### Pre-Post Gain on an Item

Question: "My sample were tested on the same items (more or less) before the intervention and after it. How can I compute gain on each item for the sample?"

Answer: In raw score terms, the movement is the average rating on an item at post-intervention minus the average rating at pre-intervention. This is probably good enough provided the data are reasonably complete. In measurement terms, you could do a "stacked" analysis of the pairs of pre- and post- records. Then the measured gain on an item is (the average overall ability of the post- sample minus the average overall ability of the pre- sample) + (the item's pre-post item DIF measure difference). So that if the overall sample has gained 2 logits, and the item's pre-post DIF indicates 1 logit easier at post-, then the sample has gained 3 logits on that item.

### Mathematics and Empirical Science

"Those who firmly believe that rigorous science must consist largely of mathematics and statistics have something to unlearn. Such a belief implies emasculating science of its basic substantive nature. Mathematics is contentless, and hence - by itself - not empirical science. As will be seen, rather rigorous treatment of content or subject matter is needed before some mathematics can be thought of as a possibly useful (but limited) partner for empirical science."
Louis Guttman in S. Levy (Ed.), Louis Guttman on theory and methodology: Selected writings (p. 82). Brookfield, VT: Dartmouth Publishing Company. Courtesy of William P. Fisher

### Deceptive Percentages

The Wall Street Journal Editorial Page, July 25, 2006:

"If the real difference between two groups, measured as it should be with means and standard deviations, remains constant, ... you can generate a curve that predicts how the point gap will change as tests are made easier or harder or as students become more or less competent."

"Question: Doesn't this mean that the same set of scores could be made to show a rising or falling group [percentage] difference just by changing the definition of a passing score?"

"Answer: Yes. At stake is not some arcane statistical nuance. The US federal government is doling out rewards and penalties to school systems across the country based on changes in pass percentages. It is an uninformative measure for many reasons, but, when it comes to measuring one of the central outcomes sought by No Child Left Behind, the closure of the achievement gap that separates poor students from rich, Latino from white, and black from white, the [percentage] measure is beyond uninformative. It is deceptive."

Charles Murray
W.H. Brady Scholar at the American Enterprise Institute
www.opinionjournal.com/editorial/feature.html

### Journal of Applied Measurement: Volume 7, Number 4. Winter 2006

Standard Systems: The Foundational Element of Measurement Theory. Marion S. Aftanas, 351-368

An Empirical Study into the Theory of Unidimensional Unfolding. Andrew Kyngdon, 369-393

Expanding an Existing Multiple Choice Test with a Mixed Format Test: Simulation Studies on Sample Size and Item Recovery in Concurrent Calibration. Insu Paek and Michael J. Young, 394-406

Fitting Polytomous Rasch Models in SAS. Karl Bang Christensen, 407-417

The Development and Validation of the Self-Directed Learning Scales (SLS). Magdalena Mo Ching Mok, Cheng Yin Cheong, Phillip John Moore, and Kerry John Kennedy, 418-449

Understanding Rasch Measurement: Using Paired Comparisons to Create the Semantic Construct of Frequency. Thomas R. O'Neill, 450-478

RMT 20:2 Miscellaneous Material, … Rasch Measurement Transactions, 2006, 20:2

Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez

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