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What is coefficient alpha? An examination of theory and applications
Abstract
Psychological research involving scale construction has been hindered considerably by a wide-spread lack of understanding of coefficient alpha and reliability theory in general. A discussion of the assumptions and meaning of coefficient alpha is presented. This discussion is followed by a demonstration of the effects of test length and dimensionality on alpha by calculating the statistic for hypothetical tests with varying numbers of items, numbers of orthogonal dimensions, and average item intercorrelations. Recommendations for the proper use of coefficient alpha are of-fered. Coefficient alpha (Cronbach, 1951) is certainly one of the most important and pervasive statistics in research involving test construction and use. A review of the Social Sciences Cita-tions Index for the literature from 1966 to 1990 revealed that Cronbach's (1951) article had been cited approximately 60 times per year and in a total of 278 different journals. In addi-tion to the areas of psychology in which one may expect to see alpha used, such as educational, industrial, social, clinical, child, community, and abnormal psychology, this list of jour-nals included representatives from experimental psychology, so-ciology, statistics, medicine, counseling, nursing, economics,
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“The reliability of each scale was tested with the Cronbach's Alpha: all the values are over 0.7, which implies that there is an overall adequate internal consistency and that the measures could be considered reliable (Cortina, 1993;Taber, 2017).”
From The self-reinforcing effect of digital and social exclusion: The inequality loop (2022) · cites this paper as Cortina, 1993
In the citing paper
“Internal consistency reliability (Cronbach’s alpha) ranged from 0.70 to 0.79, which is within what is generally considered the acceptable range of 0.65–0.80 [47,48]”
From Gender Differences in Coping and Psychological Adaptation during the COVID-19 Pandemic (2023) · cites this paper as [47]
In the citing paper
“We chose these two tools, instead of traditional measures of internal consistency (i.e., Cronbach's Alpha [Cronbach, 1951] or KR-20 for dichotomous data [Kuder and Richardson, 1937]) because unlike traditional estimates which do not assess homogeneity (Cortina, 1993; Clark and Watson, 1995), omega and CFA, simultaneously provide estimates of both.”
From A psychometric analysis of the reading the mind in the eyes test: toward a brief form for research and applied settings (2015) · cites this paper as Cortina, 1993
In the citing paper
“Also, Cronbach's alpha is highly biased by long tests; Cortina (1993) recommended Cronbach's alpha not be used for tests with more than 40 items and the Eyes Test, at 36 items, is close to this limit.”
From A psychometric analysis of the reading the mind in the eyes test: toward a brief form for research and applied settings (2015) · cites this paper as Cortina, 1993
In the citing paper
“Reliability estimates are biased towards number of items, and on scales with small numbers of items the alpha is a poor indicator of measure fit (Cortina 1993).”
From Sleep Problems Across Development: A Pathway to Adolescent Risk Taking Through Working Memory (2015) · cites this paper as Cortina 1993
Citations
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“Like other reliability tests (Cortina, 1993), sorting and rating procedures generate an estimate of the degree to which the concept map represents a reliable grouping of the data, with high stress values indicating considerable variability in the way participants grouped the statements they…”
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“Cortina (1993), in fact, suggested that coefficient alpha is virtually useless as an index of internal consistency for scales containing 40 or more items” (p. 316).”
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“In addition to this limitation, concerns have been raised by various researchers regarding both the 10 subscales and the latent constructs assessed by the LASSI (Melancon, 2002; Murphy & Alexander, 1998).”
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“Furthermore, the reliability of the scales ranged from good to excellent, confirming the internal consistency of the measures (Cortina, 1993).”
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“70 is considered to indicate good internal consistency, given that the scale is unidimensional (24,25).”
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“The low Cronbach’s a may be explained by the fact that the scale includes only six items (Cortina, 1993; Holden et al., 1991) and that two of the six items included in the subscale had low factor loading.”
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“…argued against the general use of coefficient alpha as a reliability coefficient in that the assumptions underlying alpha may be frequently violated in practice, and thus alpha is a biased estimate of reliability (Cortina, 1993; Green & Yang, 2009; Raykov, 1997b; Rozeboom, 1966; Sijtsma, 2009).”
Backgroundde Vries, M. F. R. K., Vrignaud, P., & Florent‐Treacy, E. (2004) · The International Journal of Human Resource Management · doi:10.1080/0958519042000181214 · Cited by 124
“In fact, research has found that the number of items in the calculation of alpha coefficients can appear to create confusion between internal consistency and the length of the scale (Cortina, 1993).”
BackgroundAsymptotically distribution-free (ADF) interval estimation of coefficient alpha.
Maydeu‐Olivares, A., Coffman, D. L., & Hartmann, W. M. (2007) · Psychological Methods · doi:10.1037/1082-989x.12.2.157 · Cited by 123
“, internal consistency) among the items (Cortina, 1993).”
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“However, as Cortina ( 1993 ) noted, the number of items, and item inter-correlations need to be taken into account in order to understand alpha.”
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“precision estimates) [25,26] were used to determine the number of factors extracted.”
BackgroundMethodCoefficient α as a Measure of Test Score Reliability: Review of 3 Popular Misconceptions
Morera, O. F., & Stokes, S. M. (2016) · American Journal of Public Health · doi:10.2105/ajph.2015.302993 · Cited by 123
“These include assumptions underlying classical test theory(2) and the following: (1) item responses form a unidimensional scale, (2) error scores from the items are uncorrelated, and (3) the items are essentially -equivalent, meaning that the items’ true scores diff er by an additive constant.”
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“A coefficient of .70 was considered to represent adequate reliability (Cortina, 1993).”
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“Taking into account the brevity of the scales per factor internal consistency reliability was also acceptable given the dependence of Cronbach’s alpha coefficient (Cronbach, 1951) to scale length (Cortina, 1993; Green, Lissitz, & Mulaik, 1977; Nunnally & Bernstein, 1994).”
MethodA Comparison of the Separation Ratio and Coefficient α in the Creation of Minimum Item Sets
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“data;(2) and (e) test homogeneity.(5) The first 4 are discussed below.”
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“Note, however, that alpha has been criticized, especially with regard to tests of multidimensionality (Cortina, 1993).”
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“70 represents good internal consistency or reliability of a sample (Cortina 1993).”
BackgroundInfluentialOpacka‐Juffry, J., & Mohiyeddini, C. (2011) · Stress · doi:10.3109/10253890.2011.560309 · Cited by 128
Garamendi, E., Pesudovs, K., Stevens, M. J., & Elliott, D. B. (2005) · Vision Research · doi:10.1016/j.visres.2005.07.007 · Cited by 121
“In addition, Cortina (1993) reported that Cronbach s a is dependent upon the number of items, so that an instrument with more than 20 items would have a high Cronbach s a implying high correlation among items without necessarily having high inter-item correlation at all.”
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“75 for both the physical activity environment and the social environment (suggesting adequate internal consistency) (34, 35).”
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“70 for constructs with three or four measures (Cortina, 1993).”
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“We calculated the alpha internal consistency, reliability measure using Chronbach’s alpha [33].”
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“…is independent of the number of items of a test (e.g. Cortina, 1993), (3) Alpha is an indication of the one-dimensionality of a test score (e.g. Cortina, 1993; Nunnally & Bernstein, 1994; Schmitt, 1996; Sijtsma, 2009), (4) Alpha is the best choice among reliability coefficients (e.g. Cho &…”
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“A cut-off at .60 was considered adequate because only a small number of items, a maximum of six per scale, were used (Cortina, 1993; Palant, 2007).”
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Common methodological mistakes
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“As can be seen, all of the measures showed good internal consistency (Cortina, 1993), making our plan of analysis feasible.”
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“Without reiterating his arguments, Cronbach’s suggestion that coefficient α solves all problems is a perfect example of a message that arrives at the right time when people are most perceptive (but see Cortina 1993; Green, Lissitz, &Mulaik, 1977; Schmitt, 1996, for early critical accounts).”
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“The α and CR values for nine study variables were larger than 0.7, which is the recommended level for internal consistency of the scale items (Bagozzi and Yi 1988; Cortina 1993).”
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“40 is sufficient (Cortina, 1993; Nunnally, 1978), thus showing that reliability specifications were also met for the construct propensity to trust.”
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“There are problems related to alpha that are often overlooked in psychology and sport psychology literature, including the fact that this value is highly dependent on the number of items that make up the dimension of interest (Cortina, 1993).”
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“Reliability estimates are biased towards number of items, and on scales with small numbers of items the alpha is a poor indicator of measure fit (Cortina 1993).”
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“Cortina [44] (as cited in [45]), stated that a low number of items in a scale will lead to a low Cronbach’s alpha value.”
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“…of the multiple choice, single choice, and ranked Likert-scale questions with varying scales of measurement, we applied a factorial analysis (Cortina, 1993; Green et al., 1977; Jasper, 2010; Tate, 2003) to test the reliability and validation of the data and results of the analysis done in…”
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“The Cronbach alpha was near or above 0.70 for most scales, representing a good level of fit (e.g., Cortina, 1993).”
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“More recently, Forth et al. (2003) noted that three- and fourfactor models fit the data well when using parceled confirmatory factor analysis (CFA) models.”
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“…good reliability (α= 0.79), similar to its subscales (Table 3); only “prohibited use” obtained a modest alpha, which is acceptable as it was above 0.5 as this coefficient is sensitive to the number of items in the scale (i.e., five items per PMPUQ-SV subscale; Cortina, 1993; Helmstadter, 1964).”
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“Although it may be noted that Cronbach’s alpha represents the lowest estimate of actual reliability (Cortina 1993), low scale reliability implies measurement error, which can enhance variance in the estimation of the effect size.”
BackgroundDos’Santos, T., THOMAS, C. R., Jones, P. A., & Comfort, P. (2018) · The Journal of Strength and Conditioning Research · doi:10.1519/jsc.0000000000002438 · Cited by 114
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“The Cronbach alpha reliability coefficient was .883, which is considerably above the recommended value of .6 for combining variables into a single construct (Cortina, 1993).”
BackgroundMethodChen, C., & Bozeman, B. L. (2012) · Public Management Review · doi:10.1080/14719037.2012.698853 · Cited by 128
“Cortina (1993) indicates that the level of alpha is a function of the size of the average correlations among items and can be large despite a wide range of item intercorrelations.”
BackgroundDoes Collaboration Between Sales and Marketing Affect Business Performance?
Meunier-FitzHugh, K. L., & Piercy, N. F. (2007) · Journal of Personal Selling and Sales Management · doi:10.2753/pss0885-3134270301 · Cited by 113
Study Abroad Experiences and Global Citizenship
Wynveen, C. J., Kyle, G. T., & Tarrant, M. A. (2011) · Journal of Studies in International Education · doi:10.1177/1028315311426782 · Cited by 116
“51), Cortina (1993) and Gay (1991) indicated that it was acceptable to retain factors with lower alpha values when working with new scales or factors with a low number of items.”
BackgroundLang, C. (2018) · Fashion and Textiles · doi:10.1186/s40691-018-0139-z · Cited by 113
“Cronbach’s alpha estimates of all constructs ranged from 0.748 to 0.965, which exceeded the recommended 0.70 cut off point (Cortina 1993), confirming the reliability of measurement.”
MethodInfluentialChi, N., Tsai, W., & Tseng, S.-M. (2013) · Work & Stress · doi:10.1080/02678373.2013.819046 · Cited by 113
“The slightly low alpha value could be due to the relatively small number of items used to measure state hostility (Cortina, 1993).”
BackgroundJensen‐Doss, A., & Hawley, K. M. (2011) · Administration and Policy in Mental Health and Mental Health Services Research · doi:10.1007/s10488-011-0334-3 · Cited by 112
“However, given that this scale was short, which can impact the magnitude of alpha (e.g., Cortina 1993), we also examined the corrected inter-item correlations for this scale.”
BackgroundPedersen, M. J. (2015) · Public Administration Review · doi:10.1111/puar.12325 · Cited by 118
“Th e alpha of two-item computations are thus lower-bound reliability estimates (Cortina 1993).”
BackgroundResearch note: The winds of change—Multiple identifications in the case of organizational mergers
van Dick, R., Wagner, U., & Lemmer, G. (2004) · European Journal of Work and Organizational Psychology · doi:10.1080/13594320444000038 · Cited by 112
“Table 1 also presents the internal reliability coefficients, which can be interpreted as sufficient or good with respect to the respective number of items (cf. Cortina, 1993).”
Goodness of Measurement: Reliability and Validity
Bajpai, R. C., & Bajpai, S. (2014) · International Journal of Medical Science and Public Health · doi:10.5455/ijmsph.2013.191120133 · Cited by 137
“Kuder–Richardson Formula 20 (KR-20): KR-20, first published in 1937 is a measure of internal consistency reliability for measures with dichotomous choices and it is analogous to Cronbach's α.[14,15] A high KR-20 coefficient (e.”
BackgroundOlney, D. K., Bliznashka, L., Pedehombga, A., Dillon, A., Ruel, M. T., & Heckert, J. (2016) · Journal of Nutrition · doi:10.3945/jn.115.224261 · Cited by 112
Girls' and boys' experience with teen sexting in early and late adolescence
Ševčíková, A. (2016) · Journal of Adolescence · doi:10.1016/j.adolescence.2016.06.007 · Cited by 122
Gobbens, R. J. J. (2018) · PeerJ · doi:10.7717/peerj.5425 · Cited by 115
“In this study, the (unstandardized) Cronbach’s alpha’s for ADL and IADL disability were .82 and .80, respectively, representing adequate values (Cortina, 1993) Background characteristics: sociodemographic and multimorbidity The sociodemographic background characteristics considered were age, sex,…”
MethodInfluentialYang, Q.-F., Lian, L.-W., & Zhao, J.-H. (2023) · International Journal of Educational Technology in Higher Education · doi:10.1186/s41239-023-00391-9 · Cited by 152
“The Cronbach’s alpha values for the tests were 0.80 (Cortina, 1993).”
MethodInfluentialGiangreco, A., Sebastiano, A., & Peccei, R. (2009) · The International Journal of Human Resource Management · doi:10.1080/09585190802528417 · Cited by 112
“However, given that this is only a three-item scale and that coefficient alpha tends to increase with the number of items in the scale (Cortina 1993; Field 2005), the present value, although not ideal, is acceptable.”
BackgroundUnderstanding the role of social context and user factors in video Quality of Experience
Zhu, Y., Heynderickx, I. E. J., & Redi, J. (2015) · Computers in Human Behavior · doi:10.1016/j.chb.2015.02.054 · Cited by 111
“We first tested the internal consistency between items in each sub-questionnaire, using Cronbach’s alpha (a) (Cortina, 1993).”
MethodDoron, J., Trouillet, R., Gana, K., Boiché, J. C. S., Neveu, D., & Ninot, G. (2014) · Journal of Personality Assessment · doi:10.1080/00223891.2014.886255 · Cited by 111
Crawford, J., & Kelder, J. (2018) · The Leadership Quarterly · doi:10.1016/j.leaqua.2018.07.001 · Cited by 138
Kyselá, E., Ščasný, M., & Zvěřinová, I. (2019) · Climate Policy · doi:10.1080/14693062.2019.1611534 · Cited by 135
“Nevertheless, high values of Cronbach’s α do not necessarily purport a unidimensional structure or a single underlying factor (Cortina, 1993; Schmitt, 1996).”
BackgroundBőthe, B., Tóth‐Király, I., Griffiths, M. D., Potenza, M. N., Orosz, G., & Demetrovics, Z. (2020) · Addictive Behaviors · doi:10.1016/j.addbeh.2020.106603 · Cited by 127
Evans, S. C., Corteselli, K. A., Edelman, A., Scott, H., & Weisz, J. R. (2022) · Child Psychiatry & Human Development · doi:10.1007/s10578-021-01301-8 · Cited by 118
“Brief scales tend to have lower alphas simply as a result of having fewer items [64, 65].”
BackgroundBhaduri, S., & Kumar, H. (2010) · Mind & Society · doi:10.1007/s11299-010-0081-2 · Cited by 122
“Cortina (1993: 99) indeed clarifies that Cronbach’s alpha ‘‘applies to any set of items regardless of the response scale.’’ 30 We, accordingly,”
BackgroundGrilo, C. M., McGlashan, T. H., Morey, L. C., Gunderson, J. G., Skodol, A. E., Shea, M. T., Sanislow, C. A., Zanarini, M. C., Bender, D. S., Oldham, J. M., et al. (2001) · Acta Psychiatrica Scandinavica · doi:10.1034/j.1600-0447.2001.00436.x · Cited by 111
Hulbert-Williams, N., Neal, R. D., Morrison, V. L., Hood, K., & Wilkinson, C. (2011) · Psycho-Oncology · doi:10.1002/pon.1980 · Cited by 124
“7 [40], these could not be improved through item‐reduction techniques [39].”
Development and Preliminary Validation of a Parenting Self-Regulation Scale: “Me as a Parent”
Hamilton, V., Matthews, J. M., & Crawford, S. B. (2014) · Journal of Child and Family Studies · doi:10.1007/s10826-014-0089-z · Cited by 110
“The internal reliability for each individual subscale was poorer, however, with only four items on each subscale, a lower reliability coefficient may not be unusual given that coefficient alpha is affected by test size (Cortina 1993).”
Lucke, J. F. (2004) · Applied Psychological Measurement · doi:10.1177/0146621604270882 · Cited by 110
“However, simulation studies and simple cases have thrown serious doubt on this claim (Cortina, 1993; Green, Lissitz, & Mulaik, 1977; Hattie, 1985; Miller, 1995).”
BackgroundHernandez-Palazon, J., Fuentes-García, D., Falcón-Araña, L., Roca-Calvo, M. J., Burguillos-López, S., Doménech-Asensi, P., & Jara-Rubio, R. (2017) · Journal of Cardiothoracic and Vascular Anesthesia · doi:10.1053/j.jvca.2017.04.044 · Cited by 119
The Dynamics Concept Inventory Assessment Test: A Progress Report And Some Results
Lane, J. L., Evans, D., Gray, G., Costanzo, F., Cornwell, P. J., & Self, B. (2020) · IEEE Lasers and Electro-Optics Society Annual Meeting (LEOS) · doi:10.18260/1-2--15378 · Cited by 110
Metadata
- Authors
- Cortina, J. M.
- Venue
- Journal of Applied Psychology
- Published
- 1993-02
- Volume
- 78
- Issue
- 1
- Pages
- 98-104
- ISSN
- 0021-9010 (ISSN-L)
- 1939-1854
- OpenAlex
- W2117012826
- Cited by
- 8,810
- References
- 26
- Citations by year
- 2026: 523 · 2025: 499 · 2024: 518 · 2023: 606 · 2022: 639 · 2021: 685 · 2020: 589 · 2019: 474 · 2018: 407 · 2017: 411 · 2016: 418 · 2015: 428 · 2014: 437 · 2013: 372 · 2012: 309
- FWCI
- 29.15
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Applied Psychology (publishedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Reliability and Agreement in Measurement
- Social Sciences › Psychology › Applied Psychology › Psychological Testing and Assessment
- Keywords
- Cronbach's alpha, internal consistency, reliability theory, scale development, test length, dimensionality
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