Lord’s approximation to the standard error of
measurement of a test uses only n, the number of
items. Millman’s is based on n and p̄, the mean
difficulty. Saupe has used Lord’s approximation to
derive an approximation to the reliability. Through
an empirical demonstration involving 200 classroom
tests, all three approximations are shown to be
biased. The Lord and Millman approximations
overestimate s[subscript x]√(1-KR20), and thus Saupe’s underestimates
r[subscript x, subscript x prime] for these tests. The unweighted mean
of the tests’ mean item difficulties was .68, supporting
Lord’s original warning that his approximation
be used cautiously with tests that are either
very difficult or very easy. Still, the approximations
did correlate very highly with their criteria, supporting
their continued limited use.
Kleinke, David J..
Systematic Errors in Approximations to the Standard Error of Measurement and Reliability.
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