Intervalos de confianza para las puntuaciones verdaderas: Explicitación de sus supuestos

the classical test theory was developed by starting with the linear model to which certain assumptions are added to allow the deduction of its fundamental properties. since one of the measurement objectives is to estimate the individuals' true scores, the different inferential techniques for the true scores based on the observed ones, result of interest. depending on the technique chosen, it will be necessary to add assumptions about the distribution of the classical linear model components. in the psychometric literature, two types of intervals are usually seen: one type is based on the measurement error e; and the other, on the error of estimation obtained from the prediction of true scores are predicted from a regression equation on the observed ones. both types of intervals are set down on two models, each one with its own assumptions, and the models should be differentiated. in general, the authors do not state the assumptions clearly or, at times, they do not show how the assumptions are involved in the confidence interval construction. for example, lord and novick (1968) mentioned the need of variance homogeneity, without explaining how that assumption is used in the process. the assumption of variance homogeneity when the confidence intervals are built based on the error of estimation is not needed as it is shown later on. the greatest difficulties arise when the regression equation of true scores on observed scores is used. in that case, the assumptions for the usual regression model with fixed independent variables are used, while in the linear classical model, both scores vary jointly. the authors refer to the linear regression assumptions only in a slightly way, for example, about the homocedasticity, as if they took the true score confidence interval computation as a simple particular application of the regression theory on general statistics. nevertheless, in this context the regression model is something different. in the general regression model, all