RESUMEN
A frequent topic of psychological research is the estimation of the correlation between two variables from a sample that underwent a selection process based on a third variable. Due to indirect range restriction, the sample correlation is a biased estimator of the population correlation, and a correction formula is used. In the past, bootstrap standard error and confidence intervals for the corrected correlations were examined with normal data. The present study proposes a large-sample estimate (an analytic method) for the standard error, and a corresponding confidence interval for the corrected correlation. Monte Carlo simulation studies involving both normal and non-normal data were conducted to examine the empirical performance of the bootstrap and analytic methods. Results indicated that with both normal and non-normal data, the bootstrap standard error and confidence interval were generally accurate across simulation conditions (restricted sample size, selection ratio, and population correlations) and outperformed estimates of the analytic method. However, with certain combinations of distribution type and model conditions, the analytic method has an advantage, offering reasonable estimates of the standard error and confidence interval without resorting to the bootstrap procedure's computer-intensive approach. We provide SAS code for the simulation studies.
Asunto(s)
Simulación por Computador , Intervalos de Confianza , Recolección de Datos/métodos , Modelos Estadísticos , Psicometría/métodos , Método de Montecarlo , Probabilidad , Lenguajes de Programación , Reproducibilidad de los Resultados , Tamaño de la MuestraRESUMEN
The present study explored the construct validity of the Psychometric Entrance Test (PET) for higher education in Israel, as represented by the factorial structure of the scholastic aptitudes it measures, and focused on whether the test presents a single measure of overall ability or a measure of the fields of knowledge that are being tested. In Study 1, we used Exploratory Factor Analysis to generate hypotheses regarding the factorial structure of the test. In Study 2, Confirmatory Factor Analysis was carried out to compare competing models that were constructed based on theoretical considerations and the results of Study 1. The findings indicated that a two-layered hierarchical model, encompassing both a General Ability factor and three scholastic domain-specific factors (Verbal Reasoning, Quantitative Reasoning, and English), showed the best fit. Within the framework of the CFA, several statistical procedures were applied to assess reliability (indicator and complexity) and validity (convergent and divergent.).