Mediation analysis in Single Case Experimental Designs (SCEDs) evaluates intervention mechanisms for individuals. Despite recent methodological developments, no clear guidelines exist for maximizing power to detect the indirect effect in SCEDs. This study compares frequentist and Bayesian methods, determining (1) minimum required sample size to…

Background: Power analysis and sample size planning are key components in designing cluster randomized trials (CRTs), a common study design to test treatment effect by randomizing clusters or groups of individuals. Sample size determination in two-level CRTs requires knowledge of more than one design parameter, such as the effect size and the…

Cluster sampling is common in survey practice, and the corresponding inference has been predominantly design-based. We develop a Bayesian framework for cluster sampling and account for the design effect in the outcome modeling. We consider a two-stage cluster sampling design where the clusters are first selected with probability proportional to…

Single-case design is a repeated-measures research approach for the study of the effect of an intervention, and its importance is increasingly being recognized in education and psychology. We propose a Bayesian approach for estimating intervention effects in SCD. A Bayesian inference does not rely on large sample theories and thus is particularly…

Looking times (LTs) are frequently measured in empirical research on infant cognition. We analyzed the statistical distribution of LTs across participants to develop recommendations for their treatment in infancy research. Our analyses focused on a common within-subject experimental design, in which longer looking to novel or unexpected stimuli is…

In education research, small samples are common because of financial limitations, logistical challenges, or exploratory studies. With small samples, statistical principles on which researchers rely do not hold, leading to trust issues with model estimates and possible replication issues when scaling up. Researchers are generally aware of such…

An analysis of repeated measures designs is proposed that uses an empirical Bayes estimator of the covariance matrix. The proposed analysis behaves like a univariate analysis when sample size is small or sphericity nearly satisfied, but behaves like multivariate analysis when sample size is large or sphericity is strongly violated. (SLD)

Presents two statistical topics and examples of their use in natural resource monitoring. The first topic deals with use of correlated observations in calculations of variance estimates for a regional mean, required sample size determination, and confidence intervals. The second topic concerns the use of Bayesian techniques in hypothesis testing.…

Researchers have been limited in their ability to examine multiple constructs simultaneously due to the constraints imposed by traditional statistical methods. The most notable limitations include the need for a relatively large sample size while restricting the variables to a relatively small number. The application of a newly discovered…