Given sample data, how do you calculate the value of a parameter? While this question is impossible to answer, it is frequently encountered in statistics classes when students are introduced to the distinction between a sample and a population (or between a statistic and a parameter). It is not uncommon for teachers of statistics to also confuse…

The Gini index is probably the most commonly used indicator to measure inequality. For continuous distributions, the Gini index can be computed using several equivalent formulations. However, this is not the case with discrete distributions, where controversy remains regarding the expression to be used to estimate the Gini index. We attempt to…

This article introduces an innovative sampling scheme, the median sampling (MS), utilizing individual observations over time to efficiently estimate the mean of a process characterized by a symmetric (non-uniform) probability distribution. The mean estimator based on MS is not only unbiased but also boasts enhanced precision compared to its simple…

Latent class analysis (LCA) is a widely used technique for detecting unobserved population heterogeneity in cross-sectional data. Despite its popularity, the performance of LCA is not well understood. In this study, we evaluate the performance of LCA with binary data by examining classification accuracy, parameter estimation accuracy, and coverage…

Accelerated longitudinal designs (ALDs) provide an opportunity to capture long developmental periods in a shorter time framework using a relatively small number of assessments. Prior literature has investigated whether univariate developmental processes can be characterized with data obtained from ALDs. However, many important questions in…

When analyzing large-scale assessments (LSAs) that use complex sampling designs, it is important to account for probability sampling using weights. However, the use of these weights in multilevel models has been widely debated, particularly regarding their application at different levels of the model. Yet, no consensus has been reached on the best…