Comparison of Technical and Managerial Efficiencies in Education System Using Bootstrap Data Envelopment Analysis and TIMSS Dataset

Abstract

The research aimed to determine whether 58 countries participating in the 4th grade mathematics and science exam within the scope of TIMSS 2015 effectively manage their inputs, which are thought to be related to their success. For this purpose, non-parametric resampling data envelopment analysis (bootstrap DEA) was used to estimate the relative total efficiency scores of countries. The reason for using the Bootstrap DEA approach is that the estimated bound is an easy way to analyze the sensitivity of event scores to sampling variations. The data used in this study were obtained based on the mathematics and science achievements of the students, with the IEA IDB Analyzer program of the questionnaires filled out by the students, teachers and school principals. Countries that use educational inputs that affect mathematics and science achievement relatively effectively are Russia, America and China-Taipei (Taiwan), respectively, and it has been observed that these regions operate at an almost optimal level and use their input consumption almost optimally to produce the desired stable output. The countries with the lowest efficiency are respectively; It is designated as Armenia, Montenegro, United Arab Emirates (Dubai), North Macedonia, Kuwait, Georgia and the Philippines. Turkey, on the other hand, was determined as the country closest to being active.

Keywords

• Efficiency
• Bootstrap
• Data envelopment
• TIMSS
• Education

Bootstrap Veri Zarflama Analizi ile TIMSS Verileri Kullanılarak Eğitim Sisteminde Teknik ve Yönetsel Etkinliklerin Karşılaştırılması

Abstract

Araştırma, TIMSS 2015 kapsamında 4. sınıf matematik ve fen sınavına katılan 58 ülkenin başarıları ile ilişkili olduğu düşünülen girdilerini, etkin şekilde yönetip yönetmediklerini belirlemeyi amaçlamıştır. Bu amaçla, ülkelerin göreli toplam etkinlik skorlarını tahmin etmek için parametrik olmayan yeniden örnekleme veri zarflama analizinden (bootstrap VZA) yararlanılmıştır. Bootstrap VZA yaklaşımının kullanılmasının nedeni, tahmin edilen sınırın örnekleme varyasyonlarına göre etkinlik puanlarının duyarlılığını analiz etmenin kolay bir yolu olmasıdır. Bu çalışmada değerlendirilen veriler, öğrencilerin, öğretmenlerin ve okul müdürlerinin doldurduğu anketlerin IEA IDB Analyzer programıyla öğrencilerin matematik ve fen başarılarını temel alarak elde edilmiştir. Fen ve matematik başarısına etki eden eğitim girdilerini göreceli olarak etkin kullanan ülkeler sırasıyla Rusya, Amerika ve Çin- Taipei (Tayvan) olarak bulunmuş olup, bu bölgelerin neredeyse optimal düzeyde faaliyet gösterdiği ve istenen sabit çıktıyı üretmek için girdi tüketimlerini de neredeyse optimal kullandıkları gözlemlenmiştir. En düşük etkinliğe sahip olan ülkeler ise sırasıyla; Ermenistan, Karadağ, Birleşik Arap Emirlikleri (Dubai), Kuzey Makedonya, Kuveyt, Gürcistan ve Filipinler olarak belirlenmiştir. Türkiye ise etkin olmaya en yakın ülke olarak tespit edilmiştir.

Keywords

• etkinlik
• bootstrap
• veri zarflama
• TIMSS
• eğitim

References

1. [1] Agasisti, T., & Zoido, P. 2015. The efficiency of secondary schools in an international perspective: preliminary results from PISA 2012.
2. [2] IEA. 2021. International Association for the Evaluation of Educational Achievement. Retrieved from https://timss2019.org/reports/about/
3. [3] PRILS, T. 2021. Trends in International Mathematics and Science Study. Retrieved from https://timssandpirls.bc.edu/
4. [4] Koyuncu, B., ve Ilgaz, G. 2019. Matematik Öğretimi Sürecinde Ülkelerin Eğitim Girdilerini Ne Kadar Etkin Kullandıklarının TIMSS 2015 Verilerine Göre İncelenmesi. Ilkogretim Online, 18(4).
5. [5] Giménez, V., Prior, D., & Thieme, C. 2007. Technical efficiency, managerial efficiency and objective-setting in the educational system: an international comparison. Journal of the Operational Research Society, 58(8), 996-1007.
6. [6] Agasisti, T. 2014. The efficiency of public spending on education: An empirical comparison of EU countries. European Journal of Education, 49(4), 543-557.
7. [7] Tsakiridou, H., & Stergiou, K. 2014. Explaining the efficiency differences in primary school education using data envelopment analysis. Journal of Education, Psychology and Social Sciences, 2(2), 89-96.
8. [8] Arshad, M. N. M. 2014. Efficiency of Secondary Education of a Selected OIC Countries. Global Education Review, 1(4).

9. [9] Yavuz, H., Demirtasli, R., Yalcin, S., & Dibek, M. 2017. The effects of student and teacher level variables on TIMSS 2007 and 2011 mathematics achievement of Turkish students. EGITIM VE BILIM-EDUCATION AND SCIENCE, 42(189).
10. [10] Agasisti, T., & Zoido, P. 2018. Comparing the efficiency of schools through international benchmarking: Results from an empirical analysis of OECD PISA 2012 data. Educational Researcher, 47(6), 352-362.
11. [11] Liouaeddine, M., Elatrachi, M., & Karam, E. M. 2018. The analysis of the efficiency of primary schools in Morocco: modelling using TIMSS database (2011). The journal of North African studies, 23(4), 624-647.
12. [12] Mazurek, J., & Mielcová, E. 2019. On the relationship between selected-socio-economic indicators and student performances in the PISA 2015 study.
13. [13] Haddad, M. Z., Heong, Y. M., Razzaq, A. R. B. A., & Kiong, T. T. 2021. Exploring the Innovative Methods for Evaluating Educational Efficiency. In 2021 International Conference on Decision Aid Sciences and Application (DASA)(pp. 1082-1086). IEEE.
14. [14] Farrell, M. J. 1957. The measurement of productive efficiency. Journal of the Royal Statistical Society: Series A (General), 120(3), 253-281.
15. [15] Charnes, A., Cooper, W. W., & Rhodes, E. 1981. Evaluating program and managerial efficiency: an application of data envelopment analysis to program follow through. Management science, 27(6), 668-697.
16. [16] Stumbriene, D., Camanho, A. S., & Jakaitiene, A. 2020. The performance of education systems in the light of Europe 2020 strategy. Annals of Operations Research, 288(2), 577-608.
17. [17] Charnes, A., Cooper, W. W., ve Rhodes, E. 1978. Measuring the efficiency of decision making units. European journal of operational research, 2(6), 429- 444.
18. [18] Fare, R., Grosskopf, S., ve Kokkelenberg, E. C. 1989. Measuring plant capacity, utilization and technical change: a nonparametric approach. International economic review, 655-666.
19. [19] Efron, B. 1992. Bootstrap methods: another look at the jackknife. In Breakthroughs in statistics (pp. 569-593): Springer.
20. [20] Førsund, F. R., veSarafoglou, N. 2002. On the origins of data envelopment analysis. Journal of Productivity Analysis, 17(1), 23-40.
21. [21] Cooper, W. W., Seiford, L. M., ve Zhu, J. 2011. Data envelopment analysis: History, models, and interpretations. In Handbook on data envelopment analysis (pp. 1- 39): Springer.
22. [22] Kutlar, A., ve Babacan, A. 2008. Türkiye’deki kamu üniversitelerinde CCR etkinliği- ölçek etkinliği analizi: DEA tekniği uygulaması. Kocaeli Üniversitesi Sosyal Bilimler Dergisi(15), 148-172.
23. [23] Coelli, T., ve Perelman, S. 2000. Technical efficiency of European railways: a distance function approach. Applied economics, 32(15), 1967-1976.
24. [24] Simar, L., ve Wilson, P. W. 1998. Sensitivity analysis of efficiency scores: How to bootstrap in nonparametric frontier models. Management science, 44(1), 49- 61.
25. [25] Simar, L. 1992. Estimating efficiencies from frontier models with panel data: a comparison of parametric, non-parametric and semi-parametric methods with bootstrapping. In International Applications of Productivity and Efficiency Analysis (pp. 167-199): Springer.
26. [26] Toma, P., Miglietta, P. P., Zurlini, G., Valente, D., ve Petrosillo, I. 2017. A non- parametric bootstrap-data envelopment analysis approach for environmental policy planning and management of agricultural efficiency in EU countries. Ecological indicators, 83, 132-143.
27. [27] Simar, L., ve Wilson, P. W. 2000. A general methodology for bootstrapping in non- parametric frontier models. Journal of applied statistics, 27(6), 779-802.
28. [28] Simar, L., ve Wilson, P. W. 2002. Non-parametric tests of returns to scale. European journal of operational research, 139(1), 115-132.
29. [29] Simar, L., ve Wilson, P. W. 2007. Estimation and inference in two-stage, semi- parametric models of production processes. Journal of econometrics, 136(1), 31-64.