Computerizing Woodcock's Test Construction Nomograph

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 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

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.

The URL of this page is www.rasch.org/rmt/rmt64f.htm

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