Measuring heterogeneity of the educational system Higher School of Economics, Moscow, 2014 Alina...

Measuring heterogeneity of the educational system

Higher School of Economics , Moscow, 2014

www.hse.ru

Alina Ivanova, Fuad Aleskerov, Elena Kardanova, Isak Frumin Higher School of Economics, Moscow, Russia


Heterogeneity in education

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Mass higher education

Freshmen with different social, economic and academic backgrounds

To which extent has the system of higher education become non-homogeneous?


Studying heterogeneity in education

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Different views

diversification of higher education institutions (Reichert, 2009; Carnevale; Strohl, 2010; Posselt et al., 2012)

selectivity of higher education institutions, (Calmand et al., 2009; Hurwitz, 2011; Pastine & Pastine, 2012)

heterogeneity of the student population (van Ewijk, 2010; De Paola, Scoppa, 2010; Bielinska-Kwapisz and Brown, 2012)

Different methods

statistical and econometric tools• Standard deviation, coefficient of variation (Murdoch, 2002)• Gini coefficient (Bosi, Seegmuller, 2006; Sudhir, Segal, 2008)• Multidigraphs (Fedriani and Moyano, 2011)


About our work

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Another approach to estimate heterogeneity in education

Heterogeneity of an educational system

A mathematical model based on the construction of universities’

interval order

The Unified State Examination (USE) scores of Russian students are

used to illustrate how our measure of the system’s heterogeneity

works.

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Our model:Construction of the interval order

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The set of all universities AFor each university i it is known the set of students entrance grades• Assume that each university is defined by some interval [] depending on the entrance

exam grade.• Use the mean value of grades and standard deviation to construct the interval order• If the left boundary for i lies at the right of the right boundary of j, then we include the pair

(i,j) to the interval order

Intervals for 5 universities

Graph of the interval order for the 5 universities

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5

4

3

2

1

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P

The incidence matrix


Our model:Evaluation of the heterogeneity

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1. The interval order P is constructed

2. The notion of ideal interval order Pid is defined

where ij is equal to 1 if the pair (i ; j) belongs to the interval order B1, otherwise =0; ij is equal to 1 if the pair belongs to the interval order B2 , otherwise it is equal to 0.

Comparing the matrices for the real and the ideal interval orders and using Formula we calculate the Hamming distance between two interval orders

Then as the measure of heterogeneity the Hamming distance is used.


Our model: how does it work?

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University Mean USE score

Standard deviation

Respective intervalsMean - SD Mean + SD

A 60 5 55 65B 65 5 60 70C 80 3 77 83D 90 5 85 95

Parameters of “real” universities

A B C D

A 0 0 0 0

B 0 0 0 0

C 1 1 0 0

D 1 1 1 0

Incidence matrix for ‘real’ data

• 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]

Ideal points by clustering

Ideal point left Ideal point right

iA 59 66

iB 59 66

iC 78 92

iD 78 92

Intervals for clustered data

iA iB iC iD

iA 0 0 0 0

iB 0 0 0 0

iC 1 1 0 0

iD 1 1 0 0

The incidence matrix for the interval order for clustered data

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;• 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

We examine the heterogeneity in the context of integrated groups of majors – in Economics and Management

Group of Majors Economy and management

Total number of universities 379

Total number of enrolled students 91 336

Score mean (range) 46 – 84

Standard deviation (range) 3.1 – 17.2


The notion of ideal system

• Simulated data• Experts view

Artificially ideal

• Real data• Experts view

Based on real data


Our ideal system

Ideal educational system for Economics and Management: expert view

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)

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).

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).

Interval orders for real

universities constructed

Real university replaced by

“ideal” counterpart

Interval orders for “ideal” universities constructed


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%)

Prototype for ideal system.

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.

The results


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.

Improving system


The Hamming distance between real and ideal interval orders becomes H(P,Pid)= 0.21.

Improving system: stage 2

Input artificial data

Construct ideal orders

Compare matrixes

Groups Mean Count (%)

Top 10% 75 28 (10%)

Middle 70% 68 197 (70%)

Bottom 20% 50 57 (20%)


To conclude

A new method of studying heterogeneity in the higher

education system

Our method is based on the comparison of the

hypothetical educational system to the real system

We showed how our method works on Russian data

The model proposed can be applied for any other

data, educational systems, countries


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