Physical Sciences and Mathematics Commons^™

Hockey Card Statistics Are Stagnant And Stale, Egan J. Chernoff

Journal of Humanistic Mathematics

The purchase of a coffee at a Canadian institution, Tim Hortons, turned into an informal investigation into hockey card statistics. Turns out, hockey card statistics are stagnant and stale. This was disappointing to see because the game of hockey has changed, the statistics used to keep track of the game have changed. Even the cards have changed. Well, not the back of the cards, which do not well enough paint a statistical picture of the hockey player photographed on the front of the card.

The Limits Of Data Science, David E. Drew

Journal of Humanistic Mathematics

Data science can contribute valuable predictions in diverse fields. But I write to express some concerns and red flags. I suggest that data science is being oversold. This article contains three questions that I believe data science must address as this new discipline matures. Is data science significantly different from statistics? This is a question that has haunted the field since the term first was introduced. By creating algorithms based on current societal decision rules that may be biased, even bigoted, does data science lock in and exacerbate inequality? Scholars have identified a continuum from data to information to knowledge …

Spurious Correlation Sestina, Jules Nyquist

Journal of Humanistic Mathematics

This is a sestina poem about Spurious Correlations with a magical realism angle for beginning students learning statistics for the first time during the COVID pandemic.

So Long My Friend, Bryan Mcnair

Journal of Humanistic Mathematics

No abstract provided.

Analyzing Marriage Statistics As Recorded In The Journal Of The American Statistical Association From 1889 To 2012, Annalee Soohoo

CMC Senior Theses

The United States has been tracking American marriage statistics since its founding. According to the United States Census Bureau, “marital status and marital history data help federal agencies understand marriage trends, forecast future needs of programs that have spousal benefits, and measure the effects of policies and programs that focus on the well-being of families, including tax policies and financial assistance programs.”[1] With such a wide scope of applications, it is understandable why marriage statistics are so highly studied and well-documented.

This thesis will analyze American marriage patterns over the past 100 years as documented in the Journal of …

Mary Eleanor Spear's Importance To The History Of Statistical Visualization, Melanie Williams

CMC Senior Theses

This paper will demonstrate why Mary Eleanor Spear (1897-1986) is an important figure in the history of statistical visualization. She lead an impressive career working in the federal government as a data analyst before "data analyst" became a thing. She wrote and illustrated two comprehensive textbooks which furthered the art of statistical visualization. Her textbooks cover extensive graphing knowledge still valuable to statisticians and viewers today. Most notable of her works is her development of the box plot. In addition to Spear's career and contributions, this paper will also address the lack of female representation in science, technology, engineering, and …

The Uncertainty Of Confidence, Michael J. Leach

Journal of Humanistic Mathematics

This is a free-verse poem about the estimation of population parameters in statistical models. The spacing of words is intended to reflect uncertainty.

Three Creativity-Fostering Projects Implemented In A Statistics Class, Margaret Adams

Journal of Humanistic Mathematics

Undergraduates in an introductory statistics class at a rural Southeastern college were assigned three creativity-fostering projects: statistics vocabulary crossword puzzle, word wall, and graffiti art poster. Given math anxiety, fear of failure, and lack of enthusiasm, it seemed imperative to spark interest and involvement. Rhodes 4P’s model (1961) served as the framework for this intrinsic case study involving 62 students. Independent thinking and research, peer collaboration, and use of art supplies within this model (person, press, process and product) generated remarkable learning outcomes. Grading rubrics focused on originality, quality and statistics content. Projects were classified into three qualitative categories ranging …

Mathematics Versus Statistics, Mindy B. Capaldi

Journal of Humanistic Mathematics

Mathematics and statistics are both important and useful subjects, but the former has maintained prominence in the American education system. On the other hand, statistics is more prevalent in daily life and is an increasingly marketable subject to know. This article gives a personal history of one mathematician’s bumpy road to learning and teaching statistics. Additionally, arguments for how and why to include statistics in the K-12 and college curricula are provided.

Bayesian Hierarchical Meta-Analysis Of Asymptomatic Ebola Seroprevalence, Peter Brody-Moore

CMC Senior Theses

The continued study of asymptomatic Ebolavirus infection is necessary to develop a more complete understanding of Ebola transmission dynamics. This paper conducts a meta-analysis of eight studies that measure seroprevalence (the number of subjects that test positive for anti-Ebolavirus antibodies in their blood) in subjects with household exposure or known case-contact with Ebola, but that have shown no symptoms. In our two random effects Bayesian hierarchical models, we find estimated seroprevalences of 8.76% and 9.72%, significantly higher than the 3.3% found by a previous meta-analysis of these eight studies. We also produce a variation of this meta-analysis where we exclude …

Ladies' Night, Robert Dawson

Journal of Humanistic Mathematics

"Lady" Jane is an expert at her racket. The Joint Statistical Meetings are in Vegas, and she reckons it's payday. But she's taking on the professionals.

The Battle Against Malaria: A Teachable Moment, Randy K. Schwartz

Journal of Humanistic Mathematics

Malaria has been humanity’s worst public health problem throughout recorded history. Mathematical methods are needed to understand which factors are relevant to the disease and to develop counter-measures against it. This article and the accompanying exercises provide examples of those methods for use in lower- or upper-level courses dealing with probability, statistics, or population modeling. These can be used to illustrate such concepts as correlation, causation, conditional probability, and independence. The article explains how the apparent link between sickle cell trait and resistance to malaria was first verified in Uganda using the chi-squared probability distribution. It goes on to explain …

Moneyball For Creative Writers: A Statistical Strategy For Publishing Your Work, Jon Wesick

Journal of Humanistic Mathematics

Writers face a challenge getting their poems and stories published. Rather than following the traditional strategy I model creative writing submission as a statistical process and explore the use of numerical metrics to maximize publications.

Gathering Steam In Health Care: A Student History, Michael J. Leach

The STEAM Journal

In this reflection, I demonstrate STEAM in health care by outlining my 15 years as a university student engaged in formal education, extracurricular learning, research, and employment.

A Method For Generating Realistic Correlation Matrices, Johanna S. Hardin, Stephan Ramon Garcia, David Golan

Pomona Faculty Publications and Research

Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations both have drawbacks. We develop an algorithm for adding noise, in a highly controlled manner, to general correlation matrices. In many instances, our method yields results which are superior to those obtained by simply simulating Gaussian data. Moreover, we demonstrate how our general algorithm can be tailored to a number of different correlation models. Using our results with a few different applications, we show that simulating correlation matrices …

Mathematics And The Hunger Games, Michael A. Lewis

Journal of Humanistic Mathematics

The Hunger Games plot features a dystopian future in which twelve outer districts are oppressed by a centralized capital. The story focuses on the heroism of a sixteen-year-old girl named Katniss and how she tries to rise above the oppression that she experiences. It also features a special lottery and other twists that are sources of mathematical interest. This essay focuses on some of the mathematical issues raised by The Hunger Games in an effort to show that this story can be used to teach students (as well as other interested parties) some important concepts from mathematics.

Constructing Phylogenetic Trees Using Maximum Likelihood, Anna Cho

Scripps Senior Theses

Maximum likelihood methods are used to estimate the phylogenetic trees for a set of species. The probabilities of DNA base substitutions are modeled by continuous-time Markov chains. We use these probabilities to estimate which DNA bases would produce the data that we observe. The topology of the tree is also determined using base substitution probabilities and conditional likelihoods. Felsenstein [2] introduced this method of finding an estimate for the maximum likelihood phylogenetic tree. We will explore this method in detail in this paper.

Changes Across 25 Years Of Statistics In Medicine, Johanna S. Hardin

Pomona Faculty Publications and Research

[This piece is a series of interviews with giants in the field of medicine on their views of how statistics is changing medicine. I interviewed the editor of the New England Journal of Medicine, a preeminent doctor/researcher of lung cancer, the director of the LA County Department of Public Health, and a Harvard statistician who sits on the editorial board of the New England Journal of Medicine.]

Medicine, Statistics, And Education: The Inextricable Link, Katharine K. Brieger '11, Johanna S. Hardin

Pomona Faculty Publications and Research

No abstract provided.

A Multistage Incidence Estimation Model For Diseases With Differential Mortality, Alyssa W. Dray

HMC Senior Theses

According to theWorld Health Organization, surgically removable cataract remains the leading cause of blindness worldwide. In sub-Saharan Africa, cataract surgical rate targets should ideally be set based on cataract incidence (the number of new cataracts developed each year). Unfortunately, the longitudinal studies necessary to measure incidence have not yet been feasible in these areas. Our research instead proposes a method for estimating incidence based on available cataract prevalence data. We extend a method proposed by Podgor and Leske (1986) to estimate age-specific incidence from age-specific prevalence in single diseases with differential mortality. A two-stage disease extension is created in order …

The Impact Of Directionality In Predications On Text Mining, Gondy Leroy, Marcelo Fiszman, Thomas C. Rindflesch

CGU Faculty Publications and Research

The number of publications in biomedicine is increasing enormously each year. To help researchers digest the information in these documents, text mining tools are being developed that present co-occurrence relations between concepts. Statistical measures are used to mine interesting subsets of relations. We demonstrate how directionality of these relations affects interestingness. Support and confidence, simple data mining statistics, are used as proxies for interestingness metrics. We first built a test bed of 126,404 directional relations extracted from biomedical abstracts, which we represent as graphs containing a central starting concept and 2 rings of associated relations. We manipulated directionality in four …

Analyzing Dna Microarrays With Undergraduate Statisticians, Johanna S. Hardin, Laura Hoopes, Ryan Murphy '06

Pomona Faculty Publications and Research

With advances in technology, biologists have been saddled with high dimensional data that need modern statistical methodology for analysis. DNA microarrays are able to simultaneously measure thousands of genes (and the activity of those genes) in a single sample. Biologists use microarrays to trace connections between pathways or to identify all genes that respond to a signal. The statistical tools we usually teach our undergraduates are inadequate for analyzing thousands of measurements on tens of samples. The project materials include readings on microarrays as well as computer lab activities. The topics covered include image analysis, filtering and normalization techniques, and …

An Interactive Tutorial For Teaching Statistical Power, Christopher L. Aberson '99, Dale E. Berger, Michael R. Healy '04, Victoria L. Romero '07

CGU Faculty Publications and Research

This paper describes an interactive Web-based tutorial that supplements instruction on statistical power. This freely available tutorial provides several interactive exercises that guide students as they draw multiple samples from various populations and compare results for populations with differing parameters (for example, small standard deviation versus large standard deviation). The tutorial assignment includes diagnostic multiple-choice questions with feedback addressing misconceptions, and follow-up questions suitable for grading. The sampling exercises utilize an interactive Java applet that graphically demonstrates relationships between statistical power and effect size, null and alternative populations and sampling distributions, and Type I and II error rates. The applet …