Research evaluations and comparison of the assessments of academic institutions (scientific areas, departments, universities etc.) are among the major issues in recent years in higher education systems. One method, followed by some national evaluation agencies, is to assess the research quality by the evaluation of a limited number of publications in a way that each publication is rated among $n$ classes. This method produces, for each institution, a distribution of the publications in the $n$ classes. In this paper we introduce a natural geometric way to compare these assessments by introducing an ad hoc distance from the performance of an institution to the best possible achievable assessment. Moreover, to avoid the methodological error of comparing non-homogeneous institutions, we introduce a {\em geometric score} based on such a distance. The latter represents the probability that an ideal institution, with the same configuration as the one under evaluation, performs worst. We apply our method, based on the geometric score, to rank, in two specific scientific areas, the Italian universities using the results of the evaluation exercise VQR 2011-2014.

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解释研究评估的结果：一种几何方法

研究评估和学术机构（科学领域，系，大学等）评估的比较是近年来高等教育系统中的主要问题。一些国家评估机构采用的一种方法是通过对有限数量的出版物进行评估来评估研究质量，以使每个出版物都被评为$ n $类。此方法为每个机构生成$ n $类中的出版物分发。在本文中，我们介绍了一种自然的几何方法，通过引入从机构绩效到可能的最佳可行评估的特殊距离来比较这些评估。此外，为避免比较非均质机构的方法学错误，我们基于这种距离引入了{\ em几何分数}。后者代表具有与所评估机构相同配置的理想机构表现最差的概率。我们根据几何分数应用我们的方法，使用VQR 2011-2014评估结果在两个特定的科学领域对意大利大学进行排名。