Ordinal Versions of Coefficients Alpha and Theta for Likert Rating Scales
By Bruno D. Zumbo, A. Gadermann, C. Zeisser. 2007
977 citations recorded by the source corpus.
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).
Subfields: Computer Networks and Communications, Management Science and Operations Research, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/4c48d7955fa234684b569f04bcc3c9dc992b4c9b
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Citations in the corpus
- Using Likert Type Data in Social Science Research: Confusion, Issues and Challenges (2016, methodology): “The concept of ordinal alpha was introduced by Zumbo, Gadermann, and Zeisser (2007), and which was shown to estimate reliability more accurately than Cronbach’s alpha for ordinal response scales.”
- HTMT2-an improved criterion for assessing discriminant validity in structural equation modeling (2021, methodology): “Similar has been suggested for the calculation of Cronbach’s alpha (Zumbo et al., 2007).”
- Effect of Variability on Cronbach Alpha Reliability in Research Practice (2020, background): “Reliability is also described as an essential fountain of evidence when establishing the validity of the inferences one predicate on scores from measures and tests [30].”
- Development of the International Ocean Literacy Survey: measuring knowledge across the world. (2019, methodology): “To account for the non-continuous underlying data we used the polychoric matrix for the internal consistency estimation and computed the ordinal reliability (Zumbo, Gadermann, and Zeisser 2007).”
- Self-determination and STEM education: Effects of autonomy, motivation, and self-regulated learning on high school math achievement (2015, methodology): “…account that participants' ratings were on Likert-type scales so their responses are ordered in systematic and categorical ways (Flora & Curran, 2004), we followed Zumbo, Gadermann, and Zeisser (2007)'s recommendations to treat the data as categorical measures and computed ordinal McDonald's Omega.”
- Investigating Validity Evidence of the Satisfaction with Life Scale Adapted for Children (2010, methodology): “We also computed ordinal alpha, an estimate of internal consistency that was specifically developed for items with Likert-type response formats, taking into account the ordinal nature of the data (Zumbo et al. 2007).”
- Estimating Ordinal Reliability for Likert-Type and Ordinal Item Response Data: A Conceptual, Empirical, and Practical Guide. (2012, methodology): “Review of findings from a simulation study Zumbo et al. (2007) present findings from a simulation study that compared ordinal alpha and Cronbach’s alpha for all combinations of the following conditions: (i) The theoretical reliability of a test was simulated so that it was .4, .6, .8, or .9.”