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# Statistical analysis of university rankings

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Presentation of the main results from the paper in "Osvita i upravlinnia" (2011, No 1, P. 7 - 12)

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### Statistical analysis of university rankings

1. 1. STATISTICAL ANALYSIS OF UNIVERSITY RATINGS Bakhrushin V.E. (2011), Osvita i Upravlinnia, № 1, P. 7 – 12. https://www.researchgate.net/publication/23272 7899_Statistical_analysis_of_University_rankin gs_(in_Ukrainian)/file/d912f50941e26e6bd3.pdf
2. 2. Some a priori requirements for the statistical characteristics  Satisfactory resolving power: mean value should be close to the middle of the interval of possible values; skewness must be close to zero; standard deviation should be in limits 0.13 – 0.25 from the difference between maximum and minimum scores, depending on the number of analyzed universities: The absence of correlation between components.
3. 3. Empirical distribution functions (EDF) of rating overall scores score (R/10) (R/10)
4. 4. EDF calculation and properties F(R) = n/N, where n is an sequence number of the university in the sample ordered in ascending of R; N – is the total number of universities in rating. F(R) value is a probability that the value of the outcome rating score does not exceed R. We can see that the functions for the different ratings are very different from each other. In particular, for Ukrainian TOP-200 Universities we have highly skewed distribution, and for Times and National rating of the Russian universities – inhomogeneous distributions.
5. 5. Distribution models ARWU: ( ) ( )F(R) 0,59N 29,3;3,5 0,49N 47,8;12,9= + Times: ( ) ( )F(R) 0,601N 404;90 0,399N 678;78= + Russian: ( ) ( )F(R) 0,62N 23,6;3,1 0,38N 50,9;5,3= + Ukrainian TOP-200: ( )F(R) L 2,11;0,582= N(a;b) – normal distribution; L(a;b) – lognormal distribution with parameters a and b.
6. 6. Statistical properties of score distributions Mean value Asymmetry Standard deviation (normalized) ARWU (2004-2009) 36 – 38 1,78 – 1,95 0,17 – 0,19 Sunday Times (2007 – 2011) 49 – 52 0,33 – 0,57 0,21 – 0,22 Ukrainian TOP-200 (2007 – 2009) 8 – 18 2,7 – 4,2 0,12 – 0,14 Russian-2009 35,1 1,39 0,2
7. 7. EDF for components of Sunday Times – 2007 rating
8. 8. Correlation of ARWU components For ARWU rating correlation coefficients between the components usually exceed 0.5, and in some cases may be up to 0.87.
9. 9. Correlation of the Ukrainian TOP- 200 Universities components For the rest pairs of component also there is a significant correlation Staff quality Educationquality Kharkov NU NTU “KhPI” National medical Univ. T. Shevtchenko Kyiv Univ. NTUU “KPI”
10. 10. Correlation of the Sunday Times- 2007 components For the rest pairs of component also, as a rule, there is no significant correlation Staff quality Jobplacement