Reliability of Composite Dichotomous Measurements

Abstrakt

In this paper we examine a more general definition of reliability, which is based on decomposition of variance in mixed effects model. Proposed definition covers the classical definition of reliability and it is, moreover, appropriate for dichotomous measurements, too. Newly, for the proposed definition assumptions are derived, under which the reliability of composite measurement can be predicted by reliability of single measurement (Spearman-Brown formula) and approximate validity of Spearman-Brown formula is shown for the Rasch model. Finally, as a modification of the classical estimate of reliability based on Cronbach's alpha, we examine its counterpart logistic alpha, which appears to be more appropriate for composite dichotomous measurements in some cases. The new estimate is used in binary data of computerized process of myocardial perfusion diagnosis from cardiac single proton emission computed tomography (SPECT).