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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 ...