Differential Item Functioning (DIF) compares the difficulty of an item for a person sample of interest, the Focal Group (F), with the difficulty of the item for another group, the Reference Group (R). As we plan to investigate DIF, several questions arise:
1) What difference between the two item difficulties, i.e., what DIF size, is large enough to have substantive consequences? If we lack better information about the situation, we may choose the DIF size specified by Educational Testing Service which is 1 Delta δ unit = 0.426 logits (see RMT 20:3 p. 1070), rounded up to 0.5 logits for sample-size purposes.
2) What difference between item difficulties is unlikely to be merely a chance result, i.e., when is the DIF size statistically significant? We usually choose the conventional statistical significance level, p ≤ .05 (Fisher, 1926).
3) How many members of the Focal and Reference Groups are required for the DIF size specified in (1) to meet the DIF significance criterion specified in (2)? What samples sizes are required? This nomogram provides a guide.
The nomogram is based on a Student's t-statistic with two independent groups of different sizes, NF and NR, but equal standard deviations, S. The t-statistic of the DIF size, D, is
Group size values are chosen such that the two-sided probability of observing t or greater is p = .05 for the specified DIF size, D. The standard deviation, S, is chosen at a reasonable value, 1.88 logits, based on inspection of empirical data.
Example: if our Focal group size is 100, and our Reference group size is 1000, then the DIF size will need to be 0.4 logits or more to be statistically significant.
John Michael Linacre
Fisher R.A. (1926). The arrangement of field experiments. Journal of the Ministry of Agriculture, 33: 504.
Tristan, A. (2006). An adjustment for sample size in DIF analysis. Rasch Measurement Transactions, 20:3, p. 1070-71.
Linacre J.M. (2013) Differential Item Functioning DIF Sample Size Nomogram, Rasch Measurement Transactions, 26:4 p. 1391
|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|
|Oct. 9 - Nov. 6, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|Jan. 22 -Feb. 19, 2021, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|May 21 -June 18, 2021, 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|
|Aug. 13 - Sept. 10, 2021, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith,Facets), www.statistics.com|
|June 24 - July 22, 2022, 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/rmt264a.htm