Because error variance alternatively can be considered to be the sum of systematic variance associated with unknown variables and randomness, a tripartite assumption is proposed that total variance in the dependent variable can be partitioned into three variance components. These are variance in the dependent variable that is explained by the…

The precision of estimates of treatment effects in multilevel experiments depends on the sample sizes chosen at each level. It is often desirable to choose sample sizes at each level to obtain the smallest variance for a fixed total cost, that is, to obtain optimal sample allocation. This article extends previous results on optimal allocation to…

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…

Research designs involving cluster randomization are becoming increasingly important in educational and behavioral research. Many of these designs involve two levels of clustering or nesting (students within classes and classes within schools). Researchers would like to compute effect size indexes based on the standardized mean difference to…

This article provides a way to determine adequate sample size for the confidence interval of covariate-adjusted mean difference in randomized experiments. The standard error of adjusted mean difference depends on covariate variance and balance, which are two unknown quantities at the stage of planning sample size. If covariate observations are…

Previous work on statistical power has discussed mainly single-level designs or 2-level balanced designs with random effects. Although balanced experiments are common, in practice balance cannot always be achieved. Work on class size is one example of unbalanced designs. This study provides methods for power analysis in 2-level unbalanced designs…

This study compared nonverbal numerical processing in 6-year-olds with that in nonhuman animals using a numerical bisection task. In the study, 16 children were trained on a delayed match-to-sample paradigm to match exemplars of two anchor numerosities. Children were then required to indicate whether a sample intermediate to the anchor values was…

This chapter examines the core analytic elements of randomized experiments for social research. Its goal is to provide a compact discussion for faculty members, graduate students, and applied researchers of the design and analysis of randomized experiments for measuring the impacts of social or educational interventions. Design issues considered…