We observed, using polarized light microscopy, the supercooling of the blue phase (BPI) of cholesteryl proprionate and measured the corresponding liquid crystalline phase transition temperatures. From these temperatures and additional published data we have provided, for the benefit of undergraduate physics students, a nontraditional example…

Bayesian methods for analyzing longitudinal data in social and behavioral research are recommended for their ability to incorporate prior information in estimating simple and complex models. We first summarize the basics of Bayesian methods before presenting an empirical example in which we fit a latent basis growth curve model to achievement data…

Almost all introductory and intermediate level statistics textbooks include the topic of confidence interval for the population mean. Almost all these texts introduce the median as a robust measure of central tendency. Only a few of these books, however, cover inference on the population median and in particular confidence interval for the median.…

This note considers a family of piece-wise linear functions that can be used in the classroom to illustrate various concepts involved in iteration theory such as periodicity. These functions require minimal background on the part of the student. (Contains 2 figures.)

Describing the world in terms of energy is necessarily quantitative: one must be able to do the sums for the description to gain a purchase. Whilst teaching younger children (say 11-14 years old) the full quantitative description is not available and this has made the introductory teaching of energy a contentious area. By focusing on…

The analysis explains the basis set superposition error (BSSE) and fragment relaxation involved in calculating the interaction energies using various first principle theories. Interacting the correlated fragment and increasing the size of the basis set can help in decreasing the BSSE to a great extent.

Vieta's famous product using factors that are nested radicals is the oldest infinite product as well as the first non-iterative method for finding [pi]. In this paper a simple geometric construction intimately related to this product is described. The construction provides the same approximations to [pi] as are given by partial products from…

After prolonged viewing of a slowly drifting or rotating pattern under strict fixation, the pattern appears to slow down and then momentarily stop. The authors show that grouping can slow down the process of "motion fading," suggesting that cortical configural form analysis interacts with the computation of motion signals during motion fading. The…

This article tackles several issues involved in specifying, fitting, and interpreting the results of multilevel factor models for ordinal variables. First, the problem of model specification and identification is addressed, outlining parameter interpretation. Special attention is devoted to the consequences on interpretation stemming from the…

Many students have difficulty seeing the conceptual link between bivariate data displayed in a scatterplot and the statistical summary of the relationship, "r." This article shows how to teach (and compute) "r" such that each datum's direct and indirect influences are made apparent and used in a new formula for calculating Pearson's "r."

Interest in students who exhibit characteristics with difficulties in learning can be traced as far back as 1800. In order to better understand the complexities and causes of learning disabilities, many researchers (Bannatyne, 1968, 1974; Rugal, 1974) have investigated ways to better identify learners who struggle with academics. A strong argument…

Pre-kindergarten programs are expanding in states around the nation. Decades of research on the impact of these programs show that high quality standards produce substantial benefits for children, working families, and communities. As state leaders seek to increase investments in pre-k, they face a number of choices and potential tradeoffs that…

Computational models have played a central role in the debate over language learnability. This article discusses how they have been used in different "stances", from generative views to more recently introduced explanatory frameworks based on embodiment, cognitive development and cultural evolution. By digging into the details of certain specific…

The Arab Open University (AOU) has adopted the standard deviation method (SDM) as a grading system in replacement of a fixed scale. Adopting SDM was intended to remedy a problem that has resulted from discrepancies between AOU's graduation requirements and those of its partner, UK Open University. This paper aims mainly at investigating whether…

The tendency to underestimate egocentric distances in immersive virtual environments (VEs) is not well understood. However, previous research (A. R. Richardson & D. Waller, 2007) has demonstrated that a brief period of interaction with the VE prior to making distance judgments can effectively eliminate subsequent underestimation. Here the authors…