This is the fifth in a series of statistical articles for mathematics teachers. In this article the authors discuss graphs for exploring relationships between one categorical variable and one numerical variable using stemplots and boxplots and between two numerical variables, using scatterplots and time series plots. [For "The Data Files 4:…

The article presents some notes on normalization and illustrates these procedures using graphing functions in R. Using real data, the paper also presents an R package and online Shiny app that efficiently transforms variables in large datasets.

A green chemistry experiment is presented for teaching an undergraduate quantitative analysis/analytical chemistry laboratory class through the use of black tea leaf extract for the determination of iron in supplement tablets. Dried tea leaf is a safe, low cost, and widely available source of natural extract that can be used in place of more toxic…

Course selection can be a daunting task, especially for first year students. Sub-optimal selection can lead to bad performance of students and increase the dropout rate. Given the availability of historic data about student performances, it is possible to aid students in the selection of appropriate courses. Here, we propose a method to compose a…

Graphical model validation techniques for linear normal models are often used to check the assumptions underlying a statistical model. We describe an approach to provide "instant experience" in looking at a graphical model validation plot, so it becomes easier to validate if any of the underlying assumptions are violated.

Data is critical, but data has not always lead to success. If data is not communicated clearly, the results can be disastrous. Design lets us communicate data so it can be understood. Dr. Rankin believes that "when we're fluent in visualizing our ideas, we can communicate them across global boundaries, across spoken language barriers, and…

Four rather different scatterplots of two variables X and Y are given, which, after dichotomizing X and Y, result in identical fourfold-tables misleadingly showing no association. (Contains 1 table and 1 figure.)

Instead of solving ordinary differential equations (ODEs), the damped simple harmonic motion (SHM) is surveyed qualitatively from basic mechanics and quantitatively by the instrumentality of a graph of velocity against displacement. In this way, the condition b ? [square root]4mk for the occurrence of the non-oscillating critical damping and…

Throughout the general chemistry lab curriculum, a common shortcoming is the way in which students measure, record, and manipulate quantitative data. From initial measurements with different digital and analog instruments to proper conversions, calculations, and comparisons, students are often expected to be experts before they have been taught…

The need for statistical analysis in single-subject designs presents a challenge, as analytical methods that are applied to group comparison studies are often not appropriate in single-subject research. "SSD for R" is a robust set of statistical functions with wide applicability to single-subject research. It is a comprehensive package…

This paper shows how the application of simple statistical methods can reveal to students important insights from climate data. While the popular press is filled with contradictory opinions about climate science, teachers can encourage students to use introductory-level statistics to analyze data for themselves on this important issue in public…

This paper shows how the variance and standard deviation can be represented graphically by looking at each squared deviation as a graphical object--in particular, as a square. A series of displays show how the standard deviation is the size of the average square.

We would like to share with you our ongoing experiences with "hands-on statistics" lessons we have recently carried out. We have developed a new experimental path for teaching young students using fundamental concepts of "statistics": uncertainty of the measurement, the uncertainty of the mean, the mean itself, etc. The methods…

This paper introduces a method of extending natural language-based processing of qualitative data analysis with the use of a very quantitative tool--graph theory. It is not an attempt to convert qualitative research to a positivist approach with a mathematical black box, nor is it a "graphical solution". Rather, it is a method to help qualitative…

Some statisticians have pointed out that the field of statistics essentially exists to study the variability seen in everyday life. Because variability is so foundational, the "Guidelines for Assessment and Instruction in Statistics Education" (GAISE 2007), published by the American Statistical Association (ASA), recommend that teachers…