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In the light of an increasing interest in the accountability of public institutions, this paper sets out the statistical issues involved in making quantitative comparisons between institutions in the areas of health and education. We deal in detail with the need to take account of model-based uncertainty in making comparisons. We discuss the need to establish appropriate measures of institutional ’outcomes’ and base-line measures and the need to exercise care and sensitivity when interpreting apparent differences. The paper emphasizes that statistical methods exist which can contribute to an understanding of the extent and possible reasons for differences between institutions. It also urges caution by discussing the limitations of such methods.