林大森、陳憶芬 (2006 )。臺灣高中生參加補習之效益分析。教育研究集刊. 52 (4) ,
35-70 。
林忠正、黃璀娟 (2009 )。補習文化。人文及社會科學集刊. 21 (4) '587-643 。 孫清山、黃毅志(1996 )。補習教育、文化資本與教育取得。薑灣社會學刊.19 '
95-139 。
章英華、伊慶春 (20肘， 6月) 0 Cram Schooling and Academic Achievement: A Remedial Strategy,a Proactive Strategy or Just a Mimic Behavior。論文發表於中央研究院社會 學研究所舉辦之「臺灣青少年成長歷程研究」第一次學術研討會，臺北市。
張主雲 (2004 )。矗灣教育長期追雖員料庫:第一波(2001 )圈中家長問卷【公共使用 版電子檔】、圈中學生表現評量問卷【公共使用版電子檔】。臺北市:中央研究院 調查研究專題中心【管理、釋出單位】。
張主雲( 2006a) 。薑禮教育長期追雖資料庫:第一波(2003 )園中學生問卷【公共使用 版電子檔】、國中家長問卷【公共使用版電子檔】。臺北市:中央研究院調查研究 專題中心【管理、釋出單位】。
張主雲 (2006b) 。薑灣教育長期追趾資料庫:第二波(2003 )圈中學生問卷【公共使用
8 關秉寅與李敦義 (2008 )以父母教育程度分層進一步分析國三補習數學之效果顯示，在 其他配對條件相同的假定下，父母教育程度為高中及以下之國三學生補習數學的效果 較大些。本研究進一步將父母教育程度分成國高中與大專(含)以上等兩層，以兩種 Kernel l!ii己對法進行分析後，其結果顯示，不論是哪一層，也不論是哪一階段補習.ATT
均未達顯著。這可能與分層後配對樣本數較小有關。如不論是否達顯著，以 A叮的大 小來看，國二開始補習數學者，也是父母為國高中程度者的效果稍大，但其他組則是 父母為大專以上程度者稍大。各配對組間分層的差距均小於 2 分。如讀者有興趣得知 此處分析的結果，請聯絡第一作者。
版電子檔】。臺北市:中央研究院調查研究專題中心【管理、釋出單位】。
張主雲 (2007 )。薑遭教育長期追蹤資料庫:第一波 (2001 )、第二波 (2003 )、第三 波 (2005 )資料使用手冊【公用使用版】。臺北市:中央研究院調查研究專題中 心【管理、釋出單位】。
黃毅志、陳俊瑋 (2008 )。學科補習、成擴表現與升學結果一一-以學測成績與上公立大 學為例。教育研究集刊，到(l) '117-149 。
劉正 (2006 )。補習在臺灣的變遷、效能與階層化。教育研究集刊，但 (4) '1-33 。 蔡椒鈴、塵海?原 (2002 )。臺灣教育階層化的變遷。國家科學委員會研究暈刊:人文及
社會科學， 2 (l) '98-118 。
關秉寅、李敦義 (2008 )。補習數學有用嗎?一個「反事實」的分析。薑灣社會學刊，
41 ' 97-148 。
Alexander,K. L.,Entwisle,D. R.,& Olson, L. S. (2007). Lasting consequences of summer learning gap.American SociologicalReview， 刀， 167-180.
Allalouf,A.,& Ben-Shakhar,G. (1998). The effect of coaching on the predictive validity of scholastic aptitude tests.Journal ofEducational Measurement,35,31-47.
Aronson, 1., Zimmerman,J.,& Carlos, L.(1999).Improving student achievement by extending school: Is itjust a matter oftime? Retrieved June 15, 2008 ,from http://eric.ed.gov/
ERICDocs/datalericdocs2sql!content_storage_01/00000 19b/80/15/ealc4.pdf
Baker, D. P.,Aki恤， M.,LeTendre,G. K.,& Wiseman,A. W. (2001). Worldwide shadow education: Outside-school learning,institutional quality of schooling,and cross-national mathematics achievement.Educational Evaluation and Policy Analysis,1,1-17.
Baker,D. P.,& LeTendre,G.K.(2005).Nationaldifferenc仰， global similarities: World culture and the future ofschooling.Stanford,CA: Stanford University Press.
Becker,B. J. (1990). Coaching for the scholastic aptitude test: Further synthesis and appraisal.
Review ofEducational Research,60,373-417.
Berliner,D. C.(1990). Whats allthe戶ssabout instructional time? the nature oftime in schools:
Theoretical concepts,practitionerperc中tions.New York: Teacher College Press.
Blau,P. M.,& Duncan,O. D. (1967). The American occupational structure.New York: John Wiley.
Bray,M. (1999). The shadow education system: Private tutoring and its implications for planners.Paris: UNESCO,International Institute for Educational Planning.
Bray,M. (2003). Adverse effects of private supplementary tutoring: Dimensions, implications
關秉寅、李敦義國中生數學補得愈久，數學成就愈好嗎?傾向分數配對法的分析 137
and governmental responses. Retrieved November 10,2007,from http://unesdoc.unesco.
org/images/OO 13/001330/13303ge.pdf
Briggs,D. C. (2001). The effect of admissions test preparation: Evidence from NELS: 88.
Chance,14(1),10-18
Brunner,M.,Artelt,C.,Krau鉤，S.,&Baumert J. (2007). Coaching for the PISA test.Learning andlnstrnction,17, 111-122.
Caliendo,M.,& Kopeinig,S. (2008). Some practical guidance for the implementation of propensity score matching.Journal ofEconomic Surveys,22,31-72.
Carroll,J.B.(1963). A model of schoollearning.Teachers College Record,64,723-733.
Carroll,J. B. (1989). The carroll model: A 25-year retrospective and prospective view.
Educational Research,3人 26-31.
Cooper，且， Charlton,K.,Valenti帥， J. C.,& Muhlenbruck, L. (2000). Making the most of summer school. Monographs series of the society for research in child development.
Malden,MA: Blackwell.
DiPrete, T. A.,& Gangl,M. (2004). Assessing bias in the estimation of causal effects:
Rosenbaum bounds on matching estimators and instrumental variables estimation with imperfect instruments.Sociological Methodology,34,271-310.
Dominqu試試，&Briggs,D. C. (2009). Using linear regression and propensity score matching to estimate the effect of coaching on the SAT. Mult伊IeLinear Regression Viewpoints,35(1), 12-29.
Entwisle,D. R.,Alexander,K. L., &. Olson, L. S. (1997). Children,schools and inequality.
Boulder,Colorado: Westview Press.
Entwisle,D. R.,Alexander,K. L., &. Olson, L. S. (2001). Keep the faucet flowing: Summer learning and home environment.American Educator,25(3),10-15,47.
Getting仗，M. (1985). Time allocated and time spent relative to time needed for learning as determinants of achievement.Journal ofEducational Psychology,77,3-11.
Harding,D. J.(2003). Counterfactual models of neighborhood effects: The effect neighborhood poverty on dropping out and teenage pregnancy.American Journal ofSociology, 1仰， 676
719.
Holland,P. W. (1986). Statistics and causal inference. Journal of the American Statistical Association,18,945-960
Imbens,G. W. (2000). The role of the propensity score in estimating dose-response functions.
Biometri此a，87,706-710.
Kuan,Ping-Yin (2008,August). The effect of cram schooling for math: A counterfactual
。nalysis.Paper presented at the summer meeting on Work,Poverty,and Inequality in the 21 st Century,Palo Alto,CA.
Lareau,A., & Weininger,E. B. (2003). Cultural capital in educational research: A critical assessment.Theory and Society,32, 567-606.
Lechner,M. (1999). Identification and estimation of causal effects of multiple treatments under the conditional independence assumption. IZA Discussion Papers No. 97. Retrieved May 30,20 I0,fromft:p://repec.iza.org/RePEclDiscussionpaper/dp91.pdf
Leuv凹， E.,
&
Sianesi,B. (2003). Psmatch2: Stata module to perform full mahalanobis and propensity score matching, common support graphing, and covariate imbalance testing.Retrieved October 17,2007,from http://ideas.repec.org/c/boc/bocode/s432001.html, version 3.0.0
Marks,G. N.,Cresswell,J., & Ainley,J. (2006). Explaining socioeconomic inequalities in student achievement: The role of home and school factors. Educational Research and Evaluation,12,105-128.
Morgan,S.L., & Harding,D. J. (2006). Matching estimators of causal effects prospects and pitfalls in theory and practice. Sociological Methods and Research, 35( I),3-60.
Morgan,S. L., & Winship,C. (2007). Counterfactuals and causal analysis: Methods and principles for social research. Cambridge,MA: Harvard University Press.
Powers,D. E., & Rock,D. A. (1999). Effects of coaching on SATI: Reasoning test scores.
Journal ofEducational Measurement, 36(2) ，呵-118.
Rosenbaum, P. R., & Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects.Biometri，旬， 70,41-55.
Rosenbaum,P.R. (2002). Observational studies. New York: Springer.
Shavit, Y., & Blossfeld,H.-P. (Ed.). (1993). Persistent inequality: Changing educational attainment in thirteen countries. Boulder,CO: Westview.
Silova, I., Budiene，以， & Bray,M. (Eds.). (2006). Education in a hidden marketplace Monitoring ofprivate tutoring. New York: Open Society Institute.
Stevenson,D.L., & Baker,D. P.(1992). Shadow education and allocation in formal schooling:
Transition to university in Japan. American Journal ofSociology,9 咒 1639-1657.
Stevenson,D.L., & Stigler, 1. (2002). The learning gap: Why our schools are failing,and what
關秉寅、李敦義園中生數學補得愈久，數學成就愈好嗎?傾向分數配對法的分析 139
we can learnfrom Japanese and Chinese education.New York: Summit Books.
Winship，仁，& Morgan,S.L. (1999). The estimation of causal effects from observational data.
Annual Review ofSociology.25,659-707.
Winship,C.,& Sobel,M. (2004). Causal inference in sociological studies. In M. Hardy(Ed扎
The handbook ofdata analysis(pp. 481-503). Thousand Oaks,CA: Sage.
Zeng,K. (1999).Dragon gate: Competitive examinations and their consequences. London:
Cassell.