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題名:國民小學學校效率量數之探討:SFA與DEA之比較
作者:陳河開
作者(外文):HO-KAI CHEN
校院名稱:高雄師範大學
系所名稱:教育學系
指導教授:陳麗珠
學位類別:博士
出版日期:2015
主題關鍵詞:學校效率教育成本隨機邊界法資料包絡法school efficiencyeducation coststochastic frontier analysisdata envelopment analysis
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本研究旨在探討不同取向之效率衡量方法:隨機邊界法(Stochastic Frontier Analysis,SFA)與資料包絡法(Data Envelopment Analysis,DEA),衡量學校效率結果之異同,從而分析不同方法論應用於學校效率評估之適用性。研究目的包括:(一)探討澎湖縣國小教育成本內涵與特性;(二)探討澎湖縣國小學生成績表現;(三)以DEA衡量學校效率,分析結果及參數訊息;(四)探討SFA衡量國小效率可行性,分析結果與參數訊息;(五)探討SFA與DEA效率值之異同,提供方法選用參考並就不同類型學校提供效率改善建議。
本研究以澎湖縣2011年40所國民小學為對象,以教育成本做為投入,投入變項分為公、私部門二類,公部門成本採用學校年度財務收支報表之人事費、材料費及獎補助等3項支出;以自編之家庭教育成本問卷蒐集課後學習花費、學用材料花費為私部門成本。以學生學業成就做為產出,產出變項選定2011年澎湖縣辦理之學生能力普測成績。效率衡量獲得二種方法之效率值與參數訊息,分析參數訊息並以統計分析方法探究受評學校二種效率值、分佈情形、排序以及與學校相關背景變項之關聯,檢視不同方法結果並歸納方法論之適用特性,提出學校效率分析之建議。
根據研究發現,本研究做出結論如下:(一)澎湖縣國小學生公成本每生年約25萬元,私成本每生年約2萬9仟元。公私成本反映城鄉差異。(二)澎湖縣小校學生成就表現呈兩極化現象,離島學校表現低於其他小型學校。(三)SFA適用衡量各種規模學校表現。(四) SFA效率決定於教育產出,DEA追求低投入創造高產出。(五) SFA能為所有學校設定理想目標,DEA只能提供非效率學校理想目標。 (六)二種效率排序呈現四類學校特徵,可藉以提供小型學校精進效率之策略。
根據研究結果,本研究提出建議如下:(一)效率衡量時須留意學校規模可能造成的影響,且應以SFA驗證投入產出變項之選用代表性。(二)學校應善用效率評估結果,據以相互觀摩參照。(三)利用效率衡量做為學校評比時,建議採用SFA。(四)教育成本分析應同時檢視每生與每班單位數額,並視地區性公私成本配置特徵調整教育投入。(五)應針對本研究歸納之四類效率特徵學校,施以不同之行政管理措施,以協助精進學校效率。
關鍵詞:學校效率、教育成本、隨機邊界法、資料包絡法
This study compared the performance of school efficiency in Penghu County measured by two approaches of measuring: Stochastic Frontier Analysis (SFA) and Data Envelopment Analysis (DEA), thus explored the applicability of adopting these two methodologies for school efficiency measurement. The purposes of this study include: (1) Discussing the content of education costs and the costs of public and private sectors in Penghu; (2) Interpreting the student assessment performance in 2011SY; (3) Adopting DEA to measure school efficiency; (4) Exploiting the feasibility of adopting SFA on school efficiency measurement, and comparing the results with DEA; (5) Enquiring into the characteristics of SFA and DEA, and providing improvement strategies for schools of various types grouped by these two methodologies.
In order to achieve the above purposes, the 40 elementary schools in Penghu County were adopted as the subject. The input variables were defined as the costs from both public and private sectors, the former included personnel expenditure, current operating expenditure, and grants, the latter included after-school tutoring expense and learning material expense by the families collected from questionnaires for parents. On the other hand, the output variable was defined as student test scores in 2011 assessment. Statistical measures were conducted to explore the relation between the two efficiency scores, rankings, and the background variables.
The conclusions of this study were as follows: (1) Per student cost of public sector in Penghu was NT$250,000, while the costs from private sector was only NT$29,000; The results also reflected the disparities among townships; (2) The student test scores were distributed as bimodal. Also, school students enrolled in remote islands were much lower than those enrolled in other townships; (3) SFA was more suitable for measuring schools of different sizes than DEA; (4) The efficiency scores measured by SFA were highly correlated with output variables, while the DEA scores inclined to schools of bigger size and lower costs; (5) SFA could provide each school with their own target scores, while DEA only provide basic guideline; (6) Based on the ordinal values of SFA and DEA efficiency scores of each school, the four groups of schools were provided with their own strategies of efficiency improvement.
Several recommendations were proposed based on the results of this study: (1) School size could cause statistic errors, especially measured by DEA. SFA, on the other hand, can take both input and output into consideration at the same time; (2) Efficiency scores should be adopted as the benchmark for schools in enhancing efficiency; (3) When ranking schools by their efficiency performance, SFA outperformed DEA; (4) When analyzing education cost, per-student and per-class cost should be taken into account, private cost from student families should also considered when allocating expenditures; (5) School authorities should provide administrative assistance to the four efficiency groups based on their specific needs.
Keywords: school efficiency, education cost, stochastic frontier analysis (SFA), data envelopment analysis (DEA)
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