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Formulas for parallel-form reliability coefficients are derived from two improved definitions of parallelism. One definition, based on randomly parallel test forms, leads to a new and useful derivation for the KR formula-21 coefficient. The other, based on matched test forms, leads to a formula for the least upper bound of the test reliability. A numerical example is given, showing how a standard error of measurement for each separate examinee is readily computed, and how the test reliability may be computed by averaging these standard errors.
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Frederic M. Lord (1955) studied this question.
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