Project Activities
People and institutions involved
IES program contact(s)
Products and publications
Journal article, monograph, or newsletter
Fahle, E.M., and Reardon, S.F. (2018). How Much do Test Scores Vary Among School Districts? New Estimates Using Population Data, 2009-2015. Educational Researcher, 0013189X18759524.
Ho, A.D., and Reardon, S.F. (2012). Estimating Achievement Gaps From Test Scores Reported in Ordinal "Proficiency" Categories. Journal of Educational and Behavioral Statistics, 37(4): 489-517.
Ho, A.D., and Yu, C.C. (2015). Descriptive Statistics for Modern Test Score Distributions: Skewness, Kurtosis, Discreteness, and Ceiling Effects. Educational And Psychological Measurement, 75(3), 365-388.
Reardon, S. F. (2019). Educational opportunity in early and middle childhood: Using full population administrative data to study variation by place and age. RSF: The Russell Sage Foundation Journal of the Social Sciences, 5(2), 40-68.
Reardon, S.F. (2016). School Segregation and Racial Academic Achievement Gaps. RSF:The Russell Sage Foundation Journal of the Social Sciences, 2(5): 34-57.
Reardon, S.F., and Ho, A.D. (2015). Practical Issues in Estimating Achievement Gaps From Coarsened Data. Journal of Educational and Behavioral Statistics, 40(2), 158-189.
Reardon, S. F., Fahle, E. M., Kalogrides, D., Podolsky, A., & Zárate, R. C. (2019). Gender achievement gaps in US school districts. American Educational Research Journal, 56(6), 2474-2508.
Reardon, S. F., Kalogrides, D., & Ho, A. D. (2021). Validation methods for aggregate-level test scale linking: A case study mapping school district test score distributions to a common scale. Journal of Educational and Behavioral Statistics, 46(2), 138-167.
Reardon, S. F., Kalogrides, D., & Shores, K. (2019). The geography of racial/ethnic test score gaps. American Journal of Sociology, 124(4), 1164-1221.
Reardon, S.F., Kalogrides, D., Fahle, E. M., Podolsky, A., and Zárate, R.C. (2018). The Relationship Between Test Item Format and Gender Achievement Gaps on Math And ELA Tests In Fourth And Eighth Grades. Educational Researcher, 0013189X18762105.
Reardon, S.F., Shear, B.R., Castellano, K.E., and Ho, A.D. (2017). Using Heteroskedastic Ordered Probit Models to Recover Moments of Continuous Test Score Distributions From Coarsened Data. Journal of Educational and Behavioral Statistics, 42(1), 3-45.
Yee, D., and Ho, A. (2015). Discreteness Causes Bias in Percentage-Based Comparisons: A Case Study From Educational Testing. The American Statistician, 69(3), 174-181.
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Supplemental information
Co-Principal Investigator: Ho, Andrew
Achievement gaps are used to measure differences in group achievement as well as inequities in educational advantages and opportunities to learn. However, estimated achievement gaps may be sensitive to the choice of test metric and the choice of an achievement gap statistic. In addition, estimating achievement gaps may not be possible in those states and districts that only report proficiency levels. Without access to basic distributional statistics for test scores, research linking changes in state, district, or school policies and practices to levels and changes in achievement gaps may be compromised.
The project developed and tested a set of methods for estimating these metric free achievement gap measures from widely available categorical proficiency data. Both simulated and real datasets were used to identify the methods that minimize bias and maximize efficiency across a range of idealized and real-world scenarios. This work included a strategy for computing standard errors for these nonparametric achievement gap estimates. Simulated data and data from national and state assessment were then used to assess the different nonparametric methods developed to determine if they produce unbiased estimates of achievement gaps and accurate standard errors. The overall result was a set of practical guidelines for measuring achievement gaps based on categorical proficiency data and the development of free software to enable researchers and stakeholders to estimate these gaps.
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