Optimal design of multisite randomized trials leverages sampling costs to optimize sampling ratios and ultimately identify more efficient and powerful designs. Past implementations of the optimal design framework have assumed that costs of sampling units are equal across treatment conditions. In this study, we developed a more flexible optimal…

Trend scoring constructed response items (i.e. rescoring Time A responses at Time B) gives rise to two-way data that follow a product multinomial distribution rather than the multinomial distribution that is usually assumed. Recent work has shown that the difference in sampling model can have profound negative effects on statistics usually used to…

The debate on determining sample size in qualitative research is confounded by four fundamental methodological issues: the exclusive focus on theme analysis; the diverse and imprecise use of 'qualitative'; a reliance on only two logics of inquiry, "induction" and "deduction," and the occasional confusion of…

Recent years have seen increasing interest in incorporating resampling methods into introductory statistics courses and the high school mathematics curriculum. While the use of permutation tests for data from experiments is a step forward, the use of simple bootstrap methods for sampling situations is more problematical. This article demonstrates…

Formal empirical assessments of replication have recently become more prominent in several areas of science, including psychology. These assessments have used different statistical approaches to determine if a finding has been replicated. The purpose of this article is to provide several alternative conceptual frameworks that lead to different…

There has been considerable recent interest in methods of determining sample size for qualitative research a priori, rather than through an adaptive approach such as saturation. Extending previous literature in this area, we identify four distinct approaches to determining sample size in this way: rules of thumb, conceptual models, numerical…

In this article, a numerical method integrated with statistical data simulation technique is introduced to solve a nonlinear system of ordinary differential equations with multiple random variable coefficients. The utilization of Monte Carlo simulation with central divided difference formula of finite difference (FD) method is repeated n times to…

Events such as curriculum changes or practice effects can lead to item parameter drift (IPD) in computer adaptive testing (CAT). The current investigation introduced a point- and weight-adjusted D[superscript 2] method for IPD detection for use in a CAT environment when items are suspected of drifting across test administrations. Type I error and…

Identifying mediators in variable chains as part of a causal mediation analysis can shed light on issues of causation, assessment, and intervention. However, coefficients and effect sizes in a causal mediation analysis are nearly always small. This can lead those less familiar with the approach to reject the results of causal mediation analysis.…

This article discusses the sample size requirements for the interaction, row, and column effects, respectively, by forming a linear contrast for a 2×2 factorial design for fixed-effects heterogeneous analysis of variance. The proposed method uses the Welch t test and its corresponding degrees of freedom to calculate the final sample size in a…

Structured means analysis is a very useful approach for testing hypotheses about population means on latent constructs. In such models, a z test is most commonly used for testing the statistical significance of the relevant parameter estimates or of the differences between parameter estimates, where a z value is computed based on the asymptotic…

Big qualitative data (Big Qual), or research involving large qualitative data sets, has introduced many newly evolving conventions that have begun to change the fundamental nature of some qualitative research. In this methodological essay, we first distinguish big data from big qual. We define big qual as data sets containing either primary or…

This rejoinder keeps the original focus on statistical computing pertaining to the correlation of student achievement between mathematics and science from the Trend in Mathematics and Science Study (TIMSS). Albeit the availability of student performance data in TIMSS and the emphasis of the inter-subject connection in the Next Generation Science…

Recently, studies have adopted fixed effects modeling to identify the returns to college. This method has the advantage over ordinary least squares estimates in that unobservable, individual-level characteristics that may bias the estimated returns are differenced out. But the method requires extensive longitudinal data and involves complex…

Experience-sampling methods (ESM) enable us to learn about individuals' lives in context by measuring participants' feelings, thoughts, actions, context, and/or activities as they go about their daily lives. By capturing experience, affect, and action "in the moment" and with repeated measures, ESM approaches allow researchers…