New York City's elite public specialized high schools have a long history of offering a rigorous college preparatory education to the City's most academically talented students. Though immensely popular and highly selective, their policy of admitting students on the basis of a single entrance exam has been heavily criticized. Many argue, for…

Doubly bounded continuous data are common in the social and behavioral sciences. Examples include judged probabilities, confidence ratings, derived proportions such as percent time on task, and bounded scale scores. Dependent variables of this kind are often difficult to analyze using normal theory models because their distributions may be quite…

In this study, we compared 12 statistical strategies proposed for selecting loglinear models for smoothing univariate test score distributions and for enhancing the stability of equipercentile equating functions. The major focus was on evaluating the effects of the selection strategies on equating function accuracy. Selection strategies' influence…

Null distributions of permutation tests for two-sample, paired, and block designs are simulated using the R statistical programming language. For each design and type of data, permutation tests are compared with standard normal-theory and nonparametric tests. These examples (often using real data) provide for classroom discussion use of metrics…

On the 2009 AP[c] Statistics Exam, students were asked to create a statistic to measure skewness in a distribution. This paper explores several of the most popular student responses and evaluates which statistic performs best when sampling from various skewed populations. (Contains 8 figures, 3 tables, and 4 footnotes.)

This article points out an unexpected but common misconception by students dealing with the exponential distribution.

A typical question in multiple regression analysis is to determine if a set of predictors gives the same degree of predictor power in two different populations. Olkin and Finn (1995) proposed two asymptotic-based methods for testing the equality of two population squared multiple correlations, [rho][superscript 2][subscript 1] and…

The purpose of these modules is to provide an introduction to the world of probability and statistics to accelerated mathematics students at the high school level. The materials are centered on the fictional town of Happy Shores, a coastal community which is at risk for hurricanes. Actuaries at an insurance company figure out the risks and…

This article uses simulation to compare two test equating methods under the common-item nonequivalent groups design: the frequency estimation method and the chained equipercentile method. An item response theory model is used to define the true equating criterion, simulate group differences, and generate response data. Three linear equating…

This article presents an analysis of interactions in the usage, structure, cognition, coadaptation of conversational partners, and emergence of linguistic constructions. It focuses on second language development of English verb-argument constructions (VACs: VL, verb locative; VOL, verb object locative; VOO, ditransitive) with particular reference…

Missing data are nearly always a problem in research, and missing values represent a serious threat to the validity of inferences drawn from findings. Increasingly, social science researchers are turning to multiple imputation to handle missing data. Multiple imputation, in which missing values are replaced by values repeatedly drawn from…

Developed a sandwich-type covariance matrix to evaluate parameters and provide a rescaled statistic to evaluate a hypothesized general multilevel model. A simulation study with a two-level factor model implies that the rescaled statistic is preferable. (SLD)

Restricted the range of nonnormal distributions by eliminating scores above a designated cutoff value or eliminating scores above or below the mean by a certain distance. Results of a simulation study show that range restriction sometimes increased the correlation between variables having outlier prone distributions. Discusses practical…

Examined the sampling distributions of equating coefficients produced by the characteristic curve method for tests using graded and nominal response scoring using simulated data. For both models and across all three equating situations, the sampling distributions were generally bell-shaped and peaked, and occasionally had a small degree of…

Conducted simulations to explore methods for comparing bivariate distributions corresponding to two independent groups, all of which are based on Tukey's "depth," a generalization of the notion of ranks to multivariate data. Discusses steps needed to control Type I error. (SLD)