
Many scales in social measurement constructed to measure a single variable are nevertheless composed of subscales of items which measure different aspects of the variable. Although the presence of subscales captures the complexity of a variable, and thereby increases the validity of the scale, technically, unidimensionality is compromised. As a result, the presence of subscales has received substantial attention, and in particular, it has led to the formulation of a bifactor structure in which all subscales summarize a common variable and in addition, the items within each subscale also summarize an aspect unique to that subscale. This paper shows that, with some common simplifying assumptions about a bifactor structure, the ratio of two calculations of coefficient α , one at the level of the items, the other at the level of the subscales, can be used to obtain (a) the proportion of true common variance, (b) the proportion of the true unique variance, (c) the proportion of the true common variance relative to the sum of the true common and unique variances, and (d) the summary correlation among subscales immediately corrected for attenuation due to error. The paper suggests that because the calculations are relatively simple, they can be used to provide a more comprehensive summary of the properties of a scale with subscales than is possible with a single statistic such as some form of reliability coefficient. This paper provides an example in which a scholastic aptitude test consisting of 100 items is composed of four subscales. A small simulation study shows that when the assumptions are satisfied, the estimates of the variances are stable.
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