1.2. Propuesta de investigación
2.2.3. Despliegue de la Función de Calidad (QFD)
There is no multi-collinearity between the independent variables. This assumption is considered to be met if VIF scores are below 10, and the tolerance scores above 0.2. The VIFscoreswere around 1.00 in all three regression models, and Tolerance scores were around 1.00, too. This suggests that the assumption of independence between the independent variables is satisfied.
General Finding:
159
Second analysis: 2015–2016 year
Assumption 1: Linearity
The relationship between the independent and the dependent variables is linear. This assumption can be tested by inspecting the scatter plot between the variables which should show a linear pattern for the assumption to be considered satisfied. In case that relationship between the variables is not obviously linear or non-linear, Pearson correlation coefficient was used as a measure of the linear correlation between two variables. The results showed that the relationship between School Size and AP/IB participation follow a little linear pattern. Pearson correlation coefficient between these variables is statistically significant (r=.150). It has been demonstrated that this assumption has been met.
Figure 34. The relationship between the 2015-16 School Size and AP/IB Participation
Assumption 2: Normality
The values of the residuals are normally distributed. This assumption can be tested by inspecting the P-P plots. The closer the dots lie to the diagonal line, the closer to normal the residuals are distributed. The results showed that the dots are arranged by a diagonal line. This result indicates that this assumption was satisfied.
160
Figure 35. Normal P-P plot of 2015-16 AP/IB Participation Regression Standardized Residual
Assumption 3: Homoscedasticity
The variance of the residuals is constant. If the graph looks like a funnel shape, then it is likely that this assumption is violated. The results showed that there are no obvious signs of funneling. This suggests that the assumption of homoscedasticity was satisfied.
Figure 36. 2015-16AP/IB Participation Homoscedasticity
Assumption 4: Multi-collinearity
There is no multi-collinearity between the independent variables. This assumption is considered to be met if VIF scores are below 10, and the tolerance scores above 0.2. The VIFscoreswere around 1.00 in all three regression models, and tolerance scores were around 1.00,
161
too. This suggests that the assumption of independence between the independent variables is satisfied.
General Finding:
All underlying assumptions of regression have been met.
Third analysis: 2016–2017 year
Assumption 1: Linearity
The relationship between the independent and the dependent variables is linear. This assumption can be tested by inspecting the scatter plot between the variables which should show a linear pattern for the assumption to be considered satisfied. In case that relationship between the variables is not obviously linear or non-linear, Pearson correlation coefficient was used as a measure of the linear correlation between two variables. The results showed that the relationship between School Size and AP/IB Participation do follow a little linear pattern. Pearson correlation coefficient between these variables is statistically significant (r=.125). It has been demonstrated that this assumption has been met.
162 Assumption 2: Normality
The values of the residuals are normally distributed. This assumption can be tested by inspecting the P-P plots. The closer the dots lie to the diagonal line, the closer to normal the residuals are distributed. The results showed that the dots are arranged by a diagonal line. This result indicates that this assumption was satisfied.
Figure 38. Normal P-P plot of 2016-17AP/IB Participation Regression Standardized Residual
Assumption 3: Homoscedasticity
The variance of the residuals is constant. If the graph looks like a funnel shape, then it is likely that this assumption is violated. The results showed that there are no obvious signs of funneling. This suggests that the assumption of homoscedasticity was satisfied.
163 Assumption 4: Multi-collinearity
There is no multi-collinearity between the independent variables. This assumption is considered to be met if VIF scores are below 10, and the tolerance scores above 0.2. The VIFscoreswere around 1.00 in all three regression models, and Tolerance scores were around 1.00, too. This suggests that the assumption of independence between the independent variables is satisfied.
General Finding:
All underlying assumptions of regression have been met.
Percent AP/IB Benchmark Achieved
First analysis: 2014–2015 year
Assumption 1: Linearity
The relationship between the independent and the dependent variables is linear. This assumption can be tested by inspecting the scatter plot between the variables which should show a linear pattern for the assumption to be considered satisfied. In case that relationship between the variables is not obviously linear or non-linear, Pearson correlation coefficient was used as a measure of the linear correlation between two variables. The results showed that the relationship between School Size and Percent AP/IB Benchmark Achieved follow a little linear pattern. Pearson correlation coefficient between these variables is statistically significant (r=.286). It has been demonstrated that this assumption has been met.
164
Figure 40. The relationship between the 2014-15 School Size and Percent AP/IB Benchmark Achieved
Assumption 2: Normality
The values of the residuals are normally distributed. This assumption can be tested by inspecting the P-P plots. The closer the dots lie to the diagonal line, the closer to normal the residuals are distributed. The results showed that the dots are arranged by a diagonal line. This result indicates that this assumption was satisfied.
165 Assumption 3: Homoscedasticity
The variance of the residuals is constant. If the graph looks like a funnel shape, then it is likely that this assumption is violated. The results showed that there are no obvious signs of funneling. This suggests that the assumption of homoscedasticity was satisfied.
Figure 42. 2014-15 Percent AP/IB Benchmark Achieved Homoscedasticity
Assumption 4: Multi-collinearity
There is no multi-collinearity between the independent variables. This assumption is considered to be met if VIF scores are below 10, and the tolerance scores above 0.2. The VIFscoreswere around 1.00 in all three regression models, and Tolerance scores were around 1.00, too. This suggests that the assumption of independence between the independent variables is satisfied.
General Finding:
166
Second analysis: 2015–2016 year
Assumption 1: Linearity
The relationship between the independent and the dependent variables is linear. This assumption can be tested by inspecting the scatter plot between the variables which should show a linear pattern for the assumption to be considered satisfied. In case that relationship between the variables is not obviously linear or non-linear, Pearson correlation coefficient was used as a measure of the linear correlation between two variables. The results showed that the relationship between School Size and Percent AP/IB Benchmark Achieved follow a little linear pattern. Pearson correlation coefficient between these variables is statistically significant (r=.266). It has been demonstrated that this assumption has been met.
Figure 43. The relationship between the 2015-16 School Size and Percent AP/IB Benchmark Achieved
Assumption 2: Normality
The values of the residuals are normally distributed. This assumption can be tested by inspecting the P-P plots. The closer the dots lie to the diagonal line, the closer to normal the residuals are distributed. The results showed that the dots are arranged by a diagonal line. This result indicates that this assumption was satisfied.
167
Figure 44. Normal P-P plot of 2015-16Percent AP/IB Benchmark Achieved Regression Standardized Residual
Assumption 3: Homoscedasticity
The variance of the residuals is constant. If the graph looks like a funnel shape, then it is likely that this assumption is violated. The results showed that there are no obvious signs of funneling. This suggests that the assumption of homoscedasticity was satisfied.
Figure 45. 2015-16 Percent AP/IB Benchmark Achieved Homoscedasticity
Assumption 4: Multi-collinearity
There is no multi-collinearity between the independent variables. This assumption is considered to be met if VIF scores are below 10, and the tolerance scores above 0.2. The VIFscoreswere around 1.00 in all three regression models, and Tolerance scores were around 1.00,
168
too. This suggests that the assumption of independence between the independent variables is satisfied.
General Finding
All underlying assumptions of regression have been met.
Third analysis: 2016–2017 year
Assumption 1: Linearity
The relationship between the independent and the dependent variables is linear. This assumption can be tested by inspecting the scatter plot between the variables which should show a linear pattern for the assumption to be considered satisfied. In case that relationship between the variables is not obviously linear or non-linear, Pearson correlation coefficient was used as a measure of the linear correlation between two variables. The results showed that the relationship between School Size and Percent AP/IB Benchmark Achieved do follow a little linear pattern. Pearson correlation coefficient between these variables is statistically significant (r=.186). It has been demonstrated that this assumption has been met.
169 Assumption 2: Normality
The values of the residuals are normally distributed. This assumption can be tested by inspecting the P-P plots. The closer the dots lie to the diagonal line, the closer to normal the residuals are distributed. The results showed that the dots are arranged by a diagonal line. This result indicates that this assumption was satisfied.
Figure 47. Normal P-P plot of 2016-17 Percent AP/IB Benchmark Achieved Regression Standardized Residual
Assumption 3: Homoscedasticity
The variance of the residuals is constant. If the graph looks like a funnel shape, then it is likely that this assumption is violated. The results showed that there are no obvious signs of funneling. This suggests that the assumption of homoscedasticity was satisfied.
170 Assumption 4: Multi-collinearity
There is no multi-collinearity between the independent variables. This assumption is considered to be met if VIF scores are below 10, and the tolerance scores above 0.2. The VIFscoreswere around 1.00 in all three regression models, and Tolerance scores were around 1.00, too. This suggests that the assumption of independence between the independent variables is satisfied.
General Finding:
171
References
Abel, J. R., & Deitz, R. (2014). Do the Benefits of College Still Outweigh the Costs? Current Issues in
Economics & Finance, 20(3), 1–12. Retrieved from
http://search.ebscohost.com/login.aspx?direct=true&AuthType=ip,sso&db=bsh&AN=96880995 &site=eds-live
Andrews, M., Duncombe, W., & Yinger, J. (2002). Revisiting economies of size in American education: Are We Any Closer to a Consensus?. Economics of education review, 21(3), 245–262.
Aud, S., & Hannes, G. (2011). The Condition of Education 2011 in Brief. NCES 2011-034. National
Center for Education Statistics. Retrieved from
http://search.ebscohost.com/login.aspx?direct=true&AuthType=ip,sso&db=eric&AN=ED52000 3&site=eds-live
Bahr, P. R. (2010). Making sense of disparities in mathematics remediation: What is the role of student retention? Journal of College Student Retention, 12, 25–49.
Bailey, T., Jeong, D. W., & Cho, S. (2010). Student progression through developmental sequences in community colleges. Community College Research Center. Brief No. 45.
Barker, R. G., & Gump, P. V. (1964). Big school, small school: High school size and student behavior. Palo Alto, CA, US: Stanford U. Press.
Bergeron, L. (2015). Diploma Programme students’ enrollment and outcomes at US postsecondary institutions 2008–2014. Bethesda, MD: International Baccalaureate Organization.
Berry, C. R., & West, M. R. (2008). Growing pains: The school consolidation movement and student outcomes. The Journal of Law, Economics, & Organization, 26(1), 1–29.
Blum, R.W. (2005). A Case for School Connectedness. Educational Leadership, 62(7), 16-20. Retrieved from http://www.ascd.org/publications/educational-leadership/apr05/vol62/num07/A-Case-for- School-Connectedness.aspx
Blum, R. W., Libbey, H. P., Bishop, J. H., & Bishop, M. (2004). School connectedness—Strengthening health and education outcomes for teenagers. Journal of School Health, 74(7), 231-235.
doi:10.1111/j.1746-1561.204.tb08278.
Blum, R. W., McNeely, C., & Rinehart, P. M. (2002). Improving the Odds: The Untapped Power of Schools to Improve the Health of Teens, Centre for Adolescent Health and Development.
University of Minnesota, Minneapolis, MN.
Borman, G. D., & Dowling, N. M. (2008). Teacher attrition and retention: A meta-analytic and narrative review of the research. Review of educational research, 78(3), 367–409.
Caref, C., Hainds, S., Hilgendorf, K., Jankov, P., & Russell, K. (2012). The black and white of education in Chicago’s public schools. Class, Charters. Retrieved from https://www.ctulocal1.org/wp- content/uploads/2018/10/CTU-black-and-white-of-chicago-education.pdf.
Carnegie Corp. of New York, NY. (1989). Turning Points: Preparing American Youth for the 21St
Century. The Report of the Task Force on Education of Young Adolescents. Carnegie Council on
172
CES, (ND). Coalition of Essential Schools Receives $18.7 million from Bill & Melinda Gates Foundation. Press release by Bill & Melinda Gates Foundation. Retrieved from
https://www.gatesfoundation.org/Media-Center/Press-Releases/2003/09/Coalition-of-Essential- Schools-Receives-Grant.
Cibulka, J. G. (1986). State-Level Policy Options for Dropout Prevention. Metropolitan Education, 2, 13–29.
Chajewski, M., Mattern, K. D., & Shaw, E. J. (2011). Examining the role of Advanced Placement® exam participation in four-year college enrollment. Educational Measurement: Issues and
Practice, 30(4), 16–27.
Chopin, S. L. (2003). The effect of school size, socioeconomic status, and grade-level configuration on academic achievement in Louisiana public schools (Order No. 3084536). Available from ProQuest Dissertations & Theses Global. (305321504). Retrieved from https://search-proquest- com.ezproxy.shu.edu/docview/305321504?accountid=13793.
Clark, A., & Rizzo, O. (2018, August 09). N.J. is slashing state funding for 172 districts. Retrieved January 08, 2019, from
https://www.nj.com/education/2018/08/nj_state_funding_cuts_to_schools_2018_jersey_city.htm l.
Coleman, J. S. (1968). Equality of educational opportunity. Integrated Education, 6(5), 19-28.
Chakrabarti, R., & Livingston, M. (2013, September 25). Catching Up or Falling Behind? New Jersey Schools in the Aftermath of the Great Recession. Liberty Street Economics. Retrieved from https://libertystreeteconomics.newyorkfed.org/2013/09/catching-up-or-falling-behind-new- jersey-schools-in-the-aftermath-of-the-great-recession.html.
College Board, “SAT Report,” press release. New York: September 24, 2012. Retrieved from http://secure-media.collegeboard.org/digitalServices/pdf/research/sat-report-2012-press- release.pdf.
Conant, J. B. (1940). Education for a classless society and the Jeffersonian tradition. Atlantic Monthly,
165(5), 593 – 602.
Conant, J. B. (1959). The American high school today: A first report to interested citizens. New York, NY: McGraw Hill Book Company.
Conant, J. B. (1967). The comprehensive high school: A second report to interested citizens. McGraw- Hill.
Conley, D. T. (2010). College and career ready: Helping all students succeed beyond high school. John Wiley & Sons.
Conley, D. T. (2005). College Knowledge: What It Really Takes for Students to Succeed and What We
Can Do to Get Them Ready. Jossey-Bass, An Imprint of Wiley.
Conley, D., McGaughy, C., Davis-Molin, W., Farkas, R., & Fukuda, E. (2014). International Baccalaureate Diploma Programme: Examining College Readiness. Educational Policy Improvement Center. Retrieved from https://files.eric.ed.gov/fulltext/ED571663.pdf.
173
Cotton, K. (2001). New small learning communities: Findings from recent research. Portland, OR:
Northwest Regional Education Laboratory. Retrieved from
https://files.eric.ed.gov/fulltext/ED459539.pdf.
Cubberley, E. P. (1922). Rural life and education: A study of the rural-school problem as a phase of the
rural-life problem. Houghton Mifflin.
DeAngelo, L., Franke, R., Hurtado, S., Pryor, J. H., & Tran, S. (2011). Completing college: Assessing
graduation rates at four-year institutions. Los Angeles: Higher Education Research Institute,
UCLA.
Department of the Interior, B. of E. (ED). (1918). Cardinal Principles of Secondary Education: A
Report of the Commission on the Reorganization of Secondary Education, Appointed by the National Education Association. Bulletin, 1918, No. 35. Bureau of Education, Department of the
Interior. Retrieved from https://files.eric.ed.gov/fulltext/ED541063.pdf.
Dodd, B. G., Fitzpatrick, S. J., De Ayala, R. J., & Jennings, J. A. (2002). An investigation of the validity
of AP grades of 3 and a comparison of AP and non-AP student groups. (College Board Research
Report No. 2002-9). New York: The College Board.
Dodson III, M. E., & Garrett, T. A. (2004). Inefficient education spending in public school districts: A case for consolidation?. Contemporary Economic Policy, 22(2), 270–280.
Durbin, M. K. (2002). The relationship of high school size, student achievement, and per-pupil
expenditures in South Carolina. PhD Thesis, University of South Carolina.
Education Law Center, (ND). Student demographics. Retrieved from edlawcenter.org/research/data- research.html.
Education Transformation Task Force Initial Report (pp. 1–49, Rep.). (2011). New Jersey. doi:https://www.state.nj.us/education/news/2011/1007taskA1.pdf.
Egalite, A. J., & Kisida, B. (2016). School size and student achievement: a longitudinal analysis. School
Effectiveness and School Improvement, 27(3), 406–417.
Ferris, J. S., & West, E. G. (2004). Economies of scale, school violence and the optimal size of schools.
Applied Economics, 36(15), 1677–1684.
Fetler, M. (1989). School dropout rates, academic performance, size, and poverty: Correlates of educational reform. Educational Evaluation and Policy Analysis, 11(2), 109–116.
Fowler Jr, W. J., & Walberg, H. J. (1991). School size, characteristics, and outcomes. Educational
evaluation and policy analysis, 13(2), 189–202.
Fox, W.F. (1981). Reviewing Economies of Size in Education. Journal of Education Finance, (3), 273. Retrieved from
http://search.ebscohost.com/login.aspx?direct=true&AuthType=ip,sso&db=edsjsr&AN=edsjsr.4 0703282&site=eds-live.
Funk, P. E., & Bailey, J. (1999). Small Schools, Big Results: Nebraska High School Completion and Postsecondary Enrollment Rates by Size of School District. Retrieved from
https://files.eric.ed.gov/fulltext/ED441633.pdf.
Gallagher, A., Hayes, C., & Parr, N. (2017). A Study of How Individual School Characteristics Affect School Performance. Econometric Analysis Undergraduate Research Papers. Georgia Tech.
174 Retrieved from
https://smartech.gatech.edu/bitstream/handle/1853/56621/a_study_of_how_individual_school_ch aracteristics_affect_school_performance.pdf?sequence=1&isAllowed=y.
Gordon, M. F., de la Torre, M., Cowhy, J. R., Moore, P. T., Sartain, L., & Knight, D. (2018). School
Closings in Chicago: Staff and Student Experiences and Academic Outcomes. Research Report.
University of Chicago Consortium on School Research.
Green, G. P. (2013). School consolidation and community development. Great Plains Research 23.2, 99–105. Retrieved from
https://pdfs.semanticscholar.org/f8a8/d8740ec4333e680302977354da514a82d3dd.pdf.
Greene, J. P., & Forster, G. (2003). Public High School Graduation and College Readiness Rates in the United States. Education Working Paper No. 3. Center for Civic Innovation.
Hammersley, M. (1987). Some notes on the terms ‘validity’ and ‘reliability’ [1]. British Educational
Research Journal, 13(1), 73–82.
Hendrick, I. G. (1972). The Impact of the Great Depression on Public School Support in California.
Southern California Quarterly, 54(2), 177–195.
Hess, A. (2018). The 5 states that spend the most on students. CNBC. April 17, 2018. Retrieved from https://www.cnbc.com/2018/04/16/the-5-states-that-spend-the-most-on-students.html.
Howley, C. (1994). The Academic Effectiveness of Small-Scale Schooling (An Update). ERIC Digest. Retrieved from https://files.eric.ed.gov/fulltext/ED372897.pdf.
Howley, C. B. (2008). Don’t Supersize Me: The Relationship of Construction Cost to School Enrollment in the US. Educational Planning, 23. Retrieved from http://isep.info/wp-
content/uploads/2015/03/17-2_3DontSupersizeMe.pdf.
Howley, C. B., & Bickel, R. (1999). The Matthew Project: National Report. Rural Challenge Policy