Un experimento Monte Carlo sobre el efecto de la distancia entre las medias aritméticas de los parámetros de habilidad de dos grupos poblacionales en la confiabilidad - Zegarra López, Ángel Christopher (2020)
The aim of this study is to compare the reliability estimated through the application of a single test targeted on a whole population and two tests targeted on two specific groups that compose the population, in situations that vary according to the difference between the ability parameters means from each group. A Monte Carlo experiment was carried out considering the target of the assessment (targeting the population and targeting two specific groups) and the difference between ability parameters arithmetic means (0.5, 1.0, 1.5 and 2.0 standard deviations) as independent variables. Reliability was set as the dependent variable, estimated through the person separation reliability index. The data was generated according to the dichotomous Rasch model. A sample of 5000 subjects were simulated and their true ability parameters where sampled from a standard normal distribution. A test length of 40 items was set for every scenario and their difficulty parameters were simulated as an equidistant sequence from -2.5 to 2.5 standard deviations around the ability parameters arithmetic means. 1000 replicas were executed for each of the 8 experiment conditions established by the intersection between independent variables. Results were analyzed using a robust version of the factorial analysis of variance and multiple comparisons tests designed specifically for situations where the homogeneity of variance assumption is not met. Findings show that there is a statistically significant difference between the reliability of the measures estimated through a population targeted test and through group targeted tests, in every scenario of distance between ability parameters means. Nevertheless, the effect size shows that this difference is not relevant on practice.