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On the Standard Length of a Test

Woodbury, Max A.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Office of Naval Research, Test Length, Test Reliability, Test Validity


A new concept, that of the standard length of a test, seems useful in simplifying formulas for reliability and validity coefficients for tests of altered length. The usefulness of the concept is a consequence of the fact that it is possible to define a unit of test information, this being, in fact, the amount of information in a test of standard length. The amount of information in a test is its length L in terms of its standard length as a unit. From this one computes the reliability r of the test by the formula r = L/(L + 1). For small amounts of information, the reliability and the information are approximately equal. It is readily seen that the standard length of a test is that length which would make its reliability one half. The length of a test in terms of its standard length as a unit required to produce a given reliability is given by L = r/(1 - r). Both formulas reduce to (1 + L) (1 - r) = 1.

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