The multisite trial, widely used in mental health research and education, enables experimenters to assess the average impact of a treatment across sites, the variance of treatment impact across sites, and the moderating effect of site characteristics on treatment efficacy. Key design decisions include the sample size per site and the number of sites. To consider power implications, this article proposes a standardized hierarchical linear model and uses rules of thumb similar to those proposed by J. Cohen (1988) for small, medium, and large effect sizes and for small, medium, and large treatment-by-site variance. Optimal allocation of resources within and between sites as a function of variance components and costs at each level are also considered. The approach generalizes to quasiexperiments with a similar structure. These ideas are illustrated with newly developed software.

Consider a study in which 2 groups are followed over time to assess group differences in the average rate of change, rate of acceleration, or higher degree polynomial effect. In designing such a study, one must decide on the duration of the study, frequency of observation, and number of participants. The authors consider how these choices affect statistical power and show that power depends on a standardized effect size, the sample size, and a person-specific reliability coefficient. This reliability, in turn, depends on study duration and frequency. These relations enable researchers to weigh alternative designs with respect to feasibility and power. The authors illustrate the approach using data from published studies of antisocial thinking during adolescence and vocabulary growth during infancy.

This article considers optimal sample allocation between the treatment and control condition in multilevel designs when the costs per sampling unit vary due to treatment assignment. Optimal unequal allocation may reduce the cost from that of a balanced design without sacrificing any power. The optimum sample allocation ratio depends only on the cost ratio between the treatment and control regardless of whether the randomization of sampling units occurs at levels 1, 2, or 3. Power functions for the exact tests for the main effect of treatment are derived for prototypical multilevel designs with unequal sample sizes in the treatment and control condition.

Over the past few months, the spread of the current COVID-19 epidemic has caused tremendous damage worldwide, and unstable many countries economically. Detailed scientific analysis of this event is currently underway to come. However, it is very important to have the right facts and figures to take all possible actions that are needed to avoid COVID-19. In the practice and application of big data sciences, it is always of interest to provide the best description of the data under consideration. The recent studies have shown the potential of statistical distributions in modeling data in applied sciences, especially in medical science. In this article, we continue to carry this area of research, and introduce a new statistical model called the arcsine modified Weibull distribution. The proposed model is introduced using the modified Weibull distribution with the arcsine-X approach which is based on the trigonometric strategy. The maximum likelihood estimators of the parameters of the new model are obtained and the performance these estimators are assessed by conducting a Monte Carlo simulation study. Finally, the effectiveness and utility of the arcsine modified Weibull distribution are demonstrated by modeling COVID-19 patients data. The data set represents the survival times of fifty-three patients taken from a hospital in China. The practical application shows that the proposed model out-classed the competitive models and can be chosen as a good candidate distribution for modeling COVID-19, and other related data sets.