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Achievement Gap Estimates and Deviations from Cardinal Comparability
This paper assesses the sensitivity of standard empirical methods for measuring group differences in achievement to violations in the cardinal comparability of achievement test scores. The paper defines a distance measure over possible weighting functions (scalings) of test scores. It then constructs worst-case bounds for the bias in the estimated achievement gap (or achievement gap change) that could result from using the observed rather than the true test scale, given that the true and observed scales are no more than a fixed distance from each other. The worst-case weighting functions have ...
Test Questions, Economic Outcomes, and Inequality
Standard achievement scales aggregate test questions without considering their relationship to economic outcomes. This paper uses question-level data to improve the measurement of achievement in two ways. First, the paper constructs alternative achievement scales by relating individual questions directly to school completion and labor market outcomes. Second, the paper leverages the question data to construct multiple such scales in order to correct for biases stemming from measurement error. These new achievement scales rank students differently than standard scales and typically yield ...