Department of Nephrology, Chi-Mei Medical Center, Tainan, Taiwan.
Department of Sport Management, College of Leisure and Recreation Management, Chia Nan University of Pharmacy and Science, Tainan, Taiwan.
Health Qual Life Outcomes. 2020 Apr 28;18(1):111. doi: 10.1186/s12955-020-01356-6.
Ferguson's δ and Gini coefficient (GC) are defined as contrasting statistical measures of inequality among members within populations. However, the association and cutting points for these two statistics are still unclear; a visual display is required to inspect their similarities and differences.
A simulation study was conducted to illustrate the pertinent properties of these statistics, along with Cronbach's α and dimension coefficient (DC) to assess inequality. We manipulated datasets containing four item lengths with two number combinations (0 and 33%) in item length if two domains exist. Each item difficulty with five-point polytomous responses was uniformly distributed across a ± 2 logit range. A simulated response questionnaire was designed along with known different structures of true person scores under Rasch model conditions. This was done for 20 normally distributed sample sizes. A total of 320 scenarios were administered. Four coefficients (Ferguson's δ, GC, test reliability Cronbach's α, and DC) were simultaneously calculated for each simulation dataset. Box plots were drawn to examine which of these presented the correct property of inequality on data. Two examples were illustrated to present the index on Google Maps for securing the discriminatory power of individuals.
We found that 1-Ferguson's δ coefficient has a high correlation (0.95) with GC. The cutting points of Ferguson's δ, GC, test reliability Cronbach's α, and the DC are 0.15, 0.50, 0.70, and 0.67, respectively. Two applications are shown on Google Maps with GCs of 0.14 and 0.42, respectively. Histogram legends and Lorenz curves are used to display the results.
The GC is recommended to readers as an index for measuring the extent of inequality (or lower discrimination power) in a given dataset. It can also show the study results of person measures to determine the inequality in the health-related quality of life outcomes.
弗格森的δ和基尼系数（GC）被定义为用于衡量群体内成员之间不平等的对比统计量。然而，这两个统计量的关联和切点尚不清楚；需要进行可视化显示，以检查它们的相似之处和不同之处。
进行了一项模拟研究，以说明这些统计量的相关特性，以及克朗巴赫的α和维度系数（DC）来评估不平等。我们操纵了包含四个项目长度的数据集，并在存在两个域的情况下对项目长度进行了两种数字组合（0 和 33%）的处理。每个项目难度都有五个五点多分类反应，均匀分布在一个正负 2 对数单位范围内。根据 Rasch 模型条件下的真实个体分数的不同结构，设计了一个模拟反应问卷。对于 20 个正态分布的样本量进行了此操作。共管理了 320 个场景。为每个模拟数据集同时计算了四个系数（弗格森的δ、GC、测试可靠性克朗巴赫的α和 DC）。绘制箱线图以检查这些系数中哪一个在数据上呈现了正确的不平等属性。通过两个示例来说明在 Google 地图上展示指数，以确保个体的辨别力。
我们发现，1-弗格森的δ系数与 GC 具有高度相关性（0.95）。弗格森的δ、GC、测试可靠性克朗巴赫的α和 DC 的切点分别为 0.15、0.50、0.70 和 0.67。在 Google 地图上展示了两个应用，GC 分别为 0.14 和 0.42。使用直方图图例和洛伦兹曲线显示结果。
建议读者将 GC 作为衡量给定数据集中不平等程度（或较低辨别力）的指标。它还可以显示个体测量的研究结果，以确定与健康相关的生活质量结果的不平等。
