In statistics and research, internal consistency is typically a measure based on the correlations between different items on the same test (or the same subscale on a larger test). It measures whether several items that propose to measure the same general construct produce similar scores. For example, if a respondent expressed agreement with the statements "I like to ride bicycles" and "I've enjoyed riding bicycles in the past", and disagreement with the statement "I hate bicycles", this would be indicative of good internal consistency of the test.
Internal consistency is usually measured with Cronbach's alpha, a statistic calculated from the pairwise correlations between items. Internal consistency ranges between zero and one. A commonly-accepted rule of thumb is that an α of 0.6-0.7 indicates acceptable reliability, and 0.8 or higher indicates good reliability. High reliabilities (0.95 or higher) are not necessarily desirable, as this indicates that the items may be entirely redundant. The goal in designing a reliable instrument is for scores on similar items to be related (internally consistent), but for each to contribute some unique information as well.
An alternative way of thinking about internal consistency, however, is that it is the extent to which all of the items of a test measure the same latent variable. The advantage of this perspective over the notion of a high average correlation among the items of a test - the perspective underlying Cronbach's alpha - is that the average item correlation is affected by skewness (in the distribution of item correlations) just as any other average is. Thus, whereas the modal item correlation is zero when the items of a test measure several unrelated latent variables, the average item correlation in such cases will be greater than zero. Thus, whereas the ideal of measurement is for all items of a test to measure the same latent variable, alpha has been demonstrated many times to attain quite high values even when the set of items measures several unrelated latent variables (e.g., Cortina, 1993; Cronbach, 1951; Green, Lissitz & Mulaik, 1977; Revelle, 1979; Schmitt, 1996; Zinbarg, Yovel, Revelle & McDonald, 2006). Coefficient omega_hierarchical is the most appropriate index of the extent to which all of the items in a test measure the same latent variable (McDonald, 1999; Zinbarg, Revelle, Yovel & Li, 2005).
References
- Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297-334.
- Cortina. J. M. ( 1993). What is coefficient alpha? An examination of theory and applications. Journal of Applied Psychology, 78, 98- 104.
- Green, S. B., Lissitz, R.W., & Mulaik, S. A. (1977). Limitations of coefficient alpha as an index of test unidimensionality. Educational and Psychological Measurement, 37, 827–838.
- Revelle, W. (1979). Hierarchical cluster analysis and the internal structure of tests. Multivariate Behavioral Research, 14, 57-74.
- Schmitt, N. (1996). Uses and abuses of coefficient alpha. Psychological Assessment, 8, 350-353.
- Zinbarg, R., Revelle, W., Yovel, I. & Li, W. (2005). Cronbach’s , Revelle’s , and McDonald’s : Their relations with each other and two alternative conceptualizations of reliability. Psychometrika, 70, 123-133.
- Zinbarg, R., Yovel, I., Revelle, W. & McDonald, R. (2006). Estimating generalizability to a universe of indicators that all have an attribute in common: A comparison of estimators for . Applied Psychological Measurement, 30, 121 – 144.
See also
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