Sample coefficient alpha is commonly reported for psychological measurement scales. However, how to characterize the distribution of sample coefficient alpha with the Likert-type scales typically used in social and behavioral science research is not clear. Using the Hopkins Symptom Checklist, the authors compare three characterizations of the distribution of the sample coefficient alpha: the existing normal-theory-based distribution, a newly proposed distribution based on fourth-order moments, and the bootstrap empirical distribution. Their study indicates that the normal-theory-based distribution has a systematic bias in describing the behavior of the sample coefficient alpha. The distribution based on fourth-order moments is better than the normal-theory-based one but is still not good enough with finite samples. The bootstrap automatically takes the sampling distribution and sample size into account; thus it is recommended for characterizing the behavior of sample coefficient alpha with Likert-type scales.
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