arXiv subjects

Amelia McNamara

Publications and source records attributed to Amelia McNamara.

6 recordsLinked to original sources

arXiv2024

Teaching modeling in introductory statistics: A comparison of formula and tidyverse syntaxes

There are many pedagogical considerations for incorporating programming into a statistics course. When using the programming language R, one consideration is the particular R syntax that will be used. This paper reports on a head-to-head comparison run in a pair of introductory statistics labs, one conducted fully in the formula syntax, the other in tidyverse. Analysis of pre- and post-survey data show minimal differences between the two labs, with students reporting a positive experience regardless of section. Analysis of data from YouTube and RStudio Cloud show interesting distinctions. The formula section appeared to watch a larger proportion of pre-lab YouTube videos, but spend less time computing on RStudio Cloud. Conversely, the tidyverse section watched a smaller proportion of the videos and spent more time computing. Analysis of lab materials showed tidyverse labs tended to be slightly longer in terms of lines in the provided RMarkdown materials and minutes of the associated YouTube videos. The tidyverse labs exposed students to more distinct R functions, but reused functions more frequently. Both labs relied on a relatively small vocabulary of consistent functions, which can provide a starting point for instructors interested in teaching introductory statistics in R. The instructor experience of teaching in the two syntaxes diverged primarily when discussing relationships between categorical variables, as well as when working with summary statistics for numeric variables. This work provides additional evidence for instructors looking to choose between syntaxes for introductory statistics teaching.

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arXiv2022

An educator's perspective of the tidyverse

Computing makes up a large and growing component of data science and statistics courses. Many of those courses, especially when taught by faculty who are statisticians by training, teach R as the programming language. A number of instructors have opted to build much of their teaching around use of the tidyverse. The tidyverse, in the words of its developers, "is a collection of R packages that share a high-level design philosophy and low-level grammar and data structures, so that learning one package makes it easier to learn the next". These shared principles have led to the widespread adoption of the tidyverse ecosystem. A large part of this usage is because the tidyverse tools have been intentionally designed to ease the learning process and make it easier for users to learn new functions as they engage with additional pieces of the larger ecosystem. Moreover, the functionality offered by the packages within the tidyverse spans the entire data science cycle, which includes data import, visualisation, wrangling, modeling, and communication. We believe the tidyverse provides an effective and efficient pathway for undergraduate students at all levels and majors to gain computational skills and thinking needed throughout the data science cycle. In this paper, we introduce the tidyverse from an educator's perspective. We provide a brief introduction to the tidyverse, demonstrate how foundational statistics and data science tasks are accomplished with the tidyverse, and discuss the strengths of the tidyverse, particularly in the context of teaching and learning.

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arXiv2018

Key attributes of a modern statistical computing tool

In the 1990s, statisticians began thinking in a principled way about how computation could better support the learning and doing of statistics. Since then, the pace of software development has accelerated, advancements in computing and data science have moved the goalposts, and it is time to reassess. Software continues to be developed to help do and learn statistics, but there is little critical evaluation of the resulting tools, and no accepted framework with which to critique them. This paper presents a set of attributes necessary for a modern statistical computing tool. The framework was designed to be broadly applicable to both novice and expert users, with a particular focus on making more supportive statistical computing environments. A modern statistical computing tool should be accessible, provide easy entry, privilege data as a first-order object, support exploratory and confirmatory analysis, allow for flexible plot creation, support randomization, be interactive, include inherent documentation, support narrative, publishing, and reproducibility, and be flexible to extensions. Ideally, all these attributes could be incorporated into one tool, supporting users at all levels, but a more reasonable goal is for tools designed for novices and professionals to `reach across the gap,' taking inspiration from each others' strengths.

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arXiv2017

Greater data science at baccalaureate institutions

Donoho's JCGS (in press) paper is a spirited call to action for statisticians, who he points out are losing ground in the field of data science by refusing to accept that data science is its own domain. (Or, at least, a domain that is becoming distinctly defined.) He calls on writings by John Tukey, Bill Cleveland, and Leo Breiman, among others, to remind us that statisticians have been dealing with data science for years, and encourages acceptance of the direction of the field while also ensuring that statistics is tightly integrated. As faculty at baccalaureate institutions (where the growth of undergraduate statistics programs has been dramatic), we are keen to ensure statistics has a place in data science and data science education. In his paper, Donoho is primarily focused on graduate education. At our undergraduate institutions, we are considering many of the same questions.

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arXiv2016

On the State of Computing in Statistics Education: Tools for Learning and for Doing

This paper lays out the current landscape of tools used in statistics education. In particular, it considers graphing calculators, spreadsheets, applets and microworlds, standalone educational software, statistical programming tools, tools for reproducible research and bespoke tools. The strengths and weaknesses of the tools are considered, particularly in the context of McNamara (2016)'s list of attributes for a statistical computing tool. Best practices for computing in introductory statistics are suggested.

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arXiv2012

Instabilities and Patterns in Coupled Reaction-Diffusion Layers

We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer systems of identical two-component reactions, we analyze the stability of homogeneous steady states by exploiting the block symmetric structure of the linear problem. There are eight possible primary bifurcation scenarios, including a Turing-Turing bifurcation that involves two disparate length scales whose ratio may be tuned via the inter-layer coupling. For systems of $n$-component layers and non-identical layers, the linear problem's block form allows approximate decomposition into lower-dimensional linear problems if the coupling is sufficiently weak. As an example, we apply these results to a two-layer Brusselator system. The competing length scales engineered within the linear problem are readily apparent in numerical simulations of the full system. Selecting a $\sqrt{2}$:1 length scale ratio produces an unusual steady square pattern.

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