Use of the probit model to estimate school performance in student attainment of achievement testing standards

  • W. Holmes Finch
  • Jerrell C. Cassady


In the USA, trends in educational accountability have driven several models attempting to provide quality data for decision making at the national, state, and local levels, regarding the success of schools in meeting standards for competence. Statistical methods to generate data for such decisions have generally included (a) status models that examine simple indications of number of students meeting a criterion level of achievement, (b) growth models that explore change over the course of one or more years, and (c) value-added models that attempt to control for factors deemed relevant to student achievement patterns. This study examined a new strategy for student and school achievement modeling that augments the field through the use of the probit model to estimate the likelihood of students meeting an established level standard and estimating the proportion of individuals within a school meeting the standard. Results of the study showed that the probit model was an effective tool both for providing such adjustments, as well as for adjusting them based upon salient demographic variables. Implications of these results and suggestions for further use of the model are discussed.


School assessment Standardized achievement test Probit model 


  1. Agresti, A. (2002). Categorical data analysis. New York: Wiley.CrossRefGoogle Scholar
  2. Aud, S., Wilkinson‐Flicker, S., Kristapovich, P., Rathbun, A., Wang, X., and Zhang, J. (2013). The Condition of Education 2013 (NCES 2013‐037): U.S. department of education, national center for education statistics. Washington, DC.
  3. Azen, R., & Walker, C. M. (2011). Categorical data analysis for the behavioral and social sciences. New York: Routledge.Google Scholar
  4. Baker, M., & Johnston, P. (2010). The impact of socioeconomic status on high stakes testing reexamined. Journal of Instructional Psychology, 37(3), 193–199.Google Scholar
  5. Ballou, D., Sanders, W., & Wright, P. (2004). Controlling for student background in value-added assessment of teachers. Journal of Educational and Behavioral Statistics, 21, 37–66.CrossRefGoogle Scholar
  6. Barton, P. E. (2008). The right way to measure growth. Educational Leadership, 65, 70–73.Google Scholar
  7. Braun, H. (2005). Using student progress to evaluate teachers: a primer to value-added models. Princeton: ETS.Google Scholar
  8. Briggs, D. C., & Weeks, J. P. (2009). The sensitivity of value-added modeling to the creation of a vertical score scale. Education Finance and Policy, 4(4), 385–414.CrossRefGoogle Scholar
  9. Capraro, R. M., Young, J. R., Lewis, C. W., Yetkiner, Z. E., & Woods, M. N. (2009). An examination of mathematics achievement and growth in a midwestern urban school district: implications for teachers and administrators. Journal of Urban Mathematics Education, 2(2), 46–65.Google Scholar
  10. Chiang, H. (2009). How accountability pressure on failing schools affects student achievement. Journal of Public Economics, 93, 1045–1057.CrossRefGoogle Scholar
  11. Choi, K., & Goldschmidt, P. (2012). A multilevel latent growth curve approach to predicting student proficiency. Asia Pacific Education Review, 13(2), 199–208.CrossRefGoogle Scholar
  12. IBM Corp. (2010). IBM SPSS Statistics for Windows, version 19.0. Armonk: IBM Corp.Google Scholar
  13. Darling-Hammond, L., Amerin-Beardsley, A., Haertel, E., & Rothstein, J. (2012). Evaluating teacher evaluation. Phi Delta Kappan, 93(6), 8–15.Google Scholar
  14. De Lisle, J., Smith, P., & Jules, V. (2010). Evaluating the geography of gendered achievement using large-scale assessment data from the primary school system of the Republic of Trinidad and Tobago. International Journal of Educational Development, 30(4), 405–417.CrossRefGoogle Scholar
  15. Downey, D. B., von Hippel, P. T., & Hughes, M. (2008). Are “failing” schools really failing? Using seasonal comparison to evaluate school effectiveness. Sociology of Education, 81(3), 242–270.CrossRefGoogle Scholar
  16. Fox, J. (2008). Applied regression analysis and generalized linear models. Thousand Oaks: Sage.Google Scholar
  17. Franco, M. S., & Seidel, K. (2012). Evidence for the need to more closely examine school effects in value-added modeling and related accountability policies. Education and Urban Society. doi: 10.1177/0013124511432306.Google Scholar
  18. Goldschmidt, P., Roschewski, P., Choi, L., Auty, W., Hebbler, S., Blank, R., & Williams, A. (2005). Policymakers’ guide to growth models for school accountability: How do accountability models differ? Washington DC: The Council of Chief State School Officers. Accessed 14 Jan 2014.
  19. Goldschmidt, P., Choi, K., Martinez, F., & Novak, J. (2010). Using growth models to monitor school performance: comparing the effect of the metric and the assessment. School Effectiveness and School Improvement: An International Journal of Research, Policy, and Practice, 21(2), 337–357.CrossRefGoogle Scholar
  20. Gorard, S. (2011). Now you see it, now you don’t: school effectiveness as conjuring? Research in Education, 86, 39–45.CrossRefGoogle Scholar
  21. Lee, J. (2010). Tripartite growth trajectories of reading and math achievement: tracking national academic progress at primary, middle, and high school levels. American Educational Research Journal, 47(4), 800–832.CrossRefGoogle Scholar
  22. Linn, R. L. (2000). Assessments and accountability. Educational Researcher, 29, 4–16.Google Scholar
  23. Lockwood, J. R., McCaffrey, D. F., Hamilton, L. S., Stecher, B., Le, V.-N., & Martinez, F. (2006). The sensitivity of value-added teacher effect estimates to different mathematics achievement measures. Santa Monica: RAND.Google Scholar
  24. Martineau, J. A. (2006). Distorting value added: the use of longitudinal, vertically scaled student achievement data for value-added accountability. Journal of Educational and Behavioral Statistics, 31, 35–62.CrossRefGoogle Scholar
  25. McCaffrey, D.F. (2013). Do value-added methods level the playing field for teachers? Carnegie Knowledge Network.
  26. McCaffrey, D. F., Lockwood, J. R., Koretz, D., Louis, T. A., & Hamilton, L. (2004). Models for value-added modeling of teacher effects. Journal of Educational and Behavioral Statistics, 29(1), 67–101.CrossRefGoogle Scholar
  27. Northwest Evaluation Association. (2003). Technical manual for use with measures of academic progress and achievement level tests. Portland: Northwest Evaluation Association.Google Scholar
  28. Olson, L. (2004). Value added models gain in popularity. Education Week, 24(12), 14–15.Google Scholar
  29. Perry, L. B., & McConney, A. (2010). Does the SES of the school matter? An examination of socioeconomic status and student achievement using PISA 2003. Teachers College Record, 112(4), 1137–1162.Google Scholar
  30. Scherrer, J. (2012). What’s the value of VAM (value-added modeling)? Phi Delta Kappan, 93(8), 58–60.Google Scholar
  31. Schmidt, W. H., Houang, R. T., & McKnight, C. C. (2005). Value-added research: right idea but wrong solution? In R. Lissitz (Ed.), Value added models in education: theory and practice (pp. 272–297). Maple Grove: JAM.Google Scholar
  32. Sidak, Z. (1967). Rectangular confidence regions for the means of multivariate normal distributions. Journal of American Statistical Association, 67(62), 626–633.Google Scholar
  33. Tong, H., & Lim, K. S. (1980). Threshold autoregression, limit cycles, and cyclical data. Journal of the Royal Statistical Society, Series B, 42, 245–292.Google Scholar
  34. Wainer, H. (2000). Computer adaptive testing: a primer. Mahwah: Lawrence Erlbaum.Google Scholar
  35. Weiss, M. J., & May, H. (2012). A policy analysis of the federal growth model pilot program’s measures of school performance: the Florida case. Association for Education Finance and Policy, 7(1), 44–73. doi: 10.1162/EDFP_a_00053.CrossRefGoogle Scholar
  36. Wiggan, G. (2007). Race, school achievement, and educational inequality: toward a student-based inquiry perspective. Review of Educational Research, 77(3), 310–333.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Educational PsychologyBall State UniversityMuncieUSA

Personalised recommendations