Reliability and Separation Nomograms

"What would be the effect on test reliability of shortening or lengthening my test?" These nomograms predict the reliability and person separation for tests of different lengths administered to the same sample, with other item and person characteristics held constant. Reliability has its usual (KR-20, Cronbach alpha) definition of "true" person measure variance divided by observed person measure variance. Person separation is defined as "true" person measure standard deviation divided by person measure precision (standard error).

Suppose the reported reliability of your pilot test of 100 items is 0.7. What would be the effect of adding 50 items, i.e., increasing the test length by 50%?

Answer: On the reliability nomogram), find the reported reliability of 0.7 on the X-axis. Go vertically upwards till you meet the +50% curve (see solid arrow), then go across to the Y-axis to discover the predicted reliability of almost 0.8.

Suppose reported reliability is 0.6, but you want at least 0.7. How many items must you add?

Answer: Read up vertically from the reported reliability of 0.6 (dotted arrow). Read across horizontally from the predicted reliability of 0.7 (dotted arrow). The arrows meet just above the +50% curve. To achieve the desired reliability, more than 50% extra items must be added to the test. The separation nomogram (in printed text) works the same way.

1. Reliability, separation, strata statistics, Fisher WP Jr. … 6:3 p.238
2. Reliability and separation nomograms, Linacre JM. … 1995, 9:2 p.421
3. Reliability and separation, Wright BD. … 1996, 9:4 p.472
4. Predicting Reliabilities and Separations of Different Length Tests, Linacre, J.M. … 2000, 14:3 p.767
5. Going beyond Unreliable Reliabilities, Mallinson T., Stelmack J. … 2001, 14:4 p.787-8
6. Separation, Reliability and Skewed Distributions: Statistically Different Levels of Performance, Wright B.D. … 2001, 14:4 p.786
7. Number of Person or Item Strata (4G+1)/3, Wright BD, Masters GN. … 2002, 16:3 p.888
8. Cash value of Reliability, WP Fisher … Rasch Measurement Transactions, 2008, 22:1 p. 1160

Reliability and separation nomograms. Linacre JM. … Rasch Measurement Transactions, 1995, 9:2 p.421

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
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