Background: Meta-analysis refers to the statistical methods employed to combine results of several empirical studies in a topic of interest (Hedges & Olkin, 1985). Meta-analysis is often included in literature review studies to quantitatively analyze data from a collection of studies (Valentine et al., 2010). The statistical power of a…

A linear model is often used to find the effect of a binary treatment D on a noncontinuous outcome Y with covariates X. Particularly, a binary Y gives the popular "linear probability model (LPM)," but the linear model is untenable if X contains a continuous regressor. This raises the question: what kind of treatment effect does the…

The reliability of a test score is usually underestimated and the deflation may be profound, 0.40 - 0.60 units of reliability or 46 - 71%. Eight root sources of the deflation are discussed and quantified by a simulation with 1,440 real-world datasets: (1) errors in the measurement modelling, (2) inefficiency in the estimator of reliability within…

For estimation of heterogeneity variance T[superscript 2] in meta-analysis of log-odds-ratio, we derive new mean- and median-unbiased point estimators and new interval estimators based on a generalized Q statistic, Q[subscript F], in which the weights depend on only the studies' effective sample sizes. We compare them with familiar estimators…

This study explores the usefulness of covariates on equating test scores from nonequivalent test groups. The covariates are captured by an estimated propensity score, which is used as a proxy for latent ability to balance the test groups. The objective is to assess the sensitivity of the equated scores to various misspecifications in the…

An interval estimation procedure is discussed that can be used to evaluate the probability of a particular response for a binary or binary scored item at a pre-specified point along an underlying latent continuum. The item is assumed to: (a) be part of a unidimensional multi-component measuring instrument that may contain also polytomous items,…

Most of the social science research is based on the implied assumption that measurement error is the same across key socio-demographic groups and all differences in key statistics of interest are real. Nevertheless, there is evidence that this is not the case. In this paper, the authors tackle this important topic by investigating if data quality…

This study evaluates various scoring methods including number-correct scoring, IRT theta scoring, and hybrid scoring in terms of scale-score stability over time. A simulation study was conducted to examine the relative performance of five scoring methods in terms of preserving the first two moments of scale scores for a population in a chain of…

The Karlson-Holm-Breen (KHB) method has rapidly become popular as a way of separating the impact of confounding from rescaling when comparing conditional and unconditional parameter estimates in nonlinear probability models such as the logit and probit. In this note, we show that the same estimates can be obtained in a somewhat different way to…

In a randomized controlled trial (RCT), some subjects assigned to the treatment condition may not fully comply. Often there is interest in the effect of the treatment within the "principal stratum" of subjects who would comply if assigned to treatment. However, it is unknown which control subjects would have complied if treated and which…

The Poisson distribution describes the probability of a certain number of events occurring in an interval of time when the occurrence of the individual events is independent of one another and the events occur with a fixed mean rate. Probably the best-known example of the Poisson distribution in the physics curriculum is the temporal distribution…

This study develops a theoretical model for the costs of an exam as a function of its duration. Two kind of costs are distinguished: (1) the costs of measurement errors and (2) the costs of the measurement. Both costs are expressed in time of the student. Based on a classical test theory model, enriched with assumptions on the context, the costs…

Educational assessment tests are designed to measure the same psychological constructs over extended periods. This feature is important considering that test results are often used for admittance to university programs. To ensure fair assessments, especially for those whose results weigh heavily in selection decisions, it is necessary to collect…

We consider two-level models where a continuous response R and continuous covariates C are assumed missing at random. Inferences based on maximum likelihood or Bayes are routinely made by estimating their joint normal distribution from observed data R[subscript obs] and C[subscript obs]. However, if the model for R given C includes random…

This note extends the results in the 2016 article by Raykov, Marcoulides, and Li to the case of correlated errors in a set of observed measures subjected to principal component analysis. It is shown that when at least two measures are fallible, the probability is zero for any principal component--and in particular for the first principal…