Standard errors and confidence intervals for correlations corrected for indirect range restriction: A simulation study comparing analytic and bootstrap methods.

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.

Demonstrating the validity of three general scores of PET in predicting higher education achievement in Israel / Demostrando la validez de tres puntuaciones generales del PET para predecir el rendimiento en la educación superior en Israel

BACKGROUND: The Psychometric Entrance Test (PET), used for admission to higher education in Israel together with the Matriculation (Bagrut), had in the past one general (total) score in which the weights for its domains: Verbal, Quantitative and English, were 2:2:1, respectively. In 2011, two additional total scores were introduced, with different weights for the Verbal and the Quantitative domains. This study compares the predictive validity of the three general scores of PET, and demonstrates validity in terms of utility. METHOD: Sample: 100,863 freshmen students of all Israeli universities over the classes of 2005-2009. Regression weights and correlations of the predictors with FYGPA were computed. Simulations based on these results supplied the utility estimates. RESULTS: On average, PET is slightly more predictive than the Bagrut; using them both yields a better tool than either of them alone. Assigning differential weights to the components in the respective schools further improves the validity. CONCLUSION: The introduction of the new general scores of PET is validated by gathering and analyzing evidence based on relations of test scores to other variables. The utility of using the test can be demonstrated in ways different from correlations

ANTECEDENTES: el Psychometric Entrance Test (PET), utilizado para la admisión a la educación superior en Israel junto con la Matriculation (Bagrut), tuvo en el pasado una puntuación general en la que los pesos para sus dominios: Verbal, Cuantitativo e Inglés eran 2:2:1, respectivamente. En 2011 se introdujeron dos puntuaciones totales adicionales, con pesos diferentes para los dominios Verbal y Cuantitativo. Este estudio compara la validez predictiva de las tres puntuaciones generales del PET y demuestra la validez en términos de utilidad. MÉTODO: muestra: 100.863 estudiantes de primer año de todas las universidades israelíes en los cursos de 2005 a 2009. Se calcularon los coeficientes de regresión y las correlaciones de los predictores con FYGPA. Las simulaciones basadas en estos resultados aportaron la utilidad de las estimaciones. RESULTADOS: en promedio, PET es ligeramente más predictivo que el «Bagrut». Asignar pesos diferentes a los componentes en las escuelas respectivas mejora más la validez. CONCLUSIONES: la introducción de las nuevas puntuaciones generales del PET es validada mediante la obtención y análisis de evidencia basada en las relaciones de las puntuaciones del test con otras variables. Puede demostrarse la utilidad del uso del test en formas diferentes de las correlacio

Demonstrating the validity of three general scores of PET in predicting higher education achievement in Israel.

BACKGROUND: The Psychometric Entrance Test (PET), used for admission to higher education in Israel together with the Matriculation (Bagrut), had in the past one general (total) score in which the weights for its domains: Verbal, Quantitative and English, were 2:2:1, respectively. In 2011, two additional total scores were introduced, with different weights for the Verbal and the Quantitative domains. This study compares the predictive validity of the three general scores of PET, and demonstrates validity in terms of utility. SAMPLE: 100,863 freshmen students of all Israeli universities over the classes of 2005-2009. Regression weights and correlations of the predictors with FYGPA were computed. Simulations based on these results supplied the utility estimates. RESULTS: On average, PET is slightly more predictive than the Bagrut; using them both yields a better tool than either of them alone. Assigning differential weights to the components in the respective schools further improves the validity. CONCLUSION: The introduction of the new general scores of PET is validated by gathering and analyzing evidence based on relations of test scores to other variables. The utility of using the test can be demonstrated in ways different from correlations.