Two Measures of Change in the Gaps Between the CDFs of Test-Score Distributions

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Getting Value Out of Value-Added: Report of a Workshop (2010, background): “The problem is exacerbated when looking at trends in achievement gaps (Holland, 2002).”
A Nonparametric Framework for Comparing Trends and Gaps Across Tests (2009, methodology): “This may be visualized in Figure 1, where Holland (2002) shows that the integral of D(x), the signed area under the curve representing the vertical distances between CDFs, is equal to the difference of averages.”
The Problem With “Proficiency”: Limitations of Statistics and Policy Under No Child Left Behind (2008, background): “Holland (2002) argues convincingly that these properties support the use of percentile- rather than PPS-based graphical reporting.”
Comparisons of Methodologies and Results in Vertical Scaling for Educational Achievement Tests (2007, background): “HD is defined as percentile difference on the score scale for the same percentage between two distributions ( Holland, 2002 ).”