1. Amy Wagaman Amherst College Mathematics and Statistics

2.  “Ability to communicate: ◦ Students need to be able to communicate complex statistical methods in basic terms to managers and other audiences and to visualize results in an accessible manner. ◦ They must have a clear understanding of ethical standards. ◦ Programs should provide multiple opportunities to practice and refine these statistical practice skills.” From the Curriculum Guidelines for Undergraduate Programs in Statistical Science (2014)

3.  Communication is included in our learning outcomes for Statistics majors upon graduation: “To have demonstrated in a variety of courses and in several formats, the ability to clearly communicate results of statistical analyses, as well as the ability to read and understand statistical techniques in primary research.”

4.  Presentations ◦ Formal (example: 8-12 minutes, reports on projects) ◦ Informal (example: 3 minutes to present a solution or a tidbit from an article with the class working in groups) ◦ Feedback on presentation aspects beyond statistical content is provided  Handouts ◦ Often created for presentations  Reports ◦ Length depends on the assignment ◦ Includes exercises in writing executive summaries with appropriate supporting information

5.  Writing ◦ Summaries of data analysis ◦ Slides and Handouts ◦ Introductions to expository topics  Visualization ◦ Graphics included in many materials  Speaking ◦ Ability to engage the audience ◦ Proper eye contact, not reading from slides, etc.

6.  Theoretical statistics course  Pre-requisite of 1 semester of Probability  Juniors and seniors  Statistics majors, mathematics majors, and other majors  Computing Background of students differs  Our statistics courses use R via Rstudio with Rmarkdown.

7.  Group work  Two Course Projects ◦ First course project involved:  a computational aspect (simulation performed using R)  a statistical theory component  a writing component ◦ Second course project involved:  a class presentation, with optional handout  written report summarizing, critiquing, and/or explaining an article from a curated list selected from The American Statistician

8.  Topic: Estimation and Simulation  Based on historical German tank problem  Setting: A random sample of k values from a population with individuals labeled 1,…,N is drawn.  Students derive several estimators (and examine their properties) for N.  Students brainstorm additional estimators, and use simulation (in R) to compare all estimators.  They are then tasked with writing a “report” explaining their choice of “best” estimator with support, via their calculations and the simulations.  Focus on the writing about the simulations

9.  Students should be able to explain what the simulation does.  Students should be able to extract meaningful support for their estimator from their simulation.  Support should be provided appropriately in the written document.  Students should convey (in some form) how they explored different settings for the simulation other than the toy example provided.

10.  Most students decided to summarize their simulation results with tables, supplemented with selected graphs.  Some students found writing about their tables challenging. ◦ What is too obvious to restate? ◦ What is useful to point out to the reader? Etc.  Some students included too many graphs. Organizational and size issues were apparent. Formatting comments were provided.

11.  Students were tasked with: ◦ Selecting an article from The American Statistician (TAS) from a curated list and reading it/ working through it ◦ Writing a 4-6 page (double spaced) summary of what they learned, what methods were used, etc. ◦ In the event they encountered an unfamiliar term or method, they were to do research to be able to explain it to their classmates. ◦ A 6 minute presentation to the class on the article (or what part of it they found interesting) was required.

12.  I supplied students with a curated list of TAS articles to select from.  Students indicated top choices and articles were split up.  Example articles presented in Spring 2015: ◦ Bayesian Inference on a Proportion Believed to be a Simple Fraction (Vol. 61, No. 3) ◦ Confidence Intervals for a Discrete Population Median (Vol. 62, No. 1) ◦ Hidden Dangers of Specifying Noninformative Priors (Vol. 66, No. 2)

13.  Student presentations were spread over 3 days (themed based on the articles chosen).  Students provided feedback to one another via this rubric and comment sheet (collected, and distributed to speakers anonymously).

14.  Students received feedback on their presentations (from the class and instructor) before submitting their written reports.  Reports were assessed and returned.  Students were then allowed to submit a revised report to address comments, and could earn some points back (up to half of what was originally lost).  Revisions were undertaken by 10 of the 17 students.

15.  Students received a copy of this rubric with their assessment before revisions.

16.  The project can easily be made to be group instead of individual.  The article list can be made more or less targeted on specific topics.  Different journals/magazines may be used depending on the level of the audience (e.g. Significance).  Simulations could be required (which would alter the article list).

17.  American Statistical Association Undergraduate Guidelines Workgroup (2014), "2014 Curriculum Guidelines for Undergraduate Programs in Statistical Science." Alexandria, VA: American Statistical Association. http://www.amstat.org/education/curriculumguidelines.cfm. http://www.amstat.org/education/curriculumguidelines.cfm  Wagaman, Amy. Writing about Simulations in a Theoretical Statistics Course. eCOTS 2016 virtual poster. https://www.causeweb.org/cause/ecots/ecots16/posters/b/ 8 https://www.causeweb.org/cause/ecots/ecots16/posters/b/ 8 For other neat ideas for this course, see:  Jennifer L. Green and Erin E. Blankenship (2015), “Fostering Conceptual Understanding in Mathematical Statistics.” The American Statistician, 69:4, 315-325.