Principal stratification is a widely used framework for addressing post-randomization complications. After using principal stratification to define causal effects of interest, researchers are increasingly turning to finite mixture models to estimate these quantities. Unfortunately, standard estimators of mixture parameters, like the MLE, are known…

Growth curve models are widely used in social and behavioral sciences. However, typical growth curve models often assume that the errors are normally distributed although non-normal data may be even more common than normal data. In order to avoid possible statistical inference problems in blindly assuming normality, a general Bayesian framework is…

In this article, we have suggested a new modified mixed randomized response (RR) model and studied its properties. It is shown that the proposed mixed RR model is always more efficient than the Kim and Warde's mixed RR model. The proposed mixed RR model has also been extended to stratified sampling. Numerical illustrations and graphical…

The quantal hypothesis is central to the modern understanding of how a neurotransmitter is released from synapses. This hypothesis expresses that a neurotransmitter is packaged together in quanta that are released probabilistically. The experiments that led to the quantal hypothesis are often related in introductory neuroscience textbooks, but…

One econometric rule of thumb is that greater dispersion in observations of the independent variable improves estimates of regression coefficients and therefore produces better results, i.e., lower standard errors of the estimates. Nevertheless, students often seem to mistrust precisely the observations that contribute the most to this greater…

What follows is a description of a theoretical model designed to calculate the playing frequencies of the musical pitches produced by a trombone. The model is based on quantitative treatments that demonstrate the effects of the flaring bell and cup-shaped mouthpiece sections on these frequencies and can be used to calculate frequencies that…

The authors argue that insufficient attention has been given to foundational concepts in special education. Two classes of foundational concepts are discussed: human constructions and logico-mathematical facts. Four human constructions are examined: (1) making teaching most important, (2) discriminating among ideas, (3) choosing conceptual models,…

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…

Although molecular clock theory is a commonly discussed facet of evolutionary biology, undergraduates are rarely presented with the underlying information of how this theory is examined relative to empirical data. Here a simple contextual exercise is presented that not only provides insight into molecular clocks, but is also a useful exercise for…

Emphasis on problem solving in mathematics has gained considerable attention in recent years. While statistics teaching has always been problem driven, the same cannot be said for the teaching of probability where discrete examples involving coins and playing cards are often the norm. This article describes an application of simple probability…

Describes available variance component tests and presents three new score tests. One test uses the asymptotic normal distribution of the test statistic as a reference distribution; the others use a Satterthwaite approximation for the null distribution of the test statistic. Evaluates the performance of these tests through Monte Carlo simulation.…

Four empirical laws of bibliometrics--anomalous number, Lotka's, Zipf's, and Bradford's--together with Laplace's "law of succession" and de Solla Price's cumulative advantage distribution are shown to be almost identical. A simple model shows that the frequency forms conform with inverse square law over appropriate interval. (Fifteen…

RESGEN is a computer program designed to generate simulated latent trait distributions and then dichotomous or polytomous item responses based on item response models. The latent trait distributions can be univariate or multivariate normal, log-normal, uniform, or gamma. The item response models utilized in this program may have characteristics…

Illustrates that the Poisson-lognormal model provides good fits to a diverse set of distributions commonly studied in bibliometrics and scientometrics. Topics discussed include applications to the empirical data sets related to the laws of Lotka, Bradford, and Zipf; causal processes that could generate lognormal distributions; and implications for…

Proposes and explains a modification of the mixed Poisson model for library circulations which takes into account the periods when a book is out on loan and therefore unavailable for borrowing. Highlights include frequency of circulation distributions; negative binomial distribution; and examples of the model at two universities. (Contains 34…