"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|
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|March 21, 2019, Thur.||13th annual meeting of the UK Rasch user group, Cambridge, UK, http://www.cambridgeassessment.org.uk/events/uk-rasch-user-group-2019|
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|June 4 - 7, 2019, Tue.-Fri.||In-Person Italian Rasch Analysis Workshop based on RUMM (Fabio La Porta and Serena Caselli; entirely in Italian). Prof David Andrich from Western Australia University will be hosted by the workshop. For enquiries and registration email to email@example.com|
|June 17-19, 2019, Mon.-Wed.||In-person workshop, Melbourne, Australia: Applying the Rasch Model in the Human Sciences: Introduction to Rasch measurement (Trevor Bond, Winsteps), Announcement|
|June 20-21, 2019, Thurs.-Fri.||In-person workshop, Melbourne, Australia: Applying the Rasch Model in the Human Sciences: Advanced Rasch measurement with Facets (Trevor Bond, Facets), Announcement|
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|July 2-5, 2019, Tue.-Fri.||2019 International Measurement Confederation (IMEKO) Joint Symposium, St. Petersburg, Russia,https://imeko19-spb.org|
|July 11-12 & 15-19, 2019, Thu.-Fri.||A Course in Rasch Measurement Theory (D.Andrich), University of Western Australia, Perth, Australia, flyer - http://www.education.uwa.edu.au/ppl/courses|
|Aug 5 - 10, 2019, Mon.-Sat.||6th International Summer School "Applied Psychometrics in Psychology and Education", Institute of Education at HSE University Moscow, Russia.https://ioe.hse.ru/en/announcements/248134963.html|
|Aug. 9 - Sept. 6, 2019, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com|
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|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|
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