Averages of ratios compared to ratios of averages: Mathematical results
Averages of ratios compared to ratios of averages: Mathematical results
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DOI：
10.1016/j.joi.2011.12.007
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发表时间：
2012-04-01
影响因子：
3.7
通讯作者：
Egghe, L.
中科院分区：
文献类型：
--
作者：
Egghe, L.
最近兴起的关于比率平均值 (AoR) 与平均值比率 (RoA) 相比的可用性的讨论得出了本文的数学结果。基于 Lariviere 和 Gingras (2011) 的经验结果，我们在合理的条件下证明了一组点的 AoR 和 RoA 之间的以下关系：(i) AoR 函数中的 RoA 回归线是第一等分线。(ii) 论文数量 N 函数中的 (AoR - RoA)/AoR 是由 1 根 N 和 - 1 根 N 的倍数组成的点云。(iii) (AoR - RoA)/AoR 与 RoA 相比具有递减的回归线。 (C) 2012 Elsevier Ltd. 保留所有权利。
The recently awakened discussion on the usability of averages of ratios (AoR) compared to ratios of averages (RoA) has led to the mathematical results in this paper. Based on the empirical results in Lariviere and Gingras (2011) we prove, under reasonable conditions, the following relations between AoR and RoA for a set of points:(i) The regression line of RoA in function of AoR is the first bisectrix.(ii) (AoR - RoA)/AoR in function of the number N of papers is a cloud of points comprised between a multiple of 1 root N and - 1 root N.(iii) (AoR - RoA)/AoR versus RoA has a decreasing regression line. (C) 2012 Elsevier Ltd. All rights reserved.