The accuracy of certain internal consistency estimators have been questioned in recent years. The present study tests the accuracy of six reliability estimators (Cronbach's alpha, omega, omega hierarchical, Revelle's omega, and greatest lower bound) in 140 simulated conditions of unidimensional continuous data with uncorrelated errors with varying sample sizes, number of items, population reliabilities, and factor loadings. Estimators that have been proposed to replace alpha were compared with the performance of alpha as well as to each other. Estimates of reliability were shown to be affected by sample size, degree of violation of tau equivalence, population reliability, and number of items in a scale. Under the conditions simulated here, estimates quantified by alpha and omega yielded the most accurate reflection of population reliability values. A follow-up regression comparing alpha and omega revealed alpha to be more sensitive to degree of violation of tau equivalence, whereas omega was affected greater by sample size and number of items, especially when population reliability was low.

Recent achievement research suggests that executive function (EF), a set of regulatory processes that control both thought and action necessary for goal-directed behavior, is related to typical and atypical reading performance. This project examines the relation of EF, as measured by its components, Inhibition, Updating Working Memory, and Shifting, with a hybrid model of reading disability (RD). Our sample included 420 children who participated in a broader intervention project when they were in KG-third grade (age M = 6.63 years, SD = 1.04 years, range = 4.79-10.40 years). At the time their EF was assessed, using a parent-report Behavior Rating Inventory of Executive Function (BRIEF), they had a mean age of 13.21 years (SD = 1.54 years; range = 10.47-16.63 years). The hybrid model of RD was operationalized as a composite consisting of four symptoms, and set so that any child could have any one, any two, any three, any four, or none of the symptoms included in the hybrid model. The four symptoms include low word reading achievement, unexpected low word reading achievement, poorer reading comprehension compared to listening comprehension, and dual-discrepancy response-to-intervention, requiring both low achievement and low growth in word reading. The results of our multilevel ordinal logistic regression analyses showed a significant relation between all three components of EF (Inhibition, Updating Working Memory, and Shifting) and the hybrid model of RD, and that the strength of EF's predictive power for RD classification was the highest when RD was modeled as having at least one or more symptoms. Importantly, the chances of being classified as having RD increased as EF performance worsened and decreased as EF performance improved. The question of whether any one EF component would emerge as a superior predictor was also examined and results showed that Inhibition, Updating Working Memory, and Shifting were equally valuable as predictors of the hybrid model of RD. In total, all EF components were significant and equally effective predictors of RD when RD was operationalized using the hybrid model.