimde ve Psikolojide Ölçme ve Değerlendirme Dergisi, 11(1), 76 97. https://doi.org/10.21031/epod.702191
91. Tang, X., & Zhang, D. (2020). How informal science learning experience influences students’ science performance: A cross-cultural study based on PISA 2015. International Journal of Science Education, 42(4), 598–616. https://doi.org/10.1080/09500693.2020.1719290
92. Tatar, E., Tüysüz, C., Tosun, C., & Ilhan, N. (2016). Investigation of Factors Affecting Students’ Science Achievement According to Student Science Teachers. International Journal of Instruction, 9(2), 153–166.
93. Tingir, S., & Almond, R. (2017). Using Bayesian Networks to Visually Compare the Countries: An Example from PISA. Journal of Education, 4(3), 11.
94. Topçu, M.S., Arıkan, S., & Erbilgin, E. (2015). Turkish Students’ Science Performance and Related Factors in PISA 2006 and 2009. The Australian Educational Researcher, 42(1), 117–132. https://doi.org/10.1007/s13384-014-0157-9
95. Topçu, M.S., Erbilgin, E., & Arikan, S. (2016). Factors Predicting Turkish and Korean Students’ Science and Mathematics Achievement in TIMSS 2011. EURASIA Journal of Mathematics, Science and Technology Education, 12(7). https://doi.org/10.12973/eurasia.2016.1530a
96. Torrecilla Sánchez, E.M., Olmos Miguélañez, S., & Martínez Abad, F. (2019). Explanatory factors as predictors of academic achievement in PISA tests. An analysis of the moderating effect of gender. International Journal of Educational Research, 96, 111–119. https://doi.org/10.1016/j.ijer.2019.06.002
97. Üstün, U., Özdemi̇r, E., Cansiz, M., & Cansiz, N. (2020). Türkiye’deki Öğrencilerin Fen Okuryazarlığını Etkileyen Faktörler Nelerdir? PISA 2015 Verisine Dayalı Bir Hiyerarşik Doğrusal Modelleme Çalışması [What are the Factors Affecting Students' Science Literacy in Turkey? A Hierarchical Linear Modeling Study Based on PISA 2015 Data]. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 35(3), Article 3.
98. van der Berg, S. (2008). How effective are poor schools? Poverty and educational outcomes in South Africa. Studies in Educational Evaluation, 34(3), 145 154. https://doi.org/10.1016/j.stueduc.2008.07.005
99. Wachs, S., Bilz, L., Niproschke, S., & Schubarth, W. (2019). Bullying Intervention in Schools: A Multilevel Analysis of Teachers’ Success in Handling Bullying from the Students’ Perspective. The Journal of Early Adolescence, 39(5), 642 668. https://doi.org/10.1177/0272431618780423
100. White, H. (2018). Small Class Size Has at Best a Small Effect on Academic Achievement. Plain Language Summary. In Campbell Collaboration. Campbell Collaboration. https://eric.ed.gov/?id=ED610283
101. Wong, T.-T. (2015). Performance evaluation of classification algorithms by k-fold and leave-one out cross validation. Pattern Recognition, 48(9), 2839 2846. https://doi.org/10.1016/j.patcog.2015.03.009
102. Wößmann, L. (2005). Educational production in Europe. Economic Policy, 20(43), 446–504. https://doi.org/10.1111/j.1468-0327.2005.00144.x
103. Xing, W., Li, C., Chen, G., Huang, X., Chao, J., Massicotte, J., & Xie, C. (2021). Automatic Assessment of Students’ Engineering Design Performance Using a Bayesian Network Model. Journal of Educational Computing Research, 59(2), 230 256. https://doi.org/10.1177/0735633120960422
104. Yang, Y., & Webb, G.I. (2002). A Comparative Study of Discretization Methods for Naive-Bayes Classifiers. In Proceedings of PKAW 2002: The 2002 Pacific Rim Knowledge Acquisition Workshop, 159–173.
105. Yip, D.Y., Chiu, M.M., & Ho, E.S.C. (2004). Hong Kong Student Achievement in OECD-PISA Study: Gender Differences in Science Content, Literacy Skills, and Test Item Formats. International Journal of Science and Mathematics Education, 2(1), 91–106. https://doi.org/10.1023/B:IJMA.0000026537.85199.36
106. Yıldırım, S. (2012). Teacher Support, Motivation, Learning Strategy Use, and Achievement: A Multilevel Mediation Model. The Journal of Experimental Education, 80(2), 150–172. https://doi.org/10.1080/00220973.2011.596855
107. Zhang, P. (1992). On the Distributional Properties of Model Selection Criteria. Journal of the American Statistical Association, 87(419), 732 737. https://doi.org/10.1080/01621459.1992.10475275
108. Zwick, R., & Lenaburg, L. (2009). Using Discrete Loss Functions and Weighted Kappa for Classification: An Illustration Based on Bayesian Network Analysis. Journal of Educational and Behavioral Statistics, 34(2), 190 200. https://doi.org/10.3102/1076998609332106