Sensitivity analysis, a statistical method crucial for validating inferences across disciplines, quantifies the conditions that could alter conclusions (Razavi et al., 2021). One line of work is rooted in linear models and foregrounds the sensitivity of inferences to the strength of omitted variables (Cinelli & Hazlett, 2019; Frank, 2000). A…

Beginning with debates about the effects of smoking on lung cancer, sensitivity analyses characterizing the hypothetical unobserved conditions that can alter statistical inferences have had profound impacts on public policy. One of the most ascendant techniques for sensitivity analysis is Oster's (2019) coefficient of proportionality, which…

The purpose of this dissertation is to develop principles and strategies for and identify limitations of multisite cluster randomized trials in the context of partially and fully nested designs. In the first study, I develop principles of estimation, sampling variability, and inference for studies that leverage multisite designs within the context…

Cohen's kappa coefficient was originally proposed for two raters only, and it later extended to an arbitrarily large number of raters to become what is known as Fleiss' generalized kappa. Fleiss' generalized kappa and its large-sample variance are still widely used by researchers and were implemented in several software packages, including, among…

There exists a variety of interval estimators for the overall treatment effect in a random-effects meta-analysis. A recent literature review summarizing existing methods suggested that in most situations, the Hartung-Knapp/Sidik-Jonkman (HKSJ) method was preferable. However, a quantitative comparison of those methods in a common simulation study…

Conventional estimators for indirect effects using a difference in coefficients and product of coefficients produce the same results for continuous outcomes. However, for binary outcomes, the difference in coefficient estimator systematically underestimates the indirect effects because of a scaling problem. One solution is to standardize…

When designing a study for causal mediation analysis, it is crucial to conduct a power analysis to determine the sample size required to detect the causal mediation effects with sufficient power. However, the development of power analysis methods for causal mediation analysis has lagged far behind. To fill the knowledge gap, I proposed a…

Given two 2-level factors of interest, a 2[superscript 2] split-plot design (a) takes each of the 2 [superscript 2] = 4 possible factorial combinations as a treatment, (b) identifies one factor as `whole-plot,' (c) divides the experimental units into blocks, and (d) assigns the treatments in such away that all units within the same block receive…

The analysis of covariance (ANCOVA) is a useful statistical procedure that incorporates covariate features into the adjustment of treatment effects. The consequences of omitted prognostic covariates on the statistical inferences of ANCOVA are well documented in the literature. However, the corresponding influence on sample-size calculations for…

The natural experiment proposed in this article extracts three stories from boxes of "100 paper clips". The activity requires students to apply three lessons from inferential statistics, starting with a hypothesis test and including confidence intervals as well as tolerance intervals.

Multidimensional Item Response Theory (MIRT) is widely used in assessment and evaluation of educational and psychological tests. It models the individual response patterns by specifying functional relationship between individuals' multiple latent traits and their responses to test items. One major challenge in parameter estimation in MIRT is that…

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…

Widespread availability of rich educational databases facilitates the use of conditioning strategies to estimate causal effects with nonexperimental data. With dozens, hundreds, or more potential predictors, variable selection can be useful for practical reasons related to communicating results and for statistical reasons related to improving the…

Network meta-analysis (NMA) is gaining popularity for comparing multiple treatments in a single analysis. Generalized linear mixed models provide a unifying framework for NMA, allow us to analyze datasets with dichotomous, continuous or count endpoints, and take into account multiarm trials, potential heterogeneity between trials and network…

Analysts of discrete data often face the challenge of managing the tendency of inflation on certain values. When treated improperly, such phenomenon may lead to biased estimates and incorrect inferences. This study extends the existing literature on single-value inflated models and develops a general framework to handle variables with more than…