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Reliability of Composite Dichotomous Measurements

Author(s): Patrícia Martinková, Karel Zvára

Reliability of measurement is a measure of its reproducibility under replicate conditions. The classical concept of reliability assumes that measurement Y is composed out of true value T and error term ε, two independent random variables, Y = T + ε . Reliability of measurement is defined as the ratio of the variance of the true scores to the variance of the observed scores. However, this concept is not applicable in models for dichotomous measurements which do not consider error terms and are instead defined via conditional probabilities. In this paper we examine a more general definition of reliability proposed in [1], 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 introduced in [2], which appears to be more appropriate for composite dichotomous measurements in some cases. Simulations show that the new estimate does not tend to underestimate reliability as often as the Cronbach’s alpha does. The new estimate is used in binary data of computerized process of myocardial perfusion diagnosis from cardiac single proton emission computed tomography (SPECT).