Cronbach's alpha

In his initial 1951 publication, Lee Cronbach described the coefficient as Coefficient alpha and included an additional derivation.{{cite journal|first=L.J.|last=Cronbach|title=Coefficient alpha and the internal structure of tests|journal=Psychometrika|volume=16|issue=3|pages=297–334|date=1951|doi=10.1007/BF02310555|s2cid=13820448|hdl=10983/2196|hdl-access=free}} Coefficient alpha had been used implicitly in previous studies,{{cite journal|first=C.|last=Hoyt|title=Test reliability estimated by analysis of variance|journal=Psychometrika|volume=6|issue=3|pages=153–160|date=1941|doi=10.1007/BF02289270|s2cid=122361318}}{{cite journal|first=L.|last=Guttman|title=A basis for analyzing test-retest reliability|journal=Psychometrika|volume=10|issue=4|pages=255–282|date=1945|doi=10.1007/BF02288892|pmid=21007983|s2cid=17220260}}{{cite journal|last1=Jackson|first1=R. W. B.|last2=Ferguson|first2=G. A.|title=Studies on the reliability of tests|journal=University of Toronto Department of Educational Research Bulletin|volume=12|issue=|pages=132|date=1941}}{{cite book|first=H.|last=Gulliksen|title=Theory of mental tests|publisher=Wiley|date=1950|doi=10.1037/13240-000}} but his interpretation was thought to be more intuitively attractive relative to previous studies and it became quite popular.{{Cite journal|last=Cronbach|first=Lee|date=1978|title=Citation Classics|url=http://www.garfield.library.upenn.edu/classics1978/A1978EQ39200002.pdf|journal=Current Contents|volume=13|issue=8|access-date=2022-10-21|archive-date=2022-10-22|archive-url=https://web.archive.org/web/20221022201253/http://www.garfield.library.upenn.edu/classics1978/A1978EQ39200002.pdf|url-status=live}}

• In 1967, Melvin Novick and Charles Lewis proved that it was equal to reliability if the true scores{{efn|The true score is the difference between the score observed during the test or measurement and the error in that observation. See classical test theory for further information.|name=Footnote|group=lower-roman}} of the compared tests or measures vary by a constant, which is independent of the people measured. In this case, the tests or measurements were said to be "essentially tau-equivalent."{{cite journal|last1=Novick|first1=M. R.|last2=Lewis|first2=C.|title=Coefficient alpha and the reliability of composite measurements|journal=Psychometrika|volume=32|issue=1|pages=1–13|date=1967|doi=10.1007/BF02289400|pmid=5232569|s2cid=186226312}}
• In 1978, Cronbach asserted that the reason the initial 1951 publication was widely cited was "mostly because [he] put a brand name on a common-place coefficient."{{rp|263}} He explained that he had originally planned to name other types of reliability coefficients, such as those used in inter-rater reliability and test-retest reliability, after consecutive Greek letters (i.e., $\backslash beta$, $\backslash gamma$, etc.), but later changed his mind.
• Later, in 2004, Cronbach and Richard Shavelson encouraged readers to use generalizability theory rather than $\backslash rho\_\{T\}$. Cronbach opposed the use of the name "Cronbach's alpha" and explicitly denied the existence of studies that had published the general formula of KR-20 before Cronbach's 1951 publication of the same name.

To use Cronbach's alpha as a reliability coefficient, the following conditions must be met:{{Cite journal|last=Spiliotopoulou|first=Georgia|date=2009|title=Reliability reconsidered: Cronbach's alpha and paediatric assessment in occupational therapy|url=https://onlinelibrary.wiley.com/doi/10.1111/j.1440-1630.2009.00785.x|journal=Australian Occupational Therapy Journal|language=en|volume=56|issue=3|pages=150–155|doi=10.1111/j.1440-1630.2009.00785.x|pmid=20854508|access-date=2022-10-21|archive-date=2022-10-21|archive-url=https://web.archive.org/web/20221021235248/https://onlinelibrary.wiley.com/doi/10.1111/j.1440-1630.2009.00785.x|url-status=live}}{{Cite journal|last=Cortina|first=Jose M.|date=1993|title=What is coefficient alpha? An examination of theory and applications.|url=http://doi.apa.org/getdoi.cfm?doi=10.1037/0021-9010.78.1.98|journal=Journal of Applied Psychology|language=en|volume=78|issue=1|pages=98–104|doi=10.1037/0021-9010.78.1.98|issn=1939-1854|access-date=2022-10-21|archive-date=2023-08-13|archive-url=https://web.archive.org/web/20230813121351/https://psycnet.apa.org/doiLanding?doi=10.1037/0021-9010.78.1.98|url-status=live|url-access=subscription}}

1. The data is normally distributed and linear{{Efn|This implicitly requires that the data can be ordered, and thus requires that it is not nominal.|group=lower-roman|name=Footnote2}};
2. The compared tests or measures are essentially tau-equivalent;
3. Errors in the measurements are independent.

Cronbach's alpha is calculated by taking a score from each scale item and correlating it with the total score for each observation. The resulting correlations are then compared with the variance for all individual item scores. Cronbach's alpha is best understood as a function of the number of questions or items in a measure, the average covariance between pairs of items, and the overall variance of the total measured score.{{Cite web|last=Goforth|first=Chelsea|date=November 16, 2015|title=Using and Interpreting Cronbach's Alpha - University of Virginia Library Research Data Services + Sciences|url=https://data.library.virginia.edu/using-and-interpreting-cronbachs-alpha/|access-date=2022-09-06|website=University of Virginia Library|archive-date=2022-08-09|archive-url=https://web.archive.org/web/20220809031644/https://data.library.virginia.edu/using-and-interpreting-cronbachs-alpha/|url-status=live}}

$$\backslash alpha\; =\; \{k\; \backslash over\; k-1\; \}\; \backslash left(1\; -\; \{\backslash sum\_\{i=1\}^k\; \backslash sigma^2\_\{y\_i\}\; \backslash over\; \backslash sigma^2\_y\}\; \backslash right)$$

where:

• $k$ represents the number of items in the measure
• $\backslash sigma\_\{y\_i\}^2$ the variance associated with each item i
• $\backslash sigma\_y^2$ the variance associated with the total scores, $y\; =\; \backslash sum\_\{i=1\}^k\; y\_i$

Alternatively, it can be calculated through the following formula:{{Cite AV media|title=Cronbach's Alpha (Simply explained)|url=https://www.youtube.com/watch?v=W9uPvAmtTOk&t=248|date=October 27, 2021|access-date=2023-08-01|author=DATAtab|publisher=YouTube|time=4:08}}

:$\backslash alpha\; =\; \{k\; \backslash bar\; c\; \backslash over\; \backslash bar\; v\; +\; (k\; -\; 1)\; \backslash bar\; c\}$

where:

• $\backslash bar\; v$ represents the average variance
• $\backslash bar\; c$ represents the average inter-item covariance.

{{Confusing|section|date=May 2023|talk=Talk:Cronbach's_alpha#"Common misconceptions" section is misleading|reason=it is unclear whether headings are true or false}}

Application of Cronbach's alpha is not always straightforward and can give rise to common misconceptions, some of which are detailed here.

By definition, reliability cannot be less than zero and cannot be greater than one. Many textbooks mistakenly equate $\backslash rho\_\{T\}$ with reliability and give an inaccurate explanation of its range. $\backslash rho\_\{T\}$ can be less than reliability when applied to data that are not essentially tau-equivalent. Suppose that $X\_2$ copied the value of $X\_1$ as it is, and $X\_3$ copied by multiplying the value of $X\_1$ by -1.

The covariance matrix between items is as follows, $\backslash rho\_\{T\}=-3$.

Negative $\backslash rho\_\{T\}$ can occur for reasons such as negative discrimination or mistakes in processing reversely scored items.

Unlike $\backslash rho\_\{T\}$, SEM-based reliability coefficients (e.g., $\backslash rho\_\{C\}$) are always greater than or equal to zero.

This anomaly was first pointed out by Cronbach (1943){{cite journal|first=L. J.|last=Cronbach|title=On estimates of test reliability|journal=Journal of Educational Psychology|volume=34|issue=8|pages=485–494|date=1943|doi=10.1037/h0058608}} to criticize $\backslash rho\_\{T\}$, but Cronbach (1951) did not comment on this problem in his article that otherwise discussed potentially problematic issues related $\backslash rho\_\{T\}$.{{rp|396}}{{Cite journal |last1=Waller |first1=Niels |last2=Revelle |first2=William |date=2023-05-25 |title=What are the mathematical bounds for coefficient α? |url=https://doi.apa.org/doi/10.1037/met0000583 |journal=Psychological Methods |language=en |doi=10.1037/met0000583 |pmid=37227892 |issn=1939-1463|url-access=subscription |doi-access=free }}

This anomaly also originates from the fact that $\backslash rho\_\{T\}$ underestimates reliability.

Suppose that $X\_2$ copied the value of $X\_1$ as it is, and $X\_3$ copied by multiplying the value of $X\_1$ by two.

The covariance matrix between items is as follows, $\backslash rho\_\{T\}=0.9375$.

For the above data, both $\backslash rho\_\{P\}$ and $\backslash rho\_\{C\}$ have a value of one.

The above example is presented by Cho and Kim (2015).

Many textbooks refer to $\backslash rho\_\{T\}$ as an indicator of homogeneity{{Cite web|title=APA Dictionary of Psychology|url=https://dictionary.apa.org/|access-date=2023-02-20|website=dictionary.apa.org|language=en|archive-date=2019-07-31|archive-url=https://web.archive.org/web/20190731124940/http://dictionary.apa.org/|url-status=live}} between items. This misconception stems from the inaccurate explanation of Cronbach (1951) that high $\backslash rho\_\{T\}$ values show homogeneity between the items. Homogeneity is a term that is rarely used in modern literature, and related studies interpret the term as referring to uni-dimensionality. Several studies have provided proofs or counterexamples that high $\backslash rho\_\{T\}$ values do not indicate uni-dimensionality.{{cite journal|first=J. M.|last=Cortina|title=What is coefficient alpha? An examination of theory and applications|journal=Journal of Applied Psychology|volume=78|issue=1|pages=98–104|date=1993|doi=10.1037/0021-9010.78.1.98}}{{cite journal|last1=Green|first1=S. B.|last2=Lissitz|first2=R. W.|last3=Mulaik|first3=S. A.|title=Limitations of coefficient alpha as an Index of test unidimensionality|journal=Educational and Psychological Measurement|volume=37|issue=4|pages=827–838|date=1977|doi=10.1177/001316447703700403|s2cid=122986180}}{{cite journal|first=R. P.|last=McDonald|title=The dimensionality of tests and items|journal=The British Journal of Mathematical and Statistical Psychology|volume=34|issue=1|pages=100–117|date=1981|doi=10.1111/j.2044-8317.1981.tb00621.x}}{{cite journal|first=N.|last=Schmitt|title=Uses and abuses of coefficient alpha|journal=Psychological Assessment|volume=8|issue=4|pages=350–3|date=1996|doi=10.1037/1040-3590.8.4.350}}{{cite journal|last1=Ten Berge|first1=J. M. F.|last2=Sočan|first2=G.|title=The greatest lower bound to the reliability of a test and the hypothesis of unidimensionality|journal=Psychometrika|volume=69|issue=4|pages=613–625|date=2004|doi=10.1007/BF02289858|s2cid=122674001}} See counterexamples below.

$\backslash rho\_\{T\}=0.72$ in the uni-dimensional data above.

$\backslash rho\_\{T\}=0.72$ in the multidimensional data above.

The above data have $\backslash rho\_\{T\}=0.9692$, but are multidimensional.

The above data have $\backslash rho\_\{T\}=0.4$, but are uni-dimensional.

Uni-dimensionality is a prerequisite for $\backslash rho\_\{T\}$. One should check uni-dimensionality before calculating $\backslash rho\_\{T\}$ rather than calculating $\backslash rho\_\{T\}$ to check uni-dimensionality.

The term "internal consistency" is commonly used in the reliability literature, but its meaning is not clearly defined. The term is sometimes used to refer to a certain kind of reliability (e.g., internal consistency reliability), but it is unclear exactly which reliability coefficients are included here, in addition to $\backslash rho\_\{T\}$. Cronbach (1951) used the term in several senses without an explicit definition. Cho and Kim (2015) showed that $\backslash rho\_\{T\}$ is not an indicator of any of these.

Removing an item using "alpha if item deleted"{{Clarify|reason=What is "alpha if item deleted"?|date=August 2022}} may result in 'alpha inflation,' where sample-level reliability is reported to be higher than population-level reliability.{{cite journal|last1=Kopalle|first1=P. K.|last2=Lehmann|first2=D. R.|title=Alpha inflation? The impact of eliminating scale items on Cronbach's alpha|journal=Organizational Behavior and Human Decision Processes|volume=70|issue=3|pages=189–197|date=1997|doi=10.1006/obhd.1997.2702|doi-access=free}} It may also reduce population-level reliability.{{cite journal|first=T.|last=Raykov|title=Reliability if deleted, not 'alpha if deleted': Evaluation of scale reliability following component deletion|journal=The British Journal of Mathematical and Statistical Psychology|volume=60|issue=2|pages=201–216|date=2007|doi=10.1348/000711006X115954|pmid=17971267}} The elimination of less-reliable items should be based not only on a statistical basis but also on a theoretical and logical basis. It is also recommended that the whole sample be divided into two and cross-validated.

Nunnally's book{{cite book|first=J. C.|last=Nunnally|title=Psychometric theory|publisher=McGraw-Hill|date=1967|isbn=0-07-047465-6|oclc=926852171}}{{cite book|last1=Nunnally|first1=J. C.|last2=Bernstein|first2=I. H.|title=Psychometric theory|publisher=McGraw-Hill|edition=3rd|date=1994|isbn=0-07-047849-X|pages=|oclc=28221417}} is often mentioned as the primary source for determining the appropriate level of dependability coefficients. However, his proposals contradict his aims as he suggests that different criteria should be used depending on the goal or stage of the investigation. Regardless of the type of study, whether it is exploratory research, applied research, or scale development research, a criterion of 0.7 is universally employed.{{cite journal|last1=Lance|first1=C. E.|last2=Butts|first2=M. M.|last3=Michels|first3=L. C.|title=What did they really say?|journal=Organizational Research Methods|volume=9|issue=2|pages=202–220|date=2006|doi=10.1177/1094428105284919|s2cid=144195175}} He advocated 0.7 as a criterion for the early stages of a study, most studies published in the journal do not fall under that category. Rather than 0.7, Nunnally's applied research criterion of 0.8 is more suited for most empirical studies.

His recommendation level did not imply a cutoff point. If a criterion means a cutoff point, it is important whether or not it is met, but it is unimportant how much it is over or under. He did not mean that it should be strictly 0.8 when referring to the criteria of 0.8. If the reliability has a value near 0.8 (e.g., 0.78), it can be considered that his recommendation has been met.{{cite journal|first=E.|last=Cho|title=A comprehensive review of so-called Cronbach's alpha|journal=Journal of Product Research|volume=38|issue=1|pages=9–20|date=2020|doi=}}

Nunnally's idea was that there is a cost to increasing reliability, so there is no need to try to obtain maximum reliability in every situation.

Measurements with perfect reliability lack validity. For example, a person who takes the test with a reliability of one will either receive a perfect score or a zero score, because if they answer one item correctly or incorrectly, they will answer all other items in the same manner. The phenomenon where validity is sacrificed to increase reliability is known as the attenuation paradox.{{cite journal|first=J.|last=Loevinger|title=The attenuation paradox in test theory|journal=Psychological Bulletin|volume=51|issue=5|pages=493–504|date=1954|doi=10.1002/j.2333-8504.1954.tb00485.x|pmid=13204488}}{{cite journal|first=L.|last=Humphreys|title=The normal curve and the attenuation paradox in test theory|journal=Psychological Bulletin|volume=53|issue=6|pages=472–6|date=1956|doi=10.1037/h0041091|pmid=13370692}}

A high value of reliability can conflict with content validity. To achieve high content validity, each item should comprehensively represent the content to be measured. However, a strategy of repeatedly measuring essentially the same question in different ways is often used solely to increase reliability.{{cite journal|first=G. J.|last=Boyle|title=Does item homogeneity indicate internal consistency or item redundancy in psychometric scales?|journal=Personality and Individual Differences|volume=12|issue=3|pages=291–4|date=1991|doi=10.1016/0191-8869(91)90115-R}}{{cite journal|first=D. L.|last=Streiner|title=Starting at the beginning: An introduction to coefficient alpha and internal consistency|journal=Journal of Personality Assessment|volume=80|issue=1|pages=99–103|date=2003|doi=10.1207/S15327752JPA8001_18|pmid=12584072|s2cid=3679277}}

When the other conditions are equal, reliability increases as the number of items increases. However, the increase in the number of items hinders the efficiency of measurements.

Despite the costs associated with increasing reliability discussed above, a high level of reliability may be required. The following methods can be considered to increase reliability.

Before data collection:

• Eliminate the ambiguity of the measurement item.
• Do not measure what the respondents do not know.{{Cite journal|last1=Beatty|first1=P.|last2=Herrmann|first2=D.|last3=Puskar|first3=C.|last4=Kerwin|first4=J.|date=July 1998|title="Don't know" responses in surveys: is what I know what you want to know and do I want you to know it?|url=https://pubmed.ncbi.nlm.nih.gov/9829099/|journal=Memory (Hove, England)|volume=6|issue=4|pages=407–426|doi=10.1080/741942605|issn=0965-8211|pmid=9829099|access-date=2023-02-20|archive-date=2023-02-20|archive-url=https://web.archive.org/web/20230220140847/https://pubmed.ncbi.nlm.nih.gov/9829099/|url-status=live}}
• Increase the number of items. However, care should be taken not to excessively inhibit the efficiency of the measurement.
• Use a scale that is known to be highly reliable.Lee, H. (2017). Research Methodology (2nd ed.), Hakhyunsa.
• Conduct a pretest - discover in advance the problem of reliability.
• Exclude or modify items that are different in content or form from other items (e.g., reverse-scored items).

After data collection:

• Remove the problematic items using "alpha if item deleted". However, this deletion should be accompanied by a theoretical rationale.
• Use a more accurate reliability coefficient than $\backslash rho\_\{T\}$. For example, $\backslash rho\_\{C\}$ is 0.02 larger than $\backslash rho\_\{T\}$ on average.{{cite journal|last1=Peterson|first1=R. A.|last2=Kim|first2=Y.|title=On the relationship between coefficient alpha and composite reliability|journal=Journal of Applied Psychology|volume=98|issue=1|pages=194–8|date=2013|doi=10.1037/a0030767|pmid=23127213}}

$\backslash rho\_T$ is used in an overwhelming proportion. A study estimates that approximately 97% of studies use $\backslash rho\_T$ as a reliability coefficient.

However, simulation studies comparing the accuracy of several reliability coefficients have led to the common result that $\backslash rho\_T$ is an inaccurate reliability coefficient.Kamata, A., Turhan, A., & Darandari, E. (2003). Estimating reliability for multidimensional composite scale scores. Annual Meeting of American Educational Research Association, Chicago, April 2003, April, 1–27.{{cite journal|first=H. G.|last=Osburn|title=Coefficient alpha and related internal consistency reliability coefficients|journal=Psychological Methods|volume=5|issue=3|pages=343–355|date=2000|doi=10.1037/1082-989X.5.3.343|pmid=11004872}}Tang, W., & Cui, Y. (2012). A simulation study for comparing three lower bounds to reliability. Paper Presented on April 17, 2012 at the AERA Division D: Measurement and Research Methodology, Section 1: Educational Measurement, Psychometrics, and Assessment, 1–25.{{cite journal|last1=van der Ark|first1=L. A.|last2=van der Palm|first2=D. W.|last3=Sijtsma|first3=K.|title=A latent class approach to estimating test-score reliability|journal=Applied Psychological Measurement|volume=35|issue=5|pages=380–392|date=2011|doi=10.1177/0146621610392911|s2cid=41739445|url=https://research.tilburguniversity.edu/en/publications/becd6ed2-4796-4959-9f72-e0ae24faa8a6|access-date=2023-06-04|archive-date=2023-08-13|archive-url=https://web.archive.org/web/20230813121350/https://research.tilburguniversity.edu/en/publications/a-latent-class-approach-to-estimating-test-score-reliability|url-status=live}}

Methodological studies are critical of the use of $\backslash rho\_T$. Simplifying and classifying the conclusions of existing studies are as follows.

1. Conditional use: Use $\backslash rho\_T$ only when certain conditions are met.
2. Opposition to use: $\backslash rho\_T$ is inferior and should not be used.{{cite journal|last1=Dunn|first1=T. J.|last2=Baguley|first2=T.|last3=Brunsden|first3=V.|title=From alpha to omega: A practical solution to the pervasive problem of internal consistency estimation|journal=British Journal of Psychology|volume=105|issue=3|pages=399–412|date=2014|doi=10.1111/bjop.12046|pmid=24844115|url=http://irep.ntu.ac.uk/id/eprint/4853/1/215051_Dunn.pdf|access-date=2023-06-04|archive-date=2023-03-24|archive-url=https://web.archive.org/web/20230324013930/http://irep.ntu.ac.uk/id/eprint/4853/1/215051_Dunn.pdf|url-status=live}}{{cite journal|first=G. Y.|last=Peters|title=The alpha and the omega of scale reliability and validity comprehensive assessment of scale quality|journal=The European Health Psychologist|volume=1|issue=2|pages=56–69|date=2014|doi=}}Yang, Y., & Green, S. B.{{cite journal|title=Coefficient alpha: A reliability coefficient for the 21st century?|journal=Journal of Psychoeducational Assessment|volume=29|issue=4|pages=377–392|date=2011|doi=10.1177/0734282911406668|last1=Yanyun Yang|last2=Green|first2=Samuel B.|s2cid=119926199}}

Existing studies are practically unanimous in that they oppose the widespread practice of using $\backslash rho\_T$ unconditionally for all data. However, different opinions are given on which reliability coefficient should be used instead of $\backslash rho\_T$.

Different reliability coefficients ranked first in each simulation study comparing the accuracy of several reliability coefficients.

The majority opinion is to use structural equation modeling or SEM-based reliability coefficients as an alternative to $\backslash rho\_T$.

However, there is no consensus on which of the several SEM-based reliability coefficients (e.g., uni-dimensional or multidimensional models) is the best to use.

Some people suggest $\backslash omega\_H$ as an alternative, but $\backslash omega\_H$ shows information that is completely different from reliability. $\backslash omega\_H$ is a type of coefficient comparable to Reveille's $\backslash beta$.{{cite journal|first=W.|last=Revelle|title=Hierarchical cluster analysis and the internal structure of tests|journal=Multivariate Behavioral Research|volume=14|issue=1|pages=57–74|date=1979|doi=10.1207/s15327906mbr1401_4|pmid=26766619}} They do not substitute, but complement reliability.

Among SEM-based reliability coefficients, multidimensional reliability coefficients are rarely used, and the most commonly used is $\backslash rho\_C$, also known as composite or congeneric reliability.

In addition to single estimates of reliability, Item response theory based approaches can provide estimates of conditional reliability across the full distribution of scores.{{Cite journal |last=McNeish |first=Daniel |last2=Dumas |first2=Denis |date=2025-02-10 |title=Reliability representativeness: How well does coefficient alpha summarize reliability across the score distribution? |url=https://link.springer.com/10.3758/s13428-025-02611-8 |journal=Behavior Research Methods |language=en |volume=57 |issue=3 |doi=10.3758/s13428-025-02611-8 |issn=1554-3528}}

General-purpose statistical software such as SPSS and SAS include a function to calculate $\backslash rho\_T$. Users who don't know the formula $\backslash rho\_T$ have no problem in obtaining the estimates with just a few mouse clicks.

SEM software such as AMOS, LISREL, and MPLUS does not have a function to calculate SEM-based reliability coefficients. Users need to calculate the result by inputting it to the formula. To avoid this inconvenience and possible error, even studies reporting the use of SEM rely on $\backslash rho\_T$ instead of SEM-based reliability coefficients. There are a few alternatives to automatically calculate SEM-based reliability coefficients.

1. R (free): The psych package{{cite web|title=An overview of the psych package|last=Revelle|first=William|date=7 January 2017|url=http://personality-project.org/r/overview.pdf|access-date=23 April 2020|archive-date=27 August 2020|archive-url=https://web.archive.org/web/20200827020016/http://personality-project.org/r/overview.pdf|url-status=live}} calculates various reliability coefficients.
2. EQS (paid):{{cite web|url=http://www.mvsoft.com/eqs60.htm|title=Multivariate Software, Inc.|website=www.mvsoft.com|url-status=dead|archive-url=https://web.archive.org/web/20010521070751/http://www.mvsoft.com/eqs60.htm|archive-date=2001-05-21}} This SEM software has a function to calculate reliability coefficients.
3. RelCalc (free): Available with Microsoft Excel. $\backslash rho\_C$ can be obtained without the need for SEM software. Various multidimensional SEM reliability coefficients and various types of $\backslash omega\_H$ can be calculated based on the results of SEM software.

{{notelist|group=lower-roman}}

{{Reflist|30em}}

• [http://www.open.ac.uk/socialsciences/spsstutorial/files/tutorials/cronbachs-alpha.pdf Cronbach's alpha SPSS tutorial]
• The free web interface and R package [http://comparingcronbachalphas.org cocoon] allow us to statistically compare two or more dependent or independent Cronbach alpha coefficients.

{{DEFAULTSORT:Cronbach's Alpha}}

Category:Comparison of assessments

Category:Statistical reliability

Category:Psychometrics