When does a Gap between Measures Matter?

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 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

To be emailed about new material on www.rasch.org
please enter your email address here:

I want to Subscribe: & click below
I want to Unsubscribe: & click below

Please set your SPAM filter to accept emails from Rasch.org

www.rasch.org welcomes your comments:

Your email address (if you want us to reply):

 

ForumRasch 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
Sept. 27-29, 2017, Wed.-Fri. In-person workshop: Introductory Rasch Analysis using RUMM2030, Leeds, UK (M. Horton), Announcement
Oct. 13 - Nov. 10, 2017, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Oct. 25-27, 2017, Wed.-Fri. In-person workshop: Applying the Rasch Model hands-on introductory workshop, Melbourne, Australia (T. Bond, B&FSteps), Announcement
Dec. 6-8, 2017, Wed.-Fri. In-person workshop: Introductory Rasch Analysis using RUMM2030, Leeds, UK (M. Horton), Announcement
Jan. 5 - Feb. 2, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Jan. 10-16, 2018, Wed.-Tues. In-person workshop: Advanced Course in Rasch Measurement Theory and the application of RUMM2030, Perth, Australia (D. Andrich), Announcement
Jan. 17-19, 2018, Wed.-Fri. Rasch Conference: Seventh International Conference on Probabilistic Models for Measurement, Matilda Bay Club, Perth, Australia, Website
April 13-17, 2018, Fri.-Tues. AERA, New York, NY, www.aera.net
May 25 - June 22, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 29 - July 27, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
Aug. 10 - Sept. 7, 2018, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Oct. 12 - Nov. 9, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com

 

The URL of this page is www.rasch.org/rmt/rmt183p.htm

Website: www.rasch.org/rmt/contents.htm