This article outlines a readily applicable procedure for point and interval estimation of the population discrepancy between reliability and the popular Cronbach's coefficient alpha for unidimensional multi-component measuring instruments with uncorrelated errors, which are widely used in behavioral and social research. The method is developed…

Reference intervals, or reference ranges, aid medical decision-making by containing a pre-specified proportion (e.g., 95%) of the measurements in a representative healthy population. We recently proposed three approaches for estimating a reference interval from a meta-analysis based on a random effects model: a frequentist approach, a Bayesian…

A video of darkening scenery during the 15 min prior to totality of the 21 August 2017 total solar eclipse is presented and discussed. The luminances of the scenes at 1 min intervals are obtained by averaging pixel data of stills from the video. The experimental results are compared to the theoretical model of uniform radiance from the exposed…

We present two simple, one-dimensional, stochastic models that lead to a qualitative understanding of very complex systems from biology, nanoscience and social sciences. The first model explains the complicated dynamics of microtubules, stochastic cellular highways. Using the theory of random walks in one dimension, we find analytical expressions…

Research in developmental psychology requires sampling at different time points. Accurate depictions of developmental change provide a foundation for further empirical studies and theories about developmental mechanisms. However, overreliance on widely spaced sampling intervals in cross-sectional and longitudinal designs threatens the validity of…

In a 3-tiered, prevention-oriented framework, Tier II (secondary, targeted) interventions are designed for students whose problem behaviors have not responded to Tier I but are not severe enough to warrant an individualized Tier III intervention. Tier II interventions are implemented similarly across students receiving the intervention and can be…

A method for interval estimation of scale reliability with discrete data is outlined. The approach is applicable with multi-item instruments consisting of binary measures, and is developed within the latent variable modeling methodology. The procedure is useful for evaluation of consistency of single measures and of sum scores from item sets…

It is commonly assumed that people make intertemporal choices by "discounting" the value of delayed outcomes, assigning discounted values independently to all options, and comparing the discounted values. We identify a class of anomalies to this assumption of alternative-based discounting, which collectively shows that options are not treated…

In this article we examine 2 x 2 first-order systems of ordinary differential equations and show how to identify separatrices for phase plane portraits when the system has a saddle point critical value. We describe how to use a computer algebra system to generate trajectories from contour plots, when possible, and determine the equation of the…

The linear regression model is one of the most popular models in statistics. It is also one of the simplest models in statistics. It has received applications in almost every area of science, engineering and medicine. In this article, the authors show that adding a predictor to a linear model increases the variance of the estimated regression…

Movement science faces the challenge of reconciling parallel sequences of discrete behavioral goals with observed fluid, context-sensitive motion. This challenge arises with a vengeance in the speech domain, in which gestural primitives play the role of discrete goals. The task dynamic framework has proved effective in modeling the manner in which…

Parkinson's disease (PD) is a neurodegenerative disorder primarily characterized by sensorimotor dysfunction. The neuropathology of PD includes a loss of dopamine (DA) neurons of the nigrostriatal pathway. Classic signs of the disease include rigidity, bradykinesia, and postural instability. However, as many as 90% of patients also experience…

A latent variable analysis procedure for evaluation of reliability coefficients for 2-level models is outlined. The method provides point and interval estimates of group means' reliability, overall reliability of means, and conditional reliability. In addition, the approach can be used to test simple hypotheses about these parameters. The…

Bayesian estimation of a threshold time (hereafter simply threshold) for the receipt of impulse signals is accomplished given the following: 1) data, consisting of the number of impulses received in a time interval from zero to one and the time of the largest time impulse; 2) a model, consisting of a uniform probability density of impulse time…

Longitudinal studies are necessary to examine individual change over time, with group status often being an important variable in explaining some individual differences in change. Although sample size planning for longitudinal studies has focused on statistical power, recent calls for effect sizes and their corresponding confidence intervals…