extended · article · 2019

A Comparison of Classical and Modern Measures of Internal Consistency

Pasquale Anselmi; Daiana Colledani; Egidio Robusto; John M. Linacre

Three measures of internal consistency - Kuder-Richardson Formula 20 (KR20), Cronbach's alpha (α), and person separation reliability (R) - are considered. KR20 and α are common measures in classical test theory, whereas R is developed in modern test theory and, more precisely, in Rasch measurement. These three measures specify the observed variance as the sum of true variance and error variance. However, they differ for the way in which these quantities are obtained. KR20 uses the error variance of an "average" respondent from the sample, which overestimates the error variance of respondents with high or low scores. Conversely, R uses the actual average error variance of the sample. KR20 and α use respondents' test scores in calculating the observed variance. This is potentially misleading because test scores are not linear representations of the underlying variable, whereas calculation ...