The Kuder-Richardson formula (20) is rewritten to be identical with the simplest formula, (21), except for the addition of a term involving the standard deviation, σ p , of the item p 's. If σ p can be estimated, a rapid and superior estimate of test reliability is possible in contrast to the simpler formula (21) used when the number of items and mean and standard deviation of test scores are known.
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Ledyard R Tucker (1949) studied this question.