In multisite trials, learning about treatment effect variation across sites is critical for understanding where and for whom a program works. Unadjusted comparisons, however, capture "compositional" differences in the distributions of unit-level features as well as "contextual" differences in site-level features, including…

The present simulation study indicates that a method where the regression effect of a predictor (X) on an outcome at follow-up (Y1) is calculated while adjusting for the outcome at baseline (Y0) can give spurious findings, especially when there is a strong correlation between X and Y0 and when the test-retest correlation between Y0 and Y1 is…

We derive formulas for the differential item functioning (DIF) measures that two routinely used DIF statistics are designed to estimate. The DIF measures that match on observed scores are compared to DIF measures based on an unobserved ability (theta or true score) for items that are described by either the one-parameter logistic (1PL) or…

We proposed an extended form of the Govindarajulu and Barnett margin of error (MOE) equation and used it with an analysis of variance experimental design to examine the effects of aggregating student evaluations of teaching (SET) ratings on the MOE statistic. The interpretative validity of SET ratings can be questioned when the number of students…

Humans and other animals are able to make rough estimations of quantities using what has been termed the "approximate number system" (ANS). Much evidence suggests that sensitivity to numerosity correlates with symbolic math capacity, leading to the suggestion that the ANS may serve as a start-up tool to develop symbolic math. Many…

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…

Kelley's Discrimination Index (DI) is a simple and robust, classical non-parametric short-cut to estimate the item discrimination power (IDP) in the practical educational settings. Unlike item-total correlation, DI can reach the ultimate values of +1 and -1, and it is stable against the outliers. Because of the computational easiness, DI is…

Structural equation modeling is an ideal data analytical tool for testing complex relationships among many analytical variables. It can simultaneously test multiple mediating and moderating relationships, estimate latent variables on the basis of related measures, and address practical issues such as nonnormality and missing data. To test the…

This study investigated the extent to which class-specific parameter estimates are biased by the within-class normality assumption in nonnormal growth mixture modeling (GMM). Monte Carlo simulations for nonnormal GMM were conducted to analyze and compare two strategies for obtaining unbiased parameter estimates: relaxing the within-class normality…

Many empirical economists say that the teaching of econometrics is unbalanced, and students are not well-prepared for the serious problems they will encounter with real data. Here, the author considers the problem of noisy data, which is present in most econometric studies, but receives far too little attention. Most econometric studies are done…

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.

This simulation study examines the characteristics of the Explanatory Item Response Model (EIRM) when estimating treatment effects when compared to classical test theory (CTT) sum and mean scores and item response theory (IRT)-based theta scores. Results show that the EIRM and IRT theta scores provide generally equivalent bias and false positive…

Reliable measurements are key to social science research. Multiple measures of reliability of the total score have been developed, including coefficient alpha, coefficient omega, the greatest lower bound reliability, and others. Among these, the coefficient alpha has been most widely used, and it is reported in nearly every study involving the…

Large amounts of missing data could distort item parameter estimation and lead to biased ability estimates in educational assessments. Therefore, missing responses should be handled properly before estimating any parameters. In this study, two Monte Carlo simulation studies were conducted to compare the performance of four methods in handling…

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…