Data compression is the art of using encoding techniques to represent data symbols using less storage space compared to the original data representation. The encoding process builds a relationship between the entropy of the data and the certainty of the system. The theoretical limits of this relationship are defined by the theory of entropy in…

A clear view of the ocean may be used to measure the radius of the Earth. To an observer looking out at the ocean, the horizon will always form some angle [theta] with the local horizontal plane. As the observer's elevation "h" increases, so does the angle [theta]. From measurements of the elevation "h" and the angle [theta],…

This cross-sectional study using direct motion monitoring evaluated whether short epochs increased estimates of moderate or vigorous physical activity (MPA or VPA) and enhanced differences in daily VPA comparing overweight (OW) and nonoverweight (NOW) children. Seventy-seven children (ages 8-10 years) wore accelerometers for 7 days. We calculated…

The study of intraindividual variability is central to the study of individuals in psychology. Previous research has related the variance observed in repeated measurements (time series) of individuals to traitlike measures that are logically related. Intraindividual measures, such as intraindividual standard deviation or the coefficient of…

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…

An Excel model for calculating the actual price of bonds under a 30 day/month, 360 day/year day counting assumption by nesting the DAYS360 function within the PV function is developed. When programmed into an Excel spreadsheet, the model can accommodate annual and semiannual payment bonds sold on or between interest dates using six fundamental…

A visual method for counting significant digits is presented. This easy-to-learn (and easy-to-teach) method, designated the box-and-dot method, uses the device of "boxing" significant figures based on two simple rules, then counting the number of digits in the boxes. (Contains 4 notes.)

In 1225 Fibonacci visited the court of the Holy Roman Emperor, Frederick II. Because Frederick was an important patron of learning, this visit was important to Fibonacci. During the audience, Frederick's court mathematician posed three problems to test Fibonacci. The third was to find the real solution to the equation: x[superscript 3] +…

The long-running debate over whether students should be allowed to wield calculators during mathematics exams may soon seem quaint. The latest dilemma facing professors is whether to let students turn to a Web site called WolframAlpha, which not only solves complex math problems, but also can spell out the steps leading to those solutions. In…

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…

"Quantitizing", commonly understood to refer to the numerical translation, transformation, or conversion of qualitative data, has become a staple of mixed methods research. Typically glossed are the foundational assumptions, judgments, and compromises involved in converting disparate data sets into each other and whether such conversions advance…

Cosmic ray count rates with a set of portable Geiger counters were measured at different altitudes on the way to a mountain top and aboard an aircraft, between sea level and cruise altitude. Basic measurements may constitute an educational activity even with high school teams. For the understanding of the results obtained, simulations of extensive…

We present a new practical exercise to explain the mechanisms of aggregation of some colloids which are otherwise not easy to understand. We have used tennis balls to simulate, in a visual way, the aggregation of colloids under reaction-limited colloid aggregation (RLCA) and diffusion-limited colloid aggregation (DLCA) regimes. We have used the…

A well-known ad-hoc approach to conducting structural equation modeling with missing data is to obtain a saturated maximum likelihood (ML) estimate of the population covariance matrix and then to use this estimate in the complete data ML fitting function to obtain parameter estimates. This 2-stage (TS) approach is appealing because it minimizes a…

We introduce a model of radiative transfer in circumstellar dust shells. By assuming that the shell is both isothermal and its thickness is small compared to its radius, the model is simple enough for students to grasp and yet still provides a quantitative description of the relevant physical features. The isothermal model can be used in a…