Woodcock's Test Design Nomograph (RM 6:3 p.244) is a handy graph for obtaining the expected measurement precision of a uniform test. For those designing tests by computer, I suggest a simple formula that performs the same function.
For a uniform test of L items, with logit range W = (Dh -Dl ) between the hardest and easiest items, the average item spacing is given by D = W/(L-1). An estimated person logit standard error at test center is
SE = sqrt( D / Tanh (LD/4))
where tanh() is the hyperbolic tangent. If tanh() is not available to you, compute
tanh x = (exp(x) - exp(-x)) / (exp(x) + exp(-x))
For a 75 item test of range 3 logits, this estimates a central precision of 0.25 logits as does Woodcock's Nomograph.
This formula can be applied iteratively to find the number of items required for a particular precision. How many items are required for a test of 4 logits range to measure with a precision of 0.3 logits? Start with test length at 100 items, then increase or decrease the number of items till a match to the desired precision is found. Following this procedure, the formula estimates a test length of 60 items. This result is also in agreement with Woodcock's Nomograph.
(For further discussion of the design and use of uniform tests, see Wright & Stone's Best Test Design, 1978, p. 137-140, 144-146, 212, 214.)
Computerizing Woodcock's Nomograph, P Pedler Rasch Measurement Transactions, 1993, 6:4 p. 255
|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/rmt64f.htm