Coefficient β As Extension of KR-21 Reliability for Summed and Scaled Scores for Polytomously-scored Tests

ABSTRACT KR-21 reliability and its extension (coefficient α) gives the reliability estimate of test scores under the assumption of tau-equivalent forms. KR-21 reliability gives the reliability estimate for summed scores for dichotomous items when items are randomly sampled from an infinite pool of similar items (randomly parallel forms). The article extends KR-21 to coefficient to estimate reliability of summed scores for test with any item scoring pattern under the same assumption of KR-21. Also, the article presents coefficient to estimate this reliability for nonlinearly scaled scores for any type of items. The article shows that coefficient is slightly different from the classical index of reliability. Results show that coefficient is not equal to the classical index of reliability for summed scores and scaled scores. Moreover, results using real data on psychological instruments reveal that different score scales yield different coefficient reliability estimates that are less than coefficient Gα by a function related to form-to-form differences in averages.