Agent-based models (ABMs) often rely on psychometric constructs such as 'opinions', 'stubbornness', 'happiness', etc. The measurement process for these constructs is quite different from the one used in physics as there is no standardized unit of measurement for opinion or happiness. Consequently, measurements are usually affected by 'psychometric…

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…

Data transformations have been promoted as a popular and easy-to-implement remedy to address the assumption of normally distributed errors (in the population) in linear regression. However, the application of data transformations introduces non-ignorable complexities which should be fully appreciated before their implementation. This paper adds to…

Recently Watkins, Bargagliotti, and Franklin (2014) discovered that simulations of the sampling distribution of the mean can mislead students into concluding that the mean of the sampling distribution of the mean depends on sample size. This potential error arises from the fact that the mean of a simulated sampling distribution will tend to be…

We propose a new limited-information goodness of fit test statistic C[subscript 2] for ordinal IRT models. The construction of the new statistic lies formally between the M[subscript 2] statistic of Maydeu-Olivares and Joe (2006), which utilizes first and second order marginal probabilities, and the M*[subscript 2] statistic of Cai and Hansen…

In 2011-12, graduate students received a total of $51.7 billion in federal loans and grants, institutional grants, employer support, and financial aid from other sources. In 2007-08, this figure was $36.7 billion (College Board 2008, 2012). The data presented in these Web Tables were collected through five administrations of the National…

The aim of the current study is to validate the invariance of major profile patterns derived from multidimensional scaling (MDS) by bootstrapping. Profile Analysis via Multidimensional Scaling (PAMS) was employed to obtain profiles and bootstrapping was used to construct the sampling distributions of the profile coordinates and the empirical…

A general delta method is described for computing the standard error (SE) of a chain of linear equations. The general delta method derives the SEs directly from the moments of the score distributions obtained in the equating chain. Computer simulations demonstrate the method. (SLD)

Some results on how the Alexander-Govern heteroscedastic analysis of variance (ANOVA) procedure (R. Alexander and D. Govern, 1994) performs under nonnormality are presented. This method can provide poor control of Type I errors in some cases, and in some situations power decreases as differences among the means get large. (SLD)

A probability distribution was developed for the Andrews-Pregibon (AP) statistic. The statistic, developed by D. F. Andrews and D. Pregibon (1978), identifies multivariate outliers. It is a ratio of the determinant of the data matrix with an observation deleted to the determinant of the entire data matrix. Although the AP statistic has been used…

Assuming errors of measurement are distributed binomially, this article reviews various procedures for constructing an interval for an individual's true number-correct score; presents two general interval estimation procedures for an individual's true scale score (i.e., normal approximation and endpoints conversion methods); compares various…

Sampling error refers to variability that is unique to the sample. If the sample is the entire population, then there is no sampling error. A related point is that sampling error is a function of sample size, as a hypothetical example illustrates. As the sample statistics more and more closely approximate the population parameters, the sampling…

Glass's estimator of effect size, the sample mean difference divided by the sample standard deviation, is studied in the context of an explicit statistical model. The exact distribution of Glass's estimator is obtained and the estimator is shown to have a small sample bias. Alternatives are proposed and discussed. (Author/JKS)

Large-sample standard errors of linear equating for the counterbalanced design are derived using the general delta method. Computer simulations found that standard errors derived without the normality assumption were more accurate than those derived with the normality assumption in a large sample with moderately skewed score distributions. (SLD)

The reliability coefficient is predicted from the test information function (TIF) or two modified TIF formulas and a specific trait distribution. Examples illustrate the variability of the reliability coefficient across different trait distributions, and results are compared with empirical reliability coefficients. (SLD)