"Perhaps the most paradoxical aspect of the attenuation paradox is that Gulliksen, who appears to deserve credit for discovering it, failed to include any reference to it in his comprehensive summary of mental test theory" (Loevinger 1954 p. 501).
In 1945, Gulliksen discovered that, under certain conditions, increasing the reliability of test scores decreases their validity. Professional reaction to the "attenuation paradox" of classical true-score theory (CTT) illustrates five typical reactions to challenges of familiar theories:
1) Gulliksen (1950) ignores the paradox because he decided that true-score theory provides useful results concerning test reliability anyway. All current psychometric texts follow Gulliksen's footsteps.
2) Lord (1952 p. 501) implies that the paradox is due to lack of skill on the part of psychometricians, rather than a deficient theory. He suggests a curvilinear index to produce a different summary of the relationship between reliability and validity.
3) Tucker (1946 p. 11) accepts the paradox in theory, but resists its implications for practice. "A result which seemed amazing was the low values of the item reliabilities which yielded best measurement... It is safer for the reliabilities to be too high."
4) Davis (1952 p.105) introduces an untestable hypothesis, that of "common sense" (Loevinger 1954 p.105) to save the theory. "It is not proper to deduce from Tucker's data that to obtain high test validity one should make items of low reliability. There is no inconsistency between high item reliability and efficient measurement."
5) Humphreys (1956) accepts the paradox and rejects true-score theory and its assumption that test scores are interval level data. He proposes an alternative theory based on the normal distribution in which test scores are ordinal. His theory explains and overcomes the attenuation paradox, but has its own anomalies.
Though hardly a reaction to the attenuation paradox, Rasch theory does provide a useful perspective for understanding it, as will be shown in my next column.
George Engelhard, Jr.
Davis F B (1952) Item analysis in relation to educational and psychological testing. Psychological Bulletin 49(2) 97-121
Gulliksen H (1945) The relation of item difficulty and inter-item correlation to test variance and reliability. Psychometrika 10(2) 79-91
Gulliksen H (1950) Theory of mental tests. Wiley
Humphreys L G (1956) The normal curve and the attenuation paradox in test theory. Psychological Bulletin 53(6) 472-3
Loevinger J (1954) The attenuation paradox in test theory. Psychological Bulletin 51 493-504
Lord F (1952) A theory of test scores. Psychometrika Monograph No. 7.
Tucker L R (1946) Maximum validity of a test with equivalent items. Psychometrika 11(1) 1-13
Reactions to the attenuation paradox. Engelhard G Jr. 1993, 7:2 p.294
Reactions to the attenuation paradox. Engelhard G Jr. Rasch Measurement Transactions, 1993, 1993, 7:2 p.294
|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. 11 - Nov. 8, 2019, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|Nov. 3 - Nov. 4, 2019, Sun.-Mon.||International Outcome Measurement Conference, Chicago, IL, http://jampress.org/iomc2019.htm|
|Nov. 15, 2019, Fri.||XIII International Workshop "Rasch Models in Business Administration", IUDE of Universidad de La Laguna. Tenerife. Canary Islands. Spain, https://www.ull.es/institutos/instituto-universitario-empresa/|
|Jan. 30-31, 2020, Thu.-Fri.||A Course on Rasch Measurement Theory - Part 1, Sydney, Australia, course flyer|
|Feb. 3-7, 2020, Mon.-Fri.||A Course on Rasch Measurement Theory - Part 2, Sydney, Australia, course flyer|
|Jan. 24 - Feb. 21, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|Apr. 14-17, 2020, Tue.-Fri.||International Objective Measurement Workshop (IOMW), University of California, Berkeley, https://www.iomw.org/|
|May 22 - June 19, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 26 - July 24, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
|June 29 - July 1, 2020, Mon.-Wed.||Measurement at the Crossroads 2020, Milan, Italy , https://convegni.unicatt.it/mac-home|
|July 1 - July 3, 2020, Wed.-Fri.||International Measurement Confederation (IMEKO) Joint Symposium, Warsaw, Poland, http://www.imeko-warsaw-2020.org/|
|Aug. 7 - Sept. 4, 2020, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com|
|Oct. 9 - Nov. 6, 2020, 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|
The URL of this page is www.rasch.org/rmt/rmt72k.htm