 Two Measures of Change in the Gaps Between the CDFs of Test-Score DistributionsPaul W. Holland Journal of Educational and Behavioral Statistics, 2002, vol. 27, issue 1, 3-17 Abstract: Two ways of measuring the gap between two cumulative distribution functions (CDFs) are examined—vertical and horizontal distance. The applications of interest are to the distributions of scores on tests. Vertical distance leads to gap-measures based on differences between “percents above cut-points†for a given score along the score scale. Horizontal distance leads to gap-measures based on differences between the percentiles of the two distributions for a given percent value. Both methods of measuring gaps between CDFs of score distributions are widely used. My focus here is on how the two methods behave when they are used to measure changes in gaps over time. Using a simple model in which the CDFs simply change by small shifts to the right or left, as they often do in real data (the “shift model†), I demonstrate how these two approaches can easily lead to contradictory conclusions about small changes in gaps. The theoretical analysis is illustrated using real data from the National Assessment of Educational Progress. It is recommended that when considering changes in gaps over time, gap-measures be supplemented with fuller data-displays to clarify the directions that changes in such measures can appear to indicate. Keywords: group differences; NAEP; shift models (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:27:y:2002:i:1:p:3-17 DOI: 10.3102/10769986027001003 Access Statistics for this article More articles in Journal of Educational and Behavioral Statistics |
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