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Measuring Test Measurement Error: A General Approach

Author

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  • Donald Boyd
  • Hamilton Lankford
  • Susanna Loeb
  • James Wyckoff

Abstract

Test-based accountability including value-added assessments and experimental and quasi-experimental research in education rely on achievement tests to measure student skills and knowledge. Yet we know little regarding important properties of these tests, an important example being the extent of test measurement error and its implications for educational policy and practice. While test vendors provide estimates of split-test reliability, these measures do not account for potentially important day-to-day differences in student performance. We show there is a credible, low-cost approach for estimating the total test measurement error that can be applied when one or more cohorts of students take three or more tests in the subject of interest (e.g., state assessments in three consecutive grades). Our method generalizes the test-retest framework allowing for either growth or decay in knowledge and skills between tests as well as variation in the degree of measurement error across tests. The approach maintains relatively unrestrictive, testable assumptions regarding the structure of student achievement growth. Estimation only requires descriptive statistics (e.g., correlations) for the tests. When student-level test-score data are available, the extent and pattern of measurement error heteroskedasticity also can be estimated. Utilizing math and ELA test data from New York City, we estimate the overall extent of test measurement error is more than twice as large as that reported by the test vendor and demonstrate how using estimates of the total measurement error and the degree of heteroskedasticity along with observed scores can yield meaningful improvements in the precision of student achievement and achievement-gain estimates.

Suggested Citation

  • Donald Boyd & Hamilton Lankford & Susanna Loeb & James Wyckoff, 2012. "Measuring Test Measurement Error: A General Approach," NBER Working Papers 18010, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:18010
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    References listed on IDEAS

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    1. Altonji, Joseph G & Segal, Lewis M, 1996. "Small-Sample Bias in GMM Estimation of Covariance Structures," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 353-366, July.
    2. Daniel F. McCaffrey & Tim R. Sass & J. R. Lockwood & Kata Mihaly, 2009. "The Intertemporal Variability of Teacher Effect Estimates," Education Finance and Policy, MIT Press, vol. 4(4), pages 572-606, October.
    3. Daniel Aaronson & Lisa Barrow & William Sander, 2007. "Teachers and Student Achievement in the Chicago Public High Schools," Journal of Labor Economics, University of Chicago Press, vol. 25, pages 95-135.
    4. Petra E. Todd & Kenneth I. Wolpin, 2003. "On The Specification and Estimation of The Production Function for Cognitive Achievement," Economic Journal, Royal Economic Society, vol. 113(485), pages 3-33, February.
    5. Cameron,A. Colin & Trivedi,Pravin K., 2008. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9787111235767, March.
    6. Cory Koedel & Julian Betts, 2007. "Re-Examining the Role of Teacher Quality In the Educational Production Function," Working Papers 0708, Department of Economics, University of Missouri.
    7. Dan Goldhaber & Emily Anthony, 2007. "Can Teacher Quality Be Effectively Assessed? National Board Certification as a Signal of Effective Teaching," The Review of Economics and Statistics, MIT Press, vol. 89(1), pages 134-150, February.
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    Cited by:

    1. Cory Koedel & Jiaxi Li, 2016. "The Efficiency Implications Of Using Proportional Evaluations To Shape The Teaching Workforce," Contemporary Economic Policy, Western Economic Association International, vol. 34(1), pages 47-62, January.
    2. Timothy N. Bond & Kevin Lang, 2013. "The Black-White Education-Scaled Test-Score Gap in Grades K-7," NBER Working Papers 19243, National Bureau of Economic Research, Inc.
    3. Jason A. Grissom & Demetra Kalogrides & Susanna Loeb, 2012. "Using Student Test Scores to Measure Principal Performance," NBER Working Papers 18568, National Bureau of Economic Research, Inc.
    4. repec:umc:wpaper:1308 is not listed on IDEAS
    5. Eric Parsons, 2014. "Does Attending a Low-Achieving School Affect High-Performing Student Outcomes?," Working Papers 1407, Department of Economics, University of Missouri, revised 18 Feb 2015.

    More about this item

    JEL classification:

    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education

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