Two new reliability indices, ordinal coefficient alpha and ordinal coefficient theta, are introduced. A simulation study was conducted in order to compare the new ordinal reliability estimates to each other and to coefficient alpha with Likert data. Results indicate that ordinal coefficients alpha and theta are consistently suitable estimates of the theoretical reliability, regardless of the magnitude of the theoretical reliability, the number of scale points, and the skewness of the scale point distributions. In contrast, coefficient alpha is in general a negatively biased estimate of reliability. The use of ordinal coefficients alpha and theta as alternatives to coefficient alpha when estimating the reliability based on Likert response items are recommended. The choice between the two ordinal coefficients depends on whether one is assuming a factor analysis model (ordinal coefficient alpha) or a principal components analysis model (ordinal coefficient theta).
Zumbo, Bruno D.; Gadermann, Anne M.; and Zeisser, Cornelia
"Ordinal Versions of Coefficients Alpha and Theta for Likert Rating Scales,"
Journal of Modern Applied Statistical Methods: Vol. 6
, Article 4.
Available at: http://digitalcommons.wayne.edu/jmasm/vol6/iss1/4