When two item difficulty measures (or two person measures) are located along a latent variable, how big must the gap be for it to be important?
Gaps based on probabilities: for dichotomies, these correspond to what differential chance of success would matter. If a 60% chance of success is thought to be importantly different from a 50% chance, then the logit difference is 0.4 logits, so a gap of 0.4 logits matters. For polytomies, this calculation tends is more complex.
Gaps based on substance: these usually correspond to "what is the smallest difference that an informed observer would see to be definitely different"? In many educational situations a gap that matters is about 0.5 logits, roughly half a grade level at school.
Gaps based on statistical significance: these are computed from the
standard errors of the individual measures. The more data usually
the smaller the standard errors. So for .15 logits to represent a
statistically significant gap (using a two-sided .05 t-test)
between two measures, the individual measure standard errors must
be about .05 logits, corresponding to about 250 dichotomous
responses underlying each measure.
Algebraically, t = (M1 - M2) / sqrt(SE1**2 + SE2**2) where M1 is one measure with standard errorr SE1, and M2 is the other measure with standard error SE2.
Gaps based on effect-size: these are used in education, where it is felt that students whose abilities are 2 S.D.s above the sample mean ability are in a higher performing group.
For polytomies (rating scales, partial credit, etc.): The math is more complicated and probabilistic implications hard to explain, so it usually comes down to substance. Lai & Eton (2002, RMT 15:4, 850) report 0.5 logits to be a clinically meaningful gap for one instrument.
Linacre J.M. (2004) When does a gap between measures matter?, Rasch Measurement Transactions, 18:3 p. 993
|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|
|Forum||Rasch Measurement Forum to discuss any Rasch-related topic|
Go to Top of Page
Go to index of all Rasch Measurement Transactions
AERA members: Join the Rasch Measurement SIG and receive the printed version of RMT
Some back issues of RMT are available as bound volumes
Subscribe to Journal of Applied Measurement
Go to Institute for Objective Measurement Home Page. The Rasch Measurement SIG (AERA) thanks the Institute for Objective Measurement for inviting the publication of Rasch Measurement Transactions on the Institute's website, www.rasch.org.
|Coming Rasch-related Events|
|Apr. 14-17, 2020, Tue.-Fri.||International Objective Measurement Workshop (IOMW), University of California, Berkeley, https://www.iomw.org/|
|May 22 - June 19, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 26 - July 24, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
|June 29 - July 1, 2020, Mon.-Wed.||Measurement at the Crossroads 2020, Milan, Italy , https://convegni.unicatt.it/mac-home|
|July - November, 2020||On-line course: An Introduction to Rasch Measurement Theory and RUMM2030Plus (Andrich & Marais), http://www.education.uwa.edu.au/ppl/courses|
|July 1 - July 3, 2020, Wed.-Fri.||International Measurement Confederation (IMEKO) Joint Symposium, Warsaw, Poland, http://www.imeko-warsaw-2020.org/|
|Aug. 7 - Sept. 4, 2020, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com|
|Oct. 9 - Nov. 6, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 25 - July 23, 2021, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
The URL of this page is www.rasch.org/rmt/rmt183p.htm