Decision theory for comparing institutions


  • Author: Nicholas T. Longford
  • Date: 09 January 2019
  • Copyright: Image copyright of Patrick Rhodes

Various forms of performance assessment are applied to public service institutions, such as hospitals, schools, police units, and local authorities. Difficulties arise in the interpretation of the results presented in some established formats because they require a good understanding and appreciation of the uncertainties involved. Usually the results have to be adapted to the perspectives of the users—managers of the assessed units, a consumer, or a central authority (a watchdog) that dispenses awards and sanctions. In a paper published in Statistics in Medicine, the author presents a decision‐theoretical approach to these and related problems in which the perspectives are integrated in the analysis and its results are choices from a finite list of options (alternative courses of action).

The paper is available via the link below and the authors explain their findings in further detail below:

Decision theory for comparing institutions

Nicholas T. Longford

Statistics in Medicine, Volume 37, Issue 3, 10 February 2018, pages 457-472


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Annual audits are conducted for most public service institutions in the UK and other developed countries. Their purpose is to assess whether these institutions provide services of adequate quality, and to highlight units (hospitals, schools, or the like) that are outstanding or unsatisfactory. Such assessments are associated with statistical uncertainty. As a consequence, two kinds of error may occur: a unit may be highlighted inappropriately and another unit is not highlighted, even though it should have been.

These errors are called 'false discovery' and 'failure to discover'. Established  methods to dealing with this uncertainty focus on controlling the rate (frequency) of false discovery at the expense of keeping in check the rate of failure to discover. This article proposes an alternative in which the rates of the two types of error are in a balance that reflects their consequences(ramifications), implied by the perspectives, remits and value judgements of the parties for whom the audit report is intended. Of course, these consequences have to be elicited from qualified experts and presented in a quantitative form suitable for the analysis.

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