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...reliability, Gilmer-Feldt coefficient Gilmer & L. S. Feldi, 1983).

If circumstances force a researcher to estimate reliability by the internal consistency approach, it is sometimes impossible to divide the instrument into parts of equal length. For example, suppose a test is composed of scores summed over four trials of a particular task. The trials become the "parts" of the total score, and trial scores may become more variable or less variable from the first to the last trial. If a panel of three or more judges constitutes the source of measurement data, the variances of the ratings of individual judges may vary significantly. The heterogeneity of the variances strongly suggests that the judges function as shorter or longer parts of the overall measurement of each subject.

The classical theory of measurement represents the observed score, [X.sub.ij], of subject I on part j of a test as

[X.sub.ij] = [T.sub.i] + [E.sub.ij']

where [T.sub.i] is the unchanging true score of subject i and [E.sub.ij] is the error of measurement of subject i on part j. Cronbach's alpha assumes that the variance of [T.sub.i] (over subjects) does not change from one test part to another, whereas the variance of [E.su.ij] may vary from part to part. Such measures are called tau equivalent by Lord and Novick (1968). If the variance of both [T.sub.i] and [E.sub.ij] vary from part to part (the true score would then be symbolized [T.sub.ij]), the parts are termed congeneric by Joreskog (1971). Angoff (1953) and Feldt (1975) described congeneric tests or part-tests as differing in effective or functional length. For example, in an essay test of three items, Essay 1 may contribute 20% to the total test true score, Essay 2 may contribute 30%, and Essay 3 may contribute 50%. These would constitute...

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