While the use of inferential statistics is a nearly universal practice in the social sciences, there are instances where its application is unnecessary and potentially misleading. This is true for a portion of research using administrative data in educational research in the United States. Surveying all research articles using administrative data…

The analysis of variance (ANOVA) F test is a commonly used method to test the mean equality among two or more populations. A critical assumption of ANOVA is homogeneity of variance (HOV), that is, the compared groups have equal variances. Although it is encouraged to test HOV as part of the regular ANOVA procedure, the efficacy of the initial HOV…

Factor score regression (FSR) is a popular alternative for structural equation modeling. Naively applying FSR induces bias for the estimators of the regression coefficients. Croon proposed a method to correct for this bias. Next to estimating effects without bias, interest often lies in inference of regression coefficients or in the fit of the…

In this dissertation I argue that truth-conditional semantics for vague predicates, combined with a Bayesian account of statistical inference incorporating knowledge of truth-conditions of utterances, generates false predictions regarding negations and metalinguistic inference. I thus propose a fundamentally probabilistic semantics for vagueness…

The most widely used formal approach to culture, the cultural consensus theory (CCT) of Romney, Weller, and Batchelder, originally relied on a priori definitions of cultural groups to map their unity and diversity. Retaining key features of classical CCT, we provide techniques to identify two or more cultural subgroups in a sample, whether those…

Big data analytics are prevalent in fields like business, engineering, public health, and the physical sciences, but social scientists are slower than their peers in other fields in adopting this new methodology. One major reason for this is that traditional statistical procedures are typically not suitable for the analysis of large and complex…

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…

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…

There has been increasing interest in exploring heterogeneous treatment effects using machine learning (ML) methods such as causal forests, Bayesian additive regression trees, and targeted maximum likelihood estimation. However, there is little work on applying these methods to estimate treatment effects in latent classes defined by…

Researchers in many disciplines work with ranking data. This data type is unique in that it is often deterministic in nature (the ranks of items "k"-1 determine the rank of item "k"), and the difference in a pair of rank scores separated by "k" units is equivalent regardless of the actual values of the two ranks in…

We present an instructional approach to teaching causal inference using Bayesian networks and "do"-Calculus, which requires less prerequisite knowledge of statistics than existing approaches and can be consistently implemented in beginner to advanced levels courses. Moreover, this approach aims to address the central question in causal…

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.…

According to Wollack and Schoenig (2018), benefitting from item preknowledge is one of the three broad types of test fraud that occur in educational assessments. We use tools from constrained statistical inference to suggest a new statistic that is based on item scores and response times and can be used to detect the examinees who may have…

Many existing methods of statistical inference and analysis rely heavily on the assumption that the data are normally distributed. However, the normality assumption is not fulfilled when dealing with data which does not contain negative values or are otherwise skewed--a common occurrence in diverse disciplines such as finance, economics, political…

Typically, in education and psychology research, the investigator collects data and subsequently performs descriptive and inferential statistics. For example, a researcher might compute group means and use the null hypothesis significance testing procedure to draw conclusions about the populations from which the groups were drawn. We propose an…