Cronbach's a is the most widely used index of the reliability of a scale. However, its use and interpretation can be subject to a number of errors. This article discusses the historical development of a from other indexes of internal consistency (split-half reliability and Kuder-Richardson 20) and discusses four myths associated with a: (a) that it is a fixed property of the scale, (b) that it measures only the internal consistency of the scale, (c) that higher values are always preferred over lower ones, and (d) that it is restricted to the range of 0 to 1. It provides some recommendations for acceptable values of a in different situations.
One of the central tenets of classical test theory is that scales should have a high degree of internal consistency, as evidenced by Cronbach's a, the mean interitem correlation, and a strong first component. However, there are many instances in which this rule does not apply. Following Bollen and Lennox (1991), I differentiate between questionnaires such as anxiety or depression inventories, which are composed of items that are manifestations of an underlying hypothetical construct (i.e., where the items are called effect indicators) and those such as Scale 6 of the Minnesota Multiphasic Personality Inventory (Hathaway & McKinley, 1943) and ones used to tap quality of life or activities of daily living in which the items or subscales themselves define the construct (these items are called causal indicators). Questionnaires of the first sort, which are referred to as scales in this article, meet the criteria of classical test theory, whereas the second type, which are called indexes here, do not. I discuss the implications of this difference for how items are selected, the relationship among the items, and the statistics that should and should not be used in establishing the reliability of the scale or index.
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