It has been pointed out in the literature that misspecification of the level-1 error covariance structure in latent growth modeling (LGM) has detrimental impacts on the inferences about growth parameters. Since correct covariance structure is difficult to specify by theory, the identification needs to rely on a specification search, which,…

Informally testing the fit of a probability distribution model is educationally a desirable precursor to formal methods for senior secondary school students. Limited research on how to teach such an informal approach, lack of statistically sound criteria to enable drawing of conclusions, as well as New Zealand assessment requirements led to this…

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…

We examine the effect of an integrity pilot campaign on undergraduates' behavior. As with many costly small-scale experiments and pilot programs, our statistical inference has to rely on small sample size. To tackle this issue, we perform a Bayesian retrospective power analysis. In our setup, a lecturer intentionally makes mistakes that favors…

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…

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…

Randomized controlled trials (RCTs) admit unconfounded design-based inference--randomization largely justifies the assumptions underlying statistical effect estimates--but often have limited sample sizes. However, researchers may have access to big observational data on covariates and outcomes from RCT non-participants. For example, data from A/B…

The usual role of a discussant is to clarify and correct the paper being discussed, but in this case, the author, Howard Wainer, generally agrees with everything David Thissen says in his essay, "Bad Questions: An Essay Involving Item Response Theory." This essay expands on David Thissen's statement that there are typically two principal…

Grade 6 (modal age 11) students invented and revised models of the variability generated as each measured the perimeter of a table in their classroom. To construct models, students represented variability as a linear composite of true measure (signal) and multiple sources of random error. Students revised models by developing sampling…

The uncertainty arising from item parameter estimation is often not negligible and must be accounted for when calculating latent variable (LV) scores in item response theory (IRT). It is particularly so when the calibration sample size is limited and/or the calibration IRT model is complex. In the current work, we treat two-stage IRT scoring as a…

Coefficient omega and alpha are both measures of the composite reliability for a set of items. Unlike coefficient alpha, coefficient omega remains unbiased with congeneric items with uncorrelated errors. Despite this ability, coefficient omega is not as widely used and cited in the literature as coefficient alpha. Reasons for coefficient omega's…

The effect of guessing on the point estimate of coefficient alpha has been studied in the literature, but the impact of guessing and its interactions with other test characteristics on the interval estimators for coefficient alpha has not been fully investigated. This study examined the impact of guessing and its interactions with other test…

Null hypothesis significance testing (NHST) has been the subject of debate for decades and alternative approaches to data analysis have been proposed. This article addresses this debate from the perspective of scientific inquiry and inference. Inference is an inverse problem and application of statistical methods cannot reveal whether effects…

Cluster randomized trials involving participants nested within intact treatment and control groups are commonly performed in various educational, psychological, and biomedical studies. However, recruiting and retaining intact groups present various practical, financial, and logistical challenges to evaluators and often, cluster randomized trials…

Multisite trials, which are being used with increasing frequency in education and evaluation research, provide an exciting opportunity for learning about how the effects of interventions or programs are distributed across sites. In particular, these studies can produce rigorous estimates of a cross-site mean effect of program assignment…