Building Communication Skills in a Theoretical Statistics Course

Building Communication Skills in a The oretical Statistics Course Amy Wagaman Departmen t of Ma themati cs and Statis tics, A mherst C ollege, P.O. B ox 50 00, Amh erst, MA 0100 2 Abstract The “traditional” theoretical statistics course which d evelops the theoretical und erpinnings of the discipline (usually following a probabilit y course) is undergoing near - continuous revision i n the statist ics community. In particular, recent versions of this course hav e in corpora ted more an d mo re comput ation. We take a look a t a dif ferent a spect of the r evision - b uilding stude nt commu nication s kills in the cours e, in both written and verbal f orms, to allow students t o demonstrate their ability t o explain statistical concep ts. Two separat e projects are discussed, b oth of which were engaged in b y a class of size 17 in Spring 2015. The first project had a c omputational aspect (perform ed using R), a statistical the ory compo nent, and a writi ng component , and was based on t he his torical German tank problem. Th e second project involved a c lass presentation and writt en report summarizing, critiq uing, and/or explaining an article selected from The American Statistician. In troduc tion In our st atistics cour ses, our stude nts learn qui te a bit about both data analy sis and the theo ry behind statistics. They learn to create visualizations, p erform hypothesis testing and generate confidence intervals, discuss issues rel ated to experimental desig n, derive maximum likeliho od estimators and p osterior distributions, and much m ore. With the advances in technology and statistical software, the amount o f computatio n in our courses has i ncreased, wit h students pe rforming simul ations (of ten using software, such as R (R 2009) to verify results or perfor m randomization - based procedur es. These sk ills in statistic s and in c ompu ting will s erve ou r stud ents well , bu t there is another skill s et that we need to help our students ac quire. Our stat istics stude nts need to pr actice and build s trong communi catio n skills. Being able to perform an analysis or suggest a reasonab le model means little if the student cannot communicate their resul ts and their reasoning to others, i ncluding audiences with less of a statistics vocabulary. The importance of commu nication skills for statistics students is highlighted in the recent Curriculum Guideline s for Undergraduate Programs in Statistical Scienc e which suggests programs pro vide opportunities for students to practice commu nication skills, and learn a bout ethics ( Guidel i nes 2014 ) . In th e spirit of the guidelines, we include com munication skills as a learni ng outcome for our statistics m ajors, and have worked to be sure our program pro vides multi ple avenues fo r students to pr actice thes e skills. Our stude nts engage in a variety of activities to practice communication skills inc luding presentations (both fo rmal and info rmal, with sli des and speak ing compone nts), handout c reation and use , and report writing (with varying length). Skills devel oped include writing ability (f or reports, slides, and handouts), speaking ability (maintaining eye contact, voice volu me, etc.), and the ability t o create good visualizations (for inclusion in reports, handou ts, and slides). In this article, we explore h ow two course projects in a theoretical statis t ics course allowed stu dents to build and prac tice commun icatio n skills. We pro vide a brief bac kground abo ut the course in Se ction 1 . We descr ibe th e two c ourse p rojects in Secti ons 2 a nd 3, r espec tively . Finally, we conclude with s ome discus si on in Sect ion 4. 1. Co urse Background The theore tical s tatisti cs co urse discu ssed h ere is a 300 - level (pr eviously listed as a 4 00 - level) course with a primary audience of juniors and seniors. Statisti cs majors take the course a s juniors in preparation for a senior capstone experi ence in statistics. Students from other majors, including majors in mathematics and economics, tak e the course as w ell. The course has a pre - r equ isite of on e sem ester of probability. Topics covered in the cours e include: Bayesian inference, maximum likelihood estimation, sufficien t statistic s, c onfide nce inter vals, h ypothesi s te sting an d test sel ection , no n - parametric procedures, and linear mo dels. The course uses the st atistical computing softwar e R (with RStudio and RMarkdown) f or c om put at ion s, simulations, analysis, etc. ( R 2009) . 2. Course Project I - Tanks, Any one? The first course project covers the t opics of estimation and simulation. It i s based on the historical “Germa n tank problem” and th e associa ted c ommon estima tion exer cise us ed to engag e students in this course (mul tiple exam ples of re lated projects may be found onl ine). 2.1 Pr oject Setup and S tuden t Directi ons Students a re pr esented wi th the proj ect ins tructi ons and given abou t thre e wee ks to work on th eir submis sions. A hand out de scribes th e proj ect. In short , students are told that th e y are in terested i n the following problem: A rando m sample of k values fro m a population with individuals labeled from 1 to N is drawn. An estimate for N is needed. S tuden ts are a l so p ro vided with a small data set of k values f or which the esti mate of N is needed. Students are directed to derive s everal estimators (and exa mine their properties - expec tati on and variance) for N , including the met hod of moment s estimator and the max imum likelihood estimator. Some hints are provided about trickier derivation pieces. Students are als o instructed to brainstorm additional estimators, and use si mulation (in R) to compare all their estimators. Due to one student's weak R backgro und, the cl ass was provide d with example s imulatio n code for one nonse nsical estimator. The studen ts are then tasked wi th writi ng a “ report ” explaining their choice of “ best ” estimator with support, via their calculations and the simulations. The report is actually fr amed as a letter to their commanding officer (as in an in telligence officer), which the stud ents seem to en joy the creative aspect of. Next, we exp lore the vari ous commun ication aspec ts inv olved in th e pr oject. 2.2 Communicatio n P ractice, Outcomes, and Feedback There ar e a varie ty of commun ication skills th at stu dents need to d evelop and p ractice. In this p roject, the students are focusing on writing, rather than spea king, skills. The writing incl udes a letter, with a summary of findings, appro priate su pporting inf ormation , including de rivatio ns and simulat ion results, as well a s the si mulati ons wh ere the s tuden ts write code ( though studen ts did n ot sub mit thei r code for this, due to being give n example code). General ly, stude nts did not seem to have an y issues with cr eating the letter , wri tin g about thei r fin dings, and comparing the estimators via th eir derivations. (For exa mple, it seems very s imple for students to write sen tences li ke: th e va riance of estima tor on e is less th an th at of e stimat or two, so I prefer estimator one). There were , of course, minor issues ac ross the board with spellin g and proofreading, along with some organizational issues. H owever, students had more issu es when writing ab out their simula tions, and u sing appropria te support fo r their chosen est imator in their reports. This iss ue was discussed via an eCoTs virt ual poster (Wagaman 201 6), but more detail follow s here. To unde rstand the probl ems encoun tered, we cons ider what stude nts should be abl e to do in regards to their simula tions. Firs t, students s hould be able to explain what t heir simulat ion does . They should be able to run i t and obtai n results, helpi ng them to choose a preferred est imator. Then, stu dents shoul d be able to extract meaning ful support for their estimator fro m th eir si mulation. Once stu dents have identif ied what suppo rt to include, t hat support should be provid ed appro priately in the wr itten document. Finally, in this particular cas e, since example code was provided (with example settings of N =300 and k =15 ), s tudent s should convey ( in some form) how they explore d different sett ings for the simula tion other than those provide d. In other words , their chose n support should inc lude setti ngs other than N =300 and k =15. It sho uld come as no surpris e that mos t students dec ided to summa rize their simulat ion re sults with tables of descripti ve statist ics, suppleme nted with sel ected graphs . This is in fa ct, how many of us wou ld choose to display our f indings. Ho wever, stu dents had issues w ith writing abo ut these resul ts. In particular, some students found writing ab out their tables very challeng ing. On one extreme, a student included a table an d simp ly s tated th at the t able w as su pport for their es timat or. At th e other extre me, student s were providin g multiple s enten ces about their tables (at least one sente nce per table r ow), including the majority of va lues from the table, making the text completely redun dant. Based on this anecdotal experience, it is clear that students may n eed some instruction ab out writing about tables. For example, when prepari ng a table for a paper and writing the accompanying text, stu dents m ay need to thi nk ab out: “ What i s too obvious t o restat e? ” and “ W hat is use ful to point out t o the read er? ” . In terms of graphs, it appe ars that some students nee d more guidance trying to prepare figures for report s. For example , some student s included too many gr aphs (in my op inion), and in inappr opriat e formats (e.g. 16 graphs on a page, too tiny t o really examine). Others included an appropriate number of graphs but had organizatio nal issues (e.g. 1 graph per page for 6 pages). App ropriate labels and titles were pro blems for some student s. After pr ojects w ere su bmitted, they were ass essed. S tuden ts recei ved a c opy of the ass essmen t rubric with notes ab o ut their work when proj ects were returne d. Organizat ional a nd formatti ng comments were pro vided t o assist s tu dents with the pr oble m are as describ ed ab ove, but stud ents wer e not allowed to submit a revision of this project. 3. Course Project II - Wo rk ing w ith TAS Ar ticles Students need to be abl e to apply their knowledge to new situatio ns, and our progra ms should provide some pra ctice with this task. In part icular, students shoul d be able to appl y their know ledge when reading new literature in th e field the y are studying. This course pr oject was designed t o help st udents read a new article (at an ap propriate level), process th e material, and demonstrat e their understanding via a cla ss pres entation a nd s hort writt en rep ort. Stu dents w ere all owed t o revi se the ir submiss ion, wit h access to the as sessmen t ru bric. 3.1 Pr oject Setup and S tuden t Directi ons For this second course project, s tudents choose an article fr om The American Statistician (TAS) fr om a curated list supplied by me (with articles appropriate based on their ba ckground from t he course). The students th en read and worked th rough their s elected article. In th e even t they encou ntered an unfamiliar term or meth od, they were to do research t o be able to explain it to their classmates. Aft er processin g their ar ticle, stu dents wer e task ed with pres enting their article to the class (a six minute p resentation) and writing a 4 - 6 page (double spaced) sum mary of what t hey learned, what met hods were used , etc. I n both the se assign ments, the stu dents might h av e to pick and choose w hat aspects of the articl e they sh ared wit h the class , due to leng th o f their ar ticles and need to exp lain new concep ts to their class mates. Studen ts were enc ouraged t o co me up with ex amples t o dem onstrate methods fro m their articles to the class. Si mulations could also be used to v erify results from the articles ( or generate example s), and some st udents so ught assista nce with creatin g simulations in R. 3.2 C om municat ion Practi ce, Outcome s, and Feedback Students w ere wor king on b oth a pr esentation and a written repo rt for th is pr oject. F or the present ation, most students made sl ides or prepar ed a handout, and selecting what to display to the audience was challe nging for some. For both the present ation and t he written repo rt, one key is sue encounte red by all studen ts was int roducing their a udi ence to a new set ting (wh atev er settin g was described in their article). The studen t pres entati ons occur red a few day s bef ore the written report was du e. Ind eed, s tudent presentati ons were spread o ver thr ee cla ss day s (them ed based on the articl es chosen ). Stu dents provided f eedbac k to one anoth er via a commen t she et (c ollected b y the in struc tor, and resul ts distribut ed to spe akers anonymous ly). The comm ent sheet incl uded the follow ing questio ns: • H ow well di d the p resen ter con vey the statisti cal topic at han d? Wer e new c oncep ts clearl y explain ed? • How well d id th e presen ter mainta in y our inter est? W ere you engag ed in the pre sentati on? • Overall rating of presentation Students w ere al so abl e to recei ve other com ments (s pace wa s provid ed at th e bott om of the page) from their classmates. As t he instructor, I filled out a s imilar sheet paying attenti on to the statistical conce pts conveye d and the present ation compo nents (eye conta ct, organi zation, etc. ). Stude nts were able to incorporate their pr esentation feedback into t heir written reports. This w as very important for some stu dents to realize th at addition al expl anati on of th e settin g and t erms migh t be useful for a reader. Reports were su bmitted, assesse d, and returned to the stude nts fairly prom ptly. The asses sment rubri c for the report included the following areas (which were allocated diff erent point values): • General: Writing, spelling, proofreading, grammar, etc. • Citations (at a minimum, the article its elf must be cite d). • Topic: Are main topics from the articl e conveyed? Is an appropriate subset chosen for discu ssion if the article was very l ong? • E xplanation: How well are new concepts explained? Was appropria te research/background information obtaine d and conv eyed? Is the sett ing introduc ed appropria tely? Are terms/n otation def ined before they ar e used ? • Audien ce: Is the writing app ropriate f or the t arget audien ce (an other stud ent in the cour se)? • Statistics: Are there any iss ues in the presentation of t he statistical to pics/issues? • Interest/Creativity/Effort/Visuals: For example , is the interest le vel of the reader maintained ? Were simulations used to illu strate results? Were appropriate visuals chosen? Students received a co py of this rubri c with the ir assessmen t bef ore revi sions, so they could c learly se e what areas they had struggle d in. Stude nts were the n allowed to sub mit a revised repo rt to addres s comments, and could earn some points back (up to ha lf of what was originally los t). Revisions were un dertaken by 10 of the 1 7 studen ts. Just as a n ote, re ports were requ ested to be between 4 and 6 pages lo ng. This meant that many st udents had to pick a nd choose wh at aspect of the se lected paper they wanted to wr ite ab out i n their r eports . In the end , a fe w students went over the pa ge limit, though this was not a major c oncern for me for this assign ment. But it did make me think of other assignments where enfo rcing a page l imit might make sens e and be useful assignments for the students to en gage in. Anecd otally, most students lost points in either the Ge neral, Explanation, or Statis tics assessment areas. The challenge of explaining a new setting was particul arly hard for some s tudents. However, these issues are addressable in revisions, and all students undertaking a r evision were ab le to successfully address at least some of th e original concerns with th eir submissions. 3.3 M aterials For relevant materials for t his project, including the lis t of selected articles from Sp ring 2015, and example rubrics, ple ase co ntact th e auth or. 4. Discussion The pro jects as descri bed were compl eted in a class of 17 students . A number of easy ada ptations co uld make these projects m ore deployable for your classrooms. In bo th cases, the projects can easil y be made to be group assignment s instead o f individual assignme nts. The instru ctor could ra ndomly ass ign groups o r insist groups change betwee n projects. For the first course project on the German tank probl em, the project c ould be adapted with m ore respo nsibil i ty o n students to per form the simulat ion. Indeed, example code need not be supplie d. Instead , the instru ctor could requir e stude nts to write and submit their own sim ulation code . For the writing aspect, a revision c ould be incorporated to allow students to improve their submissions. Finally , based o n the issues st udents inclu ded, inst ructors could c onside r incorporat ing an activ ity in the cours e prior to this project about writing about simulations or tables to help student s prepare for tha t compo nent. For the se cond course pro ject on present ing and writin g about a selec ted ar ticle, a number of adaptations are possible based on tailoring the article list. For example, the ar ticle list be focused on specific topics such as Bayesian inference or confidence inter vals. Simulations could be required which would impact the selection of articles for the pro vided list to students. Si milar activities could be don e using diffe rent jour nals/magazine s dependi ng on the leve l of the audience (e.g. Signific ance). In summary , both cour se projects invo lved communica tion as pe cts ranging from written reports, writing about s imulations, and class pre sentatio ns (handout and slide creatio n, present ation skills ) that allowe d students to practice their c ommunication skills as well as deep en their statistical und erstanding. This co u rse is undergoing r evision at many institutions. For more thoughts on revisions to mathematical statistic s courses, the read er is en couraged to se e Gre en and Blankensh ip (20 15). Referen ces American Statistical Association Undergraduat e Guidelines Work group, 2014 Curricul um Guide lines for Undergraduate Programs in Statistical Scienc e, American Statistical Ass ociation, 2014. A.S. Wagaman, Writing ab out Simulations in a Theoretical Statistics C ourse, eCOTS 2016 virtual poster, 2016. J.L. Gre en and E.E. Bl ankenship, Fo stering Co nceptual Under standi ng in Mathematical Statistics, The American Statistic i an, 2 015, V ol 6 9 ( 4), 3 15 - 325. R Deve lopment Core Team, R: A langua ge and env ironment for sta tistical computing, R Fo undation fo r Statistical Computing, 20 09, 3900 051070 . Note: A version of this artic le appeared as a JS M 2016 proceedings paper f or the Section on Statistical Educati on.