Assessing pupil and school performance by non-parametric and parametric techniques

Abstract

This paper discusses the use of the non-parametric free disposal hull (FDH) and the parametric multi-level model (MLM) as alternative methods for measuring pupil and school attainment where hierarchical structured data are available. Using robust FDH estimates, we show how to decompose the overall inefficiency of a unit (a pupil) into a unit specific and a higher level (a school) component. By a sample of entry and exit attainments of 3017 girls in British ordinary single sex schools, we test the robustness of the non-parametric and parametric estimates. Finally, the paper uses the traditional MLM model in a best practice framework so that pupil and school efficiencies can be computed.

Keywords:

• performance measurement
• free disposal hull
• multi-level modelling
• secondary education

Acknowledgements

The authors are grateful to the Department for Children, Schools and Families for financial support and for providing the data. The contents of the paper are the responsibility of the authors and no representation is being made that the Department shares these views.

Notes

1 Remark that we determined m=110 pupils and B=100. However, as a sensitivity test for m=110 we experimented with m=n (ie the size of the school). The sensitivity test delivered very similar results for the pupil-within-school and pupil-within-all-schools efficiency (a Pearson correlation coefficient of, respectively, 0.998 and 0.996 and an increase in the average mean of only 0.34% and 3.2%).

2 We estimated the MLM by MLwiN (Rasbash et al, 2005).

3 Note that these statistics are conditional on the assumptions of the model, that is m=110, B=100 and proportion of top attainments discounted in the MLM approach t=5%. However, even for other levels of m, B and t we find significant and high correlations.