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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
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“Specifically, coefficient alpha is a lower bound estimate (Cortina, 1993), whereas the true reliability is almost always greater than the reliability score generated by Cronbach’s alpha (Novick & Lewis, 1967).”
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“In order to ensure uni-dimensionality (Cortina, 1993), inter-item correlation coefficients were also calculated, and found to exceed r = 0.3 (range r = 0.34–0.73).”
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“This difference in the reliability is probably caused by the smaller number of questions used by us (for extended discussion on this issue, see Cortina, 1993 ).”
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“However, Cortina (1993) discussed that a low number of items can artificially deflate alpha values.”
BackgroundCerasoli, C. P., & Ford, M. T. (2013) · The Journal of Psychology · doi:10.1080/00223980.2013.783778 · Cited by 216
“Although initial scale reliabilities were within the limits of conventional acceptance (α = .81, .80, and .80), we opted to examine the scale further, as alpha alone should not be considered as an indicator of unidimensionality or precision (Cortina, 1993).”
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“[8] Although they used a different formula to calculate internal consistency, the result of these authors’ study can be compared with our result because the Cronbach’s alpha, when applied to dichotomous data like NMQ items, produces the same value as the Kuder–Richarson coefficient.[30] As Cronbach’s alpha has wider a…”
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“7 even when correlations among items are very small or when multidimensionality exists in the scale (Cortina, 1993).”
BackgroundHaberman, J. M., Brady, T. F., & Alvarez, G. A. (2015) · Journal of Experimental Psychology General · doi:10.1037/xge0000053 · Cited by 178
“Performance was highly reliable for all tasks, as measured by Cronbach’s alpha (Cortina, 1993; Cronbach, 1951): individual orientation, .”
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“Cortina (1993) confirms that fewer items may reduce the Cronbach’s alpha coefficient.”
BackgroundLee, S. W., & Tsai, C. (2010) · Computers in Human Behavior · doi:10.1016/j.chb.2010.11.016 · Cited by 194
“The Cronbach’s alpha coefficients (Cortina, 1993) for all 18 sub-scales in this study range between .844 and .905 and show high reliability for the assessment (please see Appendix B).”
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“However, a factor that has a small number of items (six or less) and with alpha value close to .60 is acceptable for an exploratory study (see Cortina, 1993; Nunnally & Bernstein, 1994).”
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“This low alpha value may be a function of the relatively few items in the scale (Bernardi, 1994; Cortina, 1993). Although below the .70 level recommended by Nunnally (1967), this reliability estimate is sufficient to use for research (Hair, Anderson, Tatham, & Black, 1998; Pierce, Gardner, Dunham, & Cummings, 1993).”
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“Equation (1) is the formula that is familiar to researchers employing indices measuring internal consistency (cf. Cortina 1993 p.99 for multiple interpretations of alpha 2 T σ ∑∑ ∑ ≠ = + = i j ij p i i T σ σ σ 1 2 2 ).”
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“The alpha of the last factor, though lower than the recommended .7 (Cortina, 1993), was above the .5 minimum value considered acceptable by Nunnally (1967) as a measure of reliability for basic research.”
BackgroundCoefficient alpha: a useful indicator of reliability?
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“Statistically, reliability of a measure increases with the amount of data measuring the construct (Cortina, 1993).”
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“This approach is recommended when the goal is data reduction (Floyd & Widaman, 1995) and assessment of the unidimensionality of a scale (Cortina, 1993).”
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“Coefficients of all study variables that were more than .7 verified the internal consistency between measurement scales (Cortina 1993).”
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“The alpha statistic assumes that the measure being assessed is unidimensional, and using alpha as a reliability estimate for multidimensional scales is inappropriate (Cortina, 1993). Although alpha may be within acceptable conventions (e.g., the ≥ .80 range), one is unable to determine whether the construct is unitary…”
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“Having said that, it should be noted that Miller (1995) recommends that coefficient alpha should be viewed as a lower bound for internal-consistency because it tends to underestimate it, especially in scales with few items (Cortina, 1993).”
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“…regulations guarantees the integrity, 1 2 3 4 5 (continued) Thus, in order to determine whether ITA is optimal, we should begin by using one of the many factor-analytic techniques currently available to make sure that there are no large departures from unidimensionality (Cortina 1993, p. 103).”
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“First, the reliability argument is null for a singular and concrete target construct that can be captured by a single item (Rossiter, 2002), and Cronbach’s alpha should be examined only after a multiple-item measure has shown to constitute a unidimensional construct (Cortina, 1993).”
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“60 and above are acceptable in constructs containing fewer than six items ( Cortina, 1993 ).”
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“Coefficient alpha is a function of the extent to which items in a test have communalities and is the lower limit of the reliability of a set of test scores (Cortina, 1993).”
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“For ensuring inner consistency, Cronbach’s alpha factor of 0.70 and above is considered as the criterion (Cortina, 1993).”
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“It should be noted that internal consistency as assessed by Cronbach’s Alpha does not inform on scale reproducibility but rather provides an indication of the interrelatedness of questionnaire items [26].”
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“Earlier, it was reported that alpha remained the reliability method of choice (Chmielewski & Watson, 2009; Cortina, 1993; Cronbach & Shavelson, 2004) among psychological researchers.”
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“As the scales analyzed included four or less items, α values higher than .60 are acceptable (cf. Cortina, 1993).”
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“A low number of items, as is the case here, has a suppressing effect on the height of the value of Cronbach’s alpha (Cortina, 1993).”
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“25 Further reliability testing and in-depth analyses of the measures, such as cognitive interviewing, should be conducted in future studies to strengthen their validity for use with tanners.”
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“6 for combining the questions of each variable together on one scale [24].”
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“First, the difficulty of obtaining a high alpha with a small number of items and sample size below 200 is well established (Cortina, 1993).”
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“33 Because the factor analysis identified > 1 dimension, the internal consistency of where k is the number of items of the factor (although each factor was represented only by items with factor loading > 0.5, the factor included all items of the scale), C i2 is the square of the factor loading of i…”
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“The Cronbach’s alpha value is 0.92, which is acceptable (Cortina, 1993 ).”
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“Cortina (1993) noted the importance of taking into account the average item intercorrelation and dimensionality when interpreting coefficient alpha.”
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“Cronbach’s alpha coefficient estimates the reliability of scale by determining the internal consistency of the test or the average correlation of items within the test (13).”
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“To avoid underestimation of internal consistency, studies in which alpha values were calculated on the basis of six or fewer items were also excluded (see Cortina, 1993; Henson, 2001; O’Rourke, Hatcher, & Stepanski, 2005).”
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“All values were within acceptable boundaries [ Cortina, 1993 ].”
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“The Cronbach's alpha coefficient results are provided in Table I, Appendix A and show that alpha values are larger than .7, which is the common recommended cut-off for reliability (Cortina 1993).”
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“Regarding these results, it should be noted that the study was exploratory using a small sample (N=30) (see Cortina, 1993), and there was a relatively small number of items for each factor (b7).”
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“From the formula of Cronbach alpha which is simply the number of items squared multiplied by the average covariance between items divided by sum of all the item variances and item covariances(18), it implies that the 2 scales can have the same or similar alpha value but it might be due to the greater number of items o…”
MethodBenevolent Sexism, Attitudes Toward Motherhood, and Reproductive Rights
Huang, Y., Davies, P. G., Sibley, C. G., & Osborne, D. (2016) · Personality and Social Psychology Bulletin · doi:10.1177/0146167216649607 · Cited by 155
Drydakis, N. (2022) · Information Systems Frontiers · doi:10.1007/s10796-022-10249-6 · Cited by 180
Schmalz, D. L., & Kerstetter, D. L. (2006) · Journal of Leisure Research · doi:10.1080/00222216.2006.11950091 · Cited by 154
“65, which is an acceptable alpha for scales of 6 items or fewer (Cortina, 1983).”
BackgroundPrice, J. C., Walker, I. A., & Boschetti, F. (2014) · Journal of Environmental Psychology · doi:10.1016/j.jenvp.2013.10.001 · Cited by 154
“7 (Cortina, 1993; Kline, 1999).”
Barbieri, C., & Sotomayor, S. (2012) · Tourism Management · doi:10.1016/j.tourman.2012.06.005 · Cited by 154
“Cronbach’s alphas were computed to assess internal reliability (Cortina, 1993) of those serious leisure qualities with more than one sub-dimension (i.e., Career; Benefits) as well as the descriptors used to evaluate the Surfing Appeal and Access and Infrastructure of the surfing tourism destination.”
MethodGeneration Y investment decision: an analysis using behavioural factors
Rahman, M., & Gan, S. S. (2020) · Managerial Finance · doi:10.1108/mf-10-2018-0534 · Cited by 201
Lin, C. (2012) · Journal of Hospitality & Tourism Research · doi:10.1177/1096348012451460 · Cited by 160
“With respect to indictor and latent construct reliability, the t value of each indicator exceeded the critical level of 1.96 (p < .05; Hatcher, 1994), and the reliability for latent constructs exceeded the recommended level of .60 (.66, .72, and .87, respectively; Cortina, 1993).”
BackgroundInfluentialElias, S. M., Smith, W. L., & Barney, C. E. (2010) · Behaviour and Information Technology · doi:10.1080/0144929x.2010.513419 · Cited by 156
“While it is certainly the case that alpha is a function of item intercorrelations, alpha should not be interpreted without taking the number of scale items into consideration (Cortina 1993).”
BackgroundA concise measure of anger in combat‐related posttraumatic stress disorder
Forbes, D., Hawthorne, G., Elliott, P., McHugh, T., Biddle, D., Creamer, M. C., & Novaco, R. W. (2004) · Journal of Traumatic Stress · doi:10.1023/b:jots.0000029268.22161.bd · Cited by 153
“The results also suggested the DAR has little itemspecific variance, implying that the high levels of internal consistency and good fit statistics were based on group factors rather than item factors (Cortina, 1993).”
Gordts, S., Uzieblo, K., Neumann, C. S., den Bussche, E. V., & Rossi, G. M. P. (2015) · Assessment · doi:10.1177/1073191115606205 · Cited by 153
“Because scale length affects Cronbach’s alpha (Cortina, 1993; Cronbach, 1951), additional mean interitem correlations indexing scale homogeneity were calculated and considered acceptable if r ≥ .”
BackgroundMethodEffect of the flipped classroom on the mathematics performance of middle school students
Wei, X., Cheng, I.-L., Chen, N., Yang, X., Liu, Y., Dong, Y., Zhai, X., & Kinshuk, K. (2020) · Educational Technology Research and Development · doi:10.1007/s11423-020-09752-x · Cited by 153
Toward an Understanding of Satisfaction with the Process and Outcomes of Teamwork
Reinig, B. A. (2003) · Journal of Management Information Systems · doi:10.1080/07421222.2003.11045750 · Cited by 153
“76, both indicating a reasonable level of inter-item reliability [16, 39].”
BackgroundHaddock, C. K., Lando, H. A., Klesges, R. C., Talcott, G. W., & Renaud, E. (1999) · Nicotine & Tobacco Research · doi:10.1080/14622299050011161 · Cited by 150
A survey on biosecurity and management practices in Belgian pig herds
Ribbens, S., Dewulf, J., Koenen, F., Mintiens, K., Sadeleer, L. D., de Kruif, A., & Maes, D. G. D. (2007) · Preventive Veterinary Medicine · doi:10.1016/j.prevetmed.2007.07.009 · Cited by 152
“For repeatability, we calculated Cronbach’s Alpha (CA) for two questions that were issued twice and pertained to the same topic (Cortina, 1993).”
MethodKil, N., Holland, S. M., Stein, T. V., & Ko, Y. J. (2011) · Journal of Sustainable Tourism · doi:10.1080/09669582.2011.610508 · Cited by 152
“The internal reliability coefficients of 0.60 or more were acceptable with six items or less for one factor structure (Cortina, 1993).”
BackgroundInfluentialRusso, I., Confente, I., Scarpi, D., & Hazen, B. T. (2019) · Journal of Cleaner Production · doi:10.1016/j.jclepro.2019.02.044 · Cited by 168
“Consequently, items should be factor-analyzed (Cortina, 1993) and load high on the factor representing the scale but low on the other factors (Clark and Watson, 1995).”
BackgroundIonescu, C. A., Paschia, L., Nicolau, N. L. G., Stănescu, S. G., Stancescu, V. M. N., Coman, M. D., & Uzlău, M. C. (2020) · Sustainability · doi:10.3390/su12219030 · Cited by 152
Stability in Depressed Mood in Adolescence: Results from a 6-Year Longitudinal Panel Study
Holsen, I., Kraft, P., & Vittersø, J. (2000) · Journal of Youth and Adolescence · doi:10.1023/a:1005121121721 · Cited by 161
“However, the exact reliability of a test is unknown, and the most commonly used estimate, Cronbach’s alpha, fails to meet certain basic criteria as an index of test homogeneity (e.g., Cortina, 1993; Miller, 1995).”
BackgroundGoldstein, S., Graham, N., Warady, B., Seikaly, M. G., McDonald, R., Burwinkle, T. M., Limbers, C., & Varni, J. (2008) · American Journal of Kidney Diseases · doi:10.1053/j.ajkd.2007.09.021 · Cited by 136
“It should be oted that the internal consistency reliability of RQOL measures for children may be lower in omparison to measures for adults,(51,52) particuarly for scales that have few items.(53,54) Furtherore, as noted by Fayers and Hand,(37) internal onsistency for a causal indicators scale is of less mportance.”
BackgroundMotivating Employees of the Public Sector: Does Public Service Motivation Matter?
Anderfuhren-Biget, S., Varone, F., Giauque, D., & Ritz, A. (2010) · International Public Management Journal · doi:10.1080/10967494.2010.503783 · Cited by 152
“On the other hand, coefficient of reliability is often misleading (Sijtsma 2009 ) and is highly influenced by the number of items (Cortina 1993 ).”
BackgroundMorrone, M., Mancl, K. M., & Carr, K. (2001) · The Journal of Environmental Education · doi:10.1080/00958960109598661 · Cited by 151
Why Do First-Time and Repeat Visitors Patronize a Destination?
Morais, D. B., & Lin, C.-H. (2010) · Journal of Travel & Tourism Marketing · doi:10.1080/10548401003590443 · Cited by 151
“66, respectively; see Table 3 ; Cortina, 1993 ).”
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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