Assessing sensitivity to unmeasured confounding is an important step in observational studies, which typically estimate effects under the assumption that all confounders are measured. In this paper, we develop a sensitivity analysis framework for balancing weights estimators, an increasingly popular approach that solves an optimization problem to…

This article offers some less-than-rigorous explanations for the notion of degrees of freedom, and for the particular formulae to be used when computing those values.

A visual aid for teaching the formula for the Mann-Whitney U statistic is proposed, inspired by 'proof without words', a didactic exercise from the mathematics literature that uses a visual approach to justify mathematical statements, including formulas and theorems.

This article advocates that introductory statistics be taught by basing all calculations on a single simple margin-of-error formula and deriving all of the standard introductory statistical concepts (confidence intervals, significance tests, comparisons of means and proportions, etc) from that one formula. It is argued that this approach will…

This monograph provides in-depth mathematical logic as the foundational rationale for the novel and innovative online instructional methodology called the 4A Metric Algorithm. The 4A Metric has been designed to address and meet the meta-competency-based education challenges faced by 21st century students who must now adapt to and learn in a…

Financial analysts generally create static formulas for the computation of NPV. When they do so, however, it is not readily apparent how sensitive the value of NPV is to changes in multiple interdependent and interrelated variables. It is the aim of this paper to analyze this variability by employing a dynamic, visually graphic presentation using…

This article provides an easy derivation of updating formulae for the sample covariance and, by extension, for the Pearson product-moment correlation coefficient.

Descripting Statistics provides methodology and tools for user-friendly presentation of random data. Among the summary measures that describe focal tendencies in random data, the mode is given the least amount of attention and it is frequently misinterpreted in many introductory textbooks on statistics. The purpose of the paper is to provide a…

Polynomial loglinear models for one-, two-, and higher-way contingency tables have important applications to measurement and assessment. They are essentially regarded as a smoothing technique, which is commonly referred to as loglinear smoothing. A SAS IML (SAS Institute, 2002a) macro was created to implement loglinear smoothing according to…

In the current time of globalization, collaboration among people in virtual environments is becoming an important precondition of success. This trend is reflected also in the educational domain where students collaborate in various short-term groups created repetitively but changing in each round (e.g. in MOOCs). Students in these kind of dynamic…

The noncentrality parameter for a contrast test in a one-way analysis of variance is based on the dot product of 2 vectors whose geometric meaning in a Euclidian space offers mnemonic hints about its constituents. Additionally, the noncentrality parameters for a set of orthogonal contrasts sum up to the noncentrality parameter for the omnibus…

Research on teaching high school mathematics shows that the topic of percentages often causes learning difficulties. This article describes a method of teaching percentages that the authors used in university bridging courses. In this method, the information from a word problem about percentages is presented in a two-way table. Such a table gives…

Power computations for one-level experimental designs that assume simple random samples are greatly facilitated by power tables such as those presented in Cohen's book about statistical power analysis. However, in education and the social sciences experimental designs have naturally nested structures and multilevel models are needed to compute the…

Studies aggressive automated word removal in text categorization in large databases based on corpus statistics to reduce the noise in free texts and to enhance the computational efficiency of categorization. Topics include stop word identification, categorization methods for comparison, tests on four document collections, and evaluation…

This note provides a scheme that can overcome difficulties in calculating statistical quantities using certain formulae because of errors in the means. Specifically the diversions and discrepancies arising from the results obtained from three groups of widely used formulae for computing the estimated regression coefficients, the gradient b and the…