alpha: Obtain coefficient alpha

View source: R/alpha.R

alphaR Documentation

Obtain coefficient alpha


Alpha, also referred to as Cronbach's alpha or tau-equivalent reliability, is the most commonly used reliability coefficient.


alpha(x, print = TRUE)



a dataframe or a matrix (unidimensional)


If TRUE, the result is printed to the screen.


History: Kuder and Richardson (1937) first developed this formula, but they did name it. At the time, it was referred to as Kuder-Richardson Formula 20. Cronbach (1951) argued that this name was strange and insisted on calling it coefficient alpha, which is now widely used.

Interpretations: Alpha can be derived with an ANOVA approach to reliability (Hoyt 1941).Alpha is lambda3, one of the six lower bound of reliability (Guttman 1945). Alpha is the average of lambda4 values obtained over all possible split-halves (Cronbach 1951). Alpha equals reliability if the x meets the condition of being essentially tau-equivalent (Novick & Lewis, 1967). Alpha is mu0, the first in Ten Berge and Socan's (1978) series of reliability coefficients.

Accuracy: Alpha is found to be inferior in several studies examining the accuracy of the reliability coefficients (Cho and Kim 2015). Alpha can produce negative reliability estimates and is sensitive to the violation of the assumption of essential tau-equivalence (Cho in press).


coefficient alpha reliability estimate


Cho, E. (in press). Neither Cronbach's alpha nor McDonald's omega: A comment on Sijtsma and Pfadt. Psychometrika.

Cho, E., & Kim, S. (2015). Cronbach's coefficient alpha: Well known but poorly understood. Organizational Research Methods, 18(2), 207-230.

Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297-334

Guttman, L. (1945). A basis for analyzing test-retest reliability. Psychometrika, 10(4), 255-282.

Hoyt, C. (1941). Test reliability estimated by analysis of variance. Psychometrika, 6(3), 153-160.

Kuder, G. F., & Richardson, M. W. (1937). The theory of the estimation of test reliability. Psychometrika, 2(3), 151-160.

Novick, M. R., & Lewis, C. (1967). Coefficient alpha and the reliability of composite measurements. Psychometrika, 32(1), 1-13.

Ten Berge, J. M. F., & Zegers, F. E. (1978). A series of lower bounds to the reliability of a test. Psychometrika, 43(4), 575-579.

See Also

[mu0()] alpha equals mu0

[psych::alpha()] for a related function of the package psych

[Lamdbda4::lambda3()] for a related function of the package Lambda4

[MBESS::ci.reliability()] for a related function of the package MBESS



eunscho/reliacoef documentation built on Jan. 30, 2023, 12:16 a.m.