Measuring heterogeneity of the educational system Alina Ivanova

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Measuring heterogeneity of the educational system Alina Ivanova, Fuad Aleskerov, Elena Kardanova, Isak Frumin

Measuring heterogeneity of the educational system Alina Ivanova, Fuad Aleskerov, Elena Kardanova, Isak Frumin Higher School of Economics, Moscow, Russia Higher School of Economics , Moscow, 2014 www. hse. ru

Heterogeneity in education Ø Mass higher education Ø Freshmen with different social, economic and

Heterogeneity in education Ø Mass higher education Ø Freshmen with different social, economic and academic backgrounds photo Ø To which extent has the system of higher education become nonhomogeneous? photo Higher School of Economics , Moscow, 2014

Studying heterogeneity in education Different views ü diversification of higher education institutions (Reichert, 2009;

Studying heterogeneity in education Different views ü diversification of higher education institutions (Reichert, 2009; photo Carnevale; Strohl, 2010; Posselt et al. , 2012) ü selectivity of higher education institutions, (Calmand et al. , 2009; Hurwitz, 2011; Pastine & Pastine, 2012) ü heterogeneity of the student population (van Ewijk, 2010; De Paola, Scoppa, 2010; Bielinska-Kwapisz and Brown, 2012) Different methods photo ü statistical and econometric tools • Standard deviation, coefficient of variation (Murdoch, 2002) • Gini coefficient (Bosi, Seegmuller, 2006; Sudhir, Segal, 2008) photo • Multidigraphs (Fedriani and Moyano, 2011) Higher School of Economics , Moscow, 2014

About our work Ø Another approach to estimate heterogeneity in education Ø Heterogeneity of

About our work Ø Another approach to estimate heterogeneity in education Ø Heterogeneity of an educational system photo Ø A mathematical model based on the construction of universities’ interval order Ø The Unified State Examination (USE) scores of Russian students are photo used to illustrate how our measure of the system’s heterogeneity works. . Higher School of Economics , Moscow, 2014 photo

Our model: Construction of the interval order photo Intervals for 5 universities photo Graph

Our model: Construction of the interval order photo Intervals for 5 universities photo Graph of the interval order for the 5 universities Higher School of Economics , Moscow, 2014 The incidence matrix

Our model: Evaluation of the heterogeneity 1. The interval order P is constructed 2.

Our model: Evaluation of the heterogeneity 1. The interval order P is constructed 2. The notion of ideal interval order Pid is defined photo Then as the measure of heterogeneity the Hamming distance is used. photo Comparing the matrices for the real and the ideal interval orders and using Formula we calculate the Hamming distance between two interval orders Higher School of Economics , Moscow, 2014 photo

Our model: how does it work? Parameters of “real” universities Mean USE score University

Our model: how does it work? Parameters of “real” universities Mean USE score University A B C D 60 65 80 90 Standard deviation 5 5 3 5 Incidence matrix for ‘real’ data Respective intervals Mean - SD Mean + SD 55 60 77 85 65 70 83 95 A B C D A 0 0 B 0 0 C 1 1 photo 0 0 D 1 1 1 0 • • Any ideal system: as an example, clustering For each university - its ideal counterpart with the mean value as the center of the cluster and with the interval [m – SD; m + SD] The incidence matrix for the interval photo Intervals for clustered data order for clustered data Ideal points by clustering Ideal point left i. A 59 66 i. B 59 66 i. C 78 92 i. D 78 92 Higher School of Economics , Moscow, 2014 Ideal point right i. A i. B i. C i. D i. A 0 0 i. B 0 0 i. C 1 1 0 0 i. D 1 1 0 0 photo The Hamming distance between real interval order and PI is equal to 0. 08.

The data The monitoring database "Quality of students’ enrollment - 2012". The database contains;

The data The monitoring database "Quality of students’ enrollment - 2012". The database contains; • Mean scores of Unified State Examination (USE) of full-time students enrolled in 2012 on the Bachelor Degree Programs, • Information on the forms of admission (on competition, out of competition, on a tuition-based basis or on a state-financed basis, etc. ). • Open data ü We examine the heterogeneity in the context of integrated groups of majors – in Economics and Management Group of Majors Total number of universities Economy and management 379 Total number of enrolled students 91 336 Score mean (range) 46 – 84 Standard deviation (range) Higher School of Economics , Moscow, 2014 3. 1 – 17. 2

The notion of ideal system • Simulated data Artificially • Experts view ideal •

The notion of ideal system • Simulated data Artificially • Experts view ideal • Real data Based on • Experts view real data Higher School of Economics , Moscow, 2014

Our ideal system Ideal educational system for Economics and Management: expert view ü 1)

Our ideal system Ideal educational system for Economics and Management: expert view ü 1) A group of best universities that train managers, strategists, high-class analysts (about 10% of universities, the average score of the whole contingent of enrolled students should not fall below 75) ü 2) A group of strong universities that train strong professionals for regional labor markets (about 70% of universities, the average score from 65 to 74). ü 3) Group of universities preparing bachelors on applied programs (about 20% of universities, an average USE score of the admitted contingent should not be lower than 55). Higher School of Economics , Moscow, 2014

The results Real university replaced by “ideal” counterpart Interval orders for real universities constructed

The results Real university replaced by “ideal” counterpart Interval orders for real universities constructed Interval orders for “ideal” universities constructed Prototype for ideal system. The scores' interval Mean St. Dev. Count (%) >75 79 2. 82 10 (3%) (65; 75] 69 3. 29 52 (14%) (55; 65] 59 2. 67 220 (58%) <=55 52 1. 26 97 (25%) Comparing the matrices P for real and ideal interval orders and using formula (2) we can calculate the Hamming distance between two interval orders: H(P, Pid)=0. 26. Higher School of Economics , Moscow, 2014

Improving system The desirable lower limit of the average USE scores for economics majors

Improving system The desirable lower limit of the average USE scores for economics majors lies at the level of 55 points 97 universities to delete The Hamming distance between real and ideal interval orders becomes H(P, Pid)= 0. 16. Higher School of Economics , Moscow, 2014

Improving system: stage 2 Construct ideal orders Input artificial data Compare matrixes Groups Mean

Improving system: stage 2 Construct ideal orders Input artificial data Compare matrixes Groups Mean Count (%) Top 10% 75 28 (10%) Middle 70% 68 197 (70%) Bottom 20% 50 57 (20%) The Hamming distance between real and ideal interval orders becomes H(P, Pid)= 0. 21. Higher School of Economics , Moscow, 2014

To conclude Ø A new method of studying heterogeneity in the higher education system

To conclude Ø A new method of studying heterogeneity in the higher education system Ø Our method is based on the comparison of the hypothetical educational system to the real system Ø We showed how our method works on Russian data Ø The model proposed can be applied for any other data, educational systems, countries Higher School of Economics , Moscow, 2014

photo Questions and comments photo Higher School of Economics , Moscow, 2014

photo Questions and comments photo Higher School of Economics , Moscow, 2014