Pearson's correlation is widely used to test for an association between two variables and also forms the basis of several multivariate statistical procedures including many latent variable models. Spearman's [rho] is a popular alternative. These procedures are compared with ranking the data and then applying the inverse normal transformation, or…

Data pooling is a powerful strategy in empirical research. However, combining multiple datasets often results in a large amount of missing data, as variables that are not present in some datasets effectively contain missing values for all participants in those datasets. Furthermore, data pooling typically leads to a mix of continuous and…

Large-scale assessments are rich sources of data that can inform a diverse range of research questions related to educational policy and practice. For this reason, datasets from large-scale assessments are available to enable secondary analysts to replicate and extend published reports of assessment results. These datasets include multiple imputed…

Causal mediation analysis has gained increasing attention in recent years. This article guides empirical researchers through the concepts and challenges of causal mediation analysis. I first clarify the difference between traditional and causal mediation analysis and highlight the importance of adjusting for the treatment-by-mediator interaction…

Individual participant data (IPD) meta-analyses of randomised trials are considered a reliable way to assess participant-level treatment effect modifiers but may not make the best use of the available data. Traditionally, effect modifiers are explored one covariate at a time, which gives rise to the possibility that evidence of treatment-covariate…

The debate about the characteristics and advantages of quantitative and qualitative methods is decades old. In their seminal monograph, "A Tale of Two Cultures" (2012, ATTC), Gary Goertz and James Mahoney argue that methods and research design practices for causal inference can be distinguished as two cultures that systematically differ…

This article presents two ways of quantifying confounding using logistic response models for binary outcomes. Drawing on the distinction between marginal and conditional odds ratios in statistics, we define two corresponding measures of confounding (marginal and conditional) that can be recovered from a simple standardization approach. We…

In any meta-analysis, it is critically important to report the dispersion in effects as well as the mean effect. If an intervention has a moderate clinical impact "on average" we also need to know if the impact is moderate for all relevant populations, or if it varies from trivial in some to major in others. Or indeed, if the…

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…

As a measure of heterogeneity in meta-analysis, the coefficient of variation (CV) has been recently considered, providing researchers with a complement to the very popular I[superscript 2] measure. While I[superscript 2] measures the proportion of total variance that is due to variance of the random effects, the CV is the ratio of the standard…

The nonequivalent groups with anchor test (NEAT) design is widely used in test equating. Under this design, two groups of examinees are administered different test forms with each test form containing a subset of common items. Because test takers from different groups are assigned only one test form, missing score data emerge by design rendering…

The variance-stabilizing Freeman-Tukey double arcsine transform was originally proposed for inference on single proportions. Subsequently, its use has been suggested in the context of meta-analysis of proportions. While some erratic behavior has been observed previously, here we point out and illustrate general issues of monotonicity and…

Test takers wishing to gain an unfair advantage often share answers with other test takers, either sharing all answers (a full key) or some (a partial key). Detecting key sharing during a tight testing window requires an efficient, easily interpretable, and rich form of analysis that is descriptive and inferential. We introduce a detection method…

The import or force of the result of a statistical test has long been portrayed as consistent with deductive reasoning. The simplest form of deductive argument has a first premise with conditional form, such as p[right arrow]q, which means that "if p is true, then q must be true." Given the first premise, one can either affirm or deny…

The number of meta-analyses of aggregate data has dramatically increased due to the facility of obtaining data from publications and the development of free, easy-to-use, and specialised statistical software. Even when meta-analyses include the same studies, their results may vary owing to different methodological choices. Assessment of the…