Should Woodcock's Test Design Nomograph be Adjusted and Applied to Polytomous Tests?

Woodcock's test design nomograph helps construct dichotomous tests (Woodcock, 1992). The computation of Woodcock's nomograph was reported by Pedler (1993) and helped us predict an estimated person logit standard error at a test's center based on item length, and logit range of a uniform test. This prompted us to use a simulation to examine whether Woodcock's expected SE values could be exactly applied to not only dichotomous tests, but also polytomous tests.

Woodcock - Tests of Between-Subjects Effects

We found Woodcock's test design nomograph cannot be directly applied to both dichotomous and polytomous tests (p < 0.001) (see Table 1). Instead, the adjusted formula (regressing Woodcock SE value to predict Rasch minimal sample logit SE) can be feasibly and optimally useful while using item length with different types of category numbers and the logit ranges to predict a person logit SE at a test's center. Dichotomous scales are statistically significantly different from the polytomous with regards to the expected SEs. In contrast, there are no statistically significant difference between polytomous scales (Figure 1).

A polytomous item of m ordered categories contains m-1 dichotomous category boundaries (Linacre, 2000). A test of k items contains Ck - k dichotomous items. The number of active categories in the known test is shown as below:

How many categories?

Comparison of Woodcock's test for SE by category number of a scale
Figure 1. Comparison of Woodcock's test for SE by category number of a scale

Tsair-Wei Chien, Chi Mei Medical Center, Taiwan
Jianfang Zou, Academy of Medical Science, Shandong, China


Woodcock, R. W. (1992). Woodcock test construction nomograph. Rasch Measurement Transactions, 6(3), 243-244. Available at:

Pedler, P. (1993). Computerizing Woodcock's test construction nomograph. Rasch Measurement Transactions, 6(4), 255. Available at:

Linacre, J.M. (2000). Predicting reliabilities and separations of different length tests. Rasch Measurement Transactions, 14(3), 767. Available at:

Should Woodcock's Test Design Nomograph be Adjusted and Applied to Polytomous Tests? Tsair-Wei Chien & Jianfang Zou … Rasch Measurement Transactions, 2013, 26:4 p. 1394-5

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