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…

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…

BASIE is a framework for interpreting impact estimates from evaluations. It is an alternative to null hypothesis significance testing. This guide walks researchers through the key steps of applying BASIE, including selecting prior evidence, reporting impact estimates, interpreting impact estimates, and conducting sensitivity analyses. The guide…

Modeling the distribution of site level effects is an important problem, but it is also an incredibly difficult one. Current methods rely on distributional assumptions in multilevel models for estimation. There it is hoped that the partial pooling of site level estimates with overall estimates, designed to take into account individual variation as…

This paper introduces a dataset and associated analysis of the scores of National Football League (NFL) games over the 2012, 2013, and first five weeks of the 2014 season. In the face of current media attention to "lopsided" scores in Thursday night games in the early part of the 2014 season, t-test results indicate no statistically…

Person-fit assessment may help the researcher to obtain additional information regarding the answering behavior of persons. Although several researchers examined person fit, there is a lack of research on person-fit assessment for mixed-format tests. In this article, the lz statistic and the ?2 statistic, both of which have been used for tests…

This thesis consists of two parts. In Chapter 2, we focus on the spatial scan statistics with overdispersion and Chapter 3 is devoted to the randomized permutation test for identifying local patterns of spatial association. The spatial scan statistic has been widely used in spatial disease surveillance and spatial cluster detection. To apply it, a…

In the modern world information has become the new power. An increasing amount of efforts are being made to gather data, resources being allocated, time being invested and tools being developed. Data collection is no longer a myth; however, it remains a great challenge to create value out of the enormous data that is being collected. Data modeling…

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This seventh installment of "Explorations in Statistics" explores regression, a technique that estimates the nature of the relationship between two things for which we may only surmise a mechanistic or predictive…

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…

This study serves as a teaching aid for teachers of introductory statistics. The aim of this study was limited to determining various sample sizes when estimating population proportion. Tables on sample sizes were generated using a C[superscript ++] program, which depends on population size, degree of precision or error level, and confidence…

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…

M. J. Kolen, B. A. Hanson, and R. L. Brennan (1992) presented a procedure for assessing the conditional standard error of measurement (CSEM) of scale scores using a strong true-score model. They also investigated the ways of using nonlinear transformation from number-correct raw score to scale score to equalize the conditional standard error along…