The DOI matches its Crossref record; 10 of the 10 references it cites were found in a registry or an index.
Coefficient Alpha and the Reliability of Composite Measurements
Abstract
Following a general approach due to Guttman, coefficient α is rederived as a lower bound on the reliability of a test. A necessary and sufficient condition under which equality is attained in this inequality and hence that α is equal to the reliability of the test is derived and shown to be closely related to the recent redefinition of the concept of parallel measurements due to Novick. This condition is then also shown to be closely related to the unit rank assumption originally adopted by Kuder and Richardson in the derivation of their formula 20. The assumption later adopted by Jackson and Ferguson and the one adopted by Gulliksen are shown to be related to the necessary and sufficient condition derived here. It is then pointed out that the statement that “coefficient α is equal to the mean of the split-half reliabilities” is true only under the restricted condition assumed by Cronbach in the body of his derivation of this result. Finally some limitations on the uses of any function of α as a measure of internal consistency are noted.
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Citations
Cites
Coefficient Alpha and the Internal Structure of Tests
Cronbach, L. J. (1951) · Psychometrika · doi:10.1007/bf02310555 · Cited by 43,931
Gulliksen, H. (1950) · John Wiley & Sons, Inc. eBooks · doi:10.1037/13240-000 · Cited by 2,177
The Theory of the Estimation of Test Reliability
Kuder, G. F., & Richardson, M. W. (1937) · Psychometrika · doi:10.1007/bf02288391 · Cited by 2,002
THEORY OF GENERALIZABILITY: A LIBERALIZATION OF RELIABILITY THEORY†
Cronbach, L. J., Rajaratnam, N., & Gleser, G. C. (1963) · British Journal of Statistical Psychology · doi:10.1111/j.2044-8317.1963.tb00206.x · Cited by 737
Test Reliability Estimated by Analysis of Variance
Hoyt, C. (1941) · Psychometrika · doi:10.1007/bf02289270 · Cited by 513
The axioms and principal results of classical test theory
Novick, M. R. (1966) · Journal of Mathematical Psychology · doi:10.1016/0022-2496(66)90002-2 · Cited by 509
Self-citationReliability Formulas that do not Assume Experimental Independence
Guttman, L. (1953) · Psychometrika · doi:10.1007/bf02289060 · Cited by 55
Statistical Inferences About True Scores
Lord, F. M. (1959) · Psychometrika · doi:10.1007/bf02289759 · Cited by 43
The Definition and Estimation of Test Reliability
Cureton, E. E. (1958) · Educational and Psychological Measurement · doi:10.1177/001316445801800404 · Cited by 42
Some Remarks on the Kuder-Richardson Reliability Coefficient
Dressel, P. L. (1940) · Psychometrika · doi:10.1007/bf02287978 · Cited by 36
Research works printed but not linked: 3
- [8] Jackson, R. W. B. , & Ferguson, G. A. Studies on the reliability of tests. Bulletin 12, Department of Educational Research, University of Toronto, 1941.
- Lyerly, 1958, The Kuder-Richardson formula (21) as a split-half coefficient and some remarks on its basic assumption, Psychometrika, 23, 267, 10.1007/BF02289239 · doi:10.1007/bf02289239
- Rulon, 1939, A simplified procedure for determining the reliability of a test by splithalves, Harvard Educ. Rev., 9, 99
Cited by
On the use, the misuse, and the very limited usefulness of Cronbach’s alpha
Sijtsma, K. (2009) · Psychometrika · doi:10.1007/s11336-008-9101-0 · Cited by 2,814
The PedsQL™* 4.0 as a Pediatric Population Health Measure: Feasibility, Reliability, and Validity
Varni, J. W., Burwinkle, T. M., Seid, M., & Skarr, D. (2003) · Ambulatory Pediatrics · doi:10.1367/1539-4409(2003)003<0329:tpaapp>2.0.co;2 · Cited by 2,324
Zinbarg, R. E., Revelle, W., Yovel, I., & Li, W. (2005) · Psychometrika · doi:10.1007/s11336-003-0974-7 · Cited by 1,439
Varni, J. W., Limbers, C. A., & Burwinkle, T. M. (2007) · Health and Quality of Life Outcomes · doi:10.1186/1477-7525-5-1 · Cited by 1,075
Methodology Review: Assessing Unidimensionality of Tests and ltenls
Hattie, J. (1985) · Applied Psychological Measurement · doi:10.1177/014662168500900204 · Cited by 1,013
Metadata
- Authors
- Novick, M. R., & Lewis, C.
- Venue
- Psychometrika
- Publisher
- Cambridge University Press (CUP)
- Published
- 1967-03
- Volume
- 32
- Issue
- 1
- Pages
- 1-13
- ISSN
- 0033-3123 (ISSN-L)
- 1860-0980
- OpenAlex
- W4244225390
- Cited by
- 466
- References
- 10
- FWCI
- 12.36
- Type
- journal article
- Language
- en
- Open access
- closed
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