Dealing With Outliers When Setting Targets by DEA
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Dealing With Outliers When Setting Targets by DEA Gary Simpson The appendix describes how the exceptionalitv
Thanasioulis and Sirnjxson (1999) on/Lined (1/1 approach Jilt setting targets by DM /àr indiziduals that will he realistic yet deni andin g. The ap/seoachfèalured the use o/DELl to identJj eceptional' indiziduals who should he dropped as potential rferents so that the targets would hr niore realistic. 77ie paper 1/Sed the example of settirg ac/ui; inc/It taigets for school children. The technical details to idn/i/iing exceptional induiduals u ere contained in an Appendix that was inadeertentli omitted ¡foin Th.anassoulis and Simpson (/999). This no/e presents the Appendix both in the context o/settng ta/gets and more generally as a n?ethod for identzjuing
index can be calculated and how to compute targets and identify peers once exceptional individuals have been removed.
1he method is drawn from Thanssoulis (1999
which although forthcoming when Thanassoulis and Simpson (1999) was published which is now in print.
This process of calculating the exceptionality index can be considered a device for identifying outliers
and as such it can he useflil more generally in
ou/lieis.
analysis of data. it differs from regression outliers in that it does not depend on some pre-specihed
functional form to which the data lias been fitted. DEA outliers can relate to multiple inputs and multiple outputs. In DEA analysis we are often interested in outliers with very large efficiency as
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Computing the exceptionality index and the final targets of an individual
these will effect the efficient boundary and hence the
attainment targets but individuals with very low
lt is desirable when setting targets for individual to
efficiency , so long as they diffrr sufficiently from the body of data.
belore establishing attainment targets. Here we will
The degree of exceptionality of an individual can he
allow for random noise ariel so we wish to drop exceptional' individuals from our reference set
measured, as here, on the basis of an exceptional level of output fbr a given set of inputs, or on the basis an exceptional level of input for a given set of
consider an individual to be exceptional if their
attainments are sufficiently higher than other comparable individuals. So, using the example of school children, a pupil will he considered exceptional if they achieve significantly higher GCSE scores than others with similar backgrounds and innate ability.
outputs.
À measure of the exceptionality of an individual is
given by the ratio the actual attainment of that
individual to the best attainment that a pupil of the
background and innate ability could be expected to achieve on the basis of the evidence provided of the attainments of the other pupils. Hence a pupi1 with an exceptionality index of 1 .5O°/
would have aclueved a GCSE score 50°/o higher than would be expected on the basis of the other pup ils.
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APPENDIX: Computing the exceptionality index and the final targets of an individual. I a't
Us
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