Geni-Derived Index Effectiveness in Educational Inequality Measurement

教育公平性測量：Gini係數衍生指標的效能分析

李茂能(Mao-Neng Li)

Gini係數 ； Lorenz曲線 ； 教育成就 ； 公平性測量 ； Gini Coefficient ； Lorenz Curve ； Education Attainment ； Inequality Measurement

嘉大教育研究學刊

30期（2013 / 03 / 30）

53 - 78

英文

本模擬研究旨在探討11種Gini係數導向的相對效能與X軸等份分割數、教育資料分配型態及離散程度屬性間之關係。一般而言，教育Gini係數的相對效能會受到資料的組別數、離散程度與分配型態所支配。教育Gini係數的測量正確性會，隨著組別數的增加或離散程度的降低而改善。不管資料的組別數、離散程度與評鑑效標為何，G1與G2指標在資料出現正偏時會產生最大的估計誤差，在資料出現負偏時會產生最小的估計誤差。其它的教育Guni指標G3, G4, G5, G6, G7僅在組別數為5且資料出現正偏時，會出現類似最大估計誤差；在組別數為10且資料出現負偏時，也會出現類似最大估計誤差；當資料呈現常態時，其估計誤差最小。除了G1之外，其它的教育Guni指標均出現低估現象。G1似乎比較適合於組別數小於5的情境。因此，指標的選擇與應用方式對於結論會產生重大的影響力。假如組別數等於或小於5或估計誤差無 法容忍時，建議將G3, G4,與G5等係數乘以向上校正因子（n/(n-1)）。

In a simulation study, eleven frequently-used Gini indices of educational inequality were investigated for their sensitivity to educational attainment distribution and the number of groups used for data analysis. In general, index effectiveness was influenced by the number of grouping, forms of distribution, and size of variance involved. The accuracy of inequality measures increases as the number of groups increases or as the size of variance decreases. G1, and G2 demonstrate greatest estimation error with positively skewed data and least estimation error with negatively skewed data, regardless of variance, grouping size, and criterion index used. The other Gini-based indices G3, G4, G5, G6, G7 produce similar patterns of maximum error with postively skewed data when the grouping size is 5; yet, when the grouping size is 10, they tend to display greatest error with negatively skewed data and least error with normal data. Indices of Gini are all under-estimated except for the G1. G1 seems an unbiased index for a small grouping size less than 5. Therefore, the choice of index and method of implementation can have critical bearing on the conclusions reached. If 5 or fewer groups are used or the estimated error is not tolerable, it is recommended that one upwardly adjust the G3, G4 or G5 estimates by a factor of n/(n-1).

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