Internal consistency or item homogeneity is often used for estimating intra-scale reliability, in terms of the item variances and covariances derived from a single occasion of measurement. While it is desirable that items in a psychometric scale measure something in common (i.e. exhibit unidimensionality), Hattie (1985) has indicated that there is still no satisfactory index. As Hattie (pp. 157-158) pointed out, a unidimensional scale (having an underlying latent trait), is not necessarily reliable, internally consistent or homogeneous. Hattie concluded that the frequent use of Cronbach's alpha coefficient as a measure of unidimensionality is not justified. Hattie further stated that,
'alpha can be high even if there is no general factor, since (1) it is influenced by the number of items and parallel repetitions of items, (2) it increases as the number of factors pertaining to each item increases, and (3) it decreases moderately as the item communalities increase.'
The subsequent assertion by Ray (1988) that internal consistency of a psychometric scale should be maximised, represents a further restatement of classical itemetric theory, and ignores the previous work of Hattie (1985), and many others, as outlined below. There is an optimal range of internal consistency/item homogeneity, if significant item redundancy is to be avoided (Boyle, 1983, 1985, 1986).