An associate professor at the University of Virginia’s School of Data Science, Prince Afriyie, has been appointed to the Centers for Disease Control and Prevention in the United States.
Dr Afriyie, who is a Ghanaian, will serve for the next three years on the statistics review committee of CDC, an official communication said.
The goal of the statistics review committee (SRC) is to advance understanding and dissemination of statistical methods and testing in the field of public health and to help practitioners use this statistical knowledge to decrease chronic disease and improve health across the lifespan.
PCD’s SRC members are volunteers with training and expertise in statistics and biostatistics who assist the journal with assessing peer-reviewed articles to determine the appropriateness of the research and evaluation questions.
The following interview, published by www.tandfonline.com traces Dr Afriyie’s early beginnings from Adisadel College in Ghana through to the USA.
AR: Thanks very much, Prince, for agreeing to be interviewed for the Journal of Statistics Education. One of my standard questions for opening these interviews is: Where were you, and what were your career aspirations, at age eighteen?
PA: First of all, thank you Allan, for this singular and unimaginable opportunity. Looking at the list of your past interviewees and their stature in statistics education, I am deeply humbled and honored to be considered for such a role in the Journal of Statistics Education.
At the age of eighteen, I was a recent graduate from Adisadel College high school in Ghana, West Africa. I was also in the process of applying to a university. Yes, a university because at the time, there were four choices of universities to apply to in Ghana. With a concentration in Science in high school, my ultimate choice was the most selective university for science: Kwame Nkrumah University of Science and Technology (KNUST). Born in a patriarchal country, my father wanted me to choose medicine as a career path.
Flashback to middle school: My math teacher, known as Mr. Silence, helped me to become infatuated with mathematics by offering a small monetary reward, equivalent to about twenty U.S. cents, for solving a question relating to simultaneous equations. I was extremely motivated to solve the question because I grew up in a somewhat impecunious household, so the prize money was a potential treasure. Well, I did not win the prize, but I became obsessed with mathematics afterward—math became my video game. With no readily available textbooks or help outside of lectures, I would badger Mr. Silence after class to solicit example math questions, spend every spare moment solving the questions, and run speedily to Mr. Silence’s house for grading. My classmates quickly noticed my progress in erudition in mathematics and started seeking my help. The most rewarding part of my new daily routine was teaching my classmates how to solve math questions! This trend continued throughout my high school years, and I became known as “the unofficial math teacher.” Thus, when applying to KNUST, I wanted math to be my first choice of program of study. My father disagreed, but he agreed to list it as a third choice. Luckily, I did not get the first two choices—medicine and civil engineering, respectively—but was accepted into the mathematics program! From then on, I always knew that my true calling was to be an educator in mathematics or a related field.
AR: Lucky for us that you did not get one of your top two choices! I know very little about Ghana, so please pardon my ignorance. How unusual was your going to college—do you have any sense for what percentage of Ghana schoolchildren did? How about from your hometown—how common was going to college?
PA: That is good question because it will test my knowledge of statistical inference. However, I will have to go with my intuition and anecdotal recollection since I don’t have access to a random sample. Attending college is very unusual in Ghana. I conjecture that less than five percent of Ghanaians have a college degree. Despite the small percentage, people are communally aware of the importance of education. A ubiquitous phrase you would hear from your grandmother to a random person you meet on the street is “education is the key.” The percentage of college attendees is much smaller in my agrestic hometown. My mother was classified as educated in my hometown by virtue of her commercial/vocational school training and her subsequent job as a typist for the forestry department. My father had some high school education but left to start his own business, which is a common occurrence. Both of my parents were very keen and supportive of my (and my siblings’) educational endeavors, as they knew a college degree would be life-changing. They continued to encourage me even when that meant I would be extremely far from home pursuing my dreams of becoming an educator. Growing up, adults would describe going to college abstractly and with reverence. In fact, I did not personally know anyone attending college or with a college degree up until high school. If my memory serves me right, the first person I knew who was attending college was Mr. Silence, because I recall exchanging letters with him when I was in high school and he would write about his experiences in college.
AR: Please tell us about your experiences at KNUST. Did everything go as planned with your study of mathematics there?
PA: As stated earlier, getting into the mathematics program at KNUST was a dream come true. The excitement of getting into college and the comfort of studying mathematics made the transition fairly smooth. KNUST had the cohort model where, for example, all math majors (comprising of about 150 students per cohort) were enrolled in the same courses, including general education courses, for the entire duration of their study. We were all enrolled in 7–8 courses (equivalent to 21–24 credit units), on average, per semester. The expectations for each class were one midterm exam (worth 30%) and a final exam (worth 70%). It was assumed that students would study independently, which meant finding textbooks and appropriate example questions to supplement the lectures. The cohort model made it easy for me to make friends and find study partners, which made the independent learning style accomplishable. In between semesters, I would find a part-time job teaching mathematics even when there was no stipend for the position. In one summer break, I was able to find a full-time teaching position at Dormaa Secondary School, the local high school in my hometown. This was the first time I was an independent instructor for a course, and I relished every moment of it!
I was on track with my cohort and excelled in all my courses at KNUST. During my third year, I learned about a program called summer work abroad, where a local travel agent served as a guide for students applying to summer jobs internationally. The success stories of the program helped me germinate the idea of such a possibility. Consequently, I applied and came to work at an amusement park in New Jersey! In early June of 2004, I arrived in the U.S. full of hope and vigor. That summer, I worked full-time as a photographer and part-time as a paintball target on the boardwalk of the amusement park. I enjoyed my stay in the U.S. and made lots of friends from other countries, including Russia, Bulgaria, and Romania, who pursued a similar work program.
Let me preface the rest of the story after summer 2004 by saying that as a statistician now, I really appreciate the word “random” because random events happen in life all the time. Two days after my work study program ended, I went shopping in preparation for my return to Ghana, as my flight was scheduled to leave the following day. Whilst shopping, I randomly ran into someone I met on the plane from Ghana who also came to the U.S. for a similar position. In conversation, he told me that he was in the process of transferring to a university in Kentucky. There and then, I inquired if he would help me do the same. He acceded with alacrity and my chapter of life in Ghana changed forever. Just like that, my plans to go back home were volatilized. Subsequently, with the help of the international student’s office, I successfully transferred to Northern Kentucky University (NKU).
AR: Wow, do you still include being a part-time paintball target among your job experiences on your curriculum vita? That’s not really my question. Before we leave behind your life in Ghana, I want to ask about language: Were your classes taught in English throughout your education? What language did you speak at home?
PA: Perhaps, I should include paintball target on my CV to illustrate my humble beginnings in the U.S. I should also say that I had a shield and a thick outfit to prevent the sting of the high-velocity paintballs. There are about 80 different spoken languages in Ghana with English as the official one. The most commonly spoken language is Twi, which is the only one I speak fluently. English was inherited from our colonial masters and is the primary, if not the only, medium for education—from K-12 through tertiary—in Ghana.
AR: Did you move directly from New Jersey to Kentucky, or did you return to Ghana in between?
PA: I moved directly to Highland Heights, Kentucky from New Jersey and did not return to Ghana until 2016, 12 years later.
Education in the United States
AR: Did you continue to major in mathematics at Northern Kentucky? Were you able to get credit for much of your coursework from KNUST?
PA: I had my transcripts evaluated by the World Education Services, and it turned out that most of my math courses from KNUST transferred as physics. It also turned out that I had enough credit units to graduate but as a transfer student, I needed 15 credits from the math department and an additional 28 credits of general education courses to be able to graduate with a mathematics degree from NKU. Moreover, since most of my credits transferred as physics, I needed one additional course in the physics department to get a minor in physics. Well, there were a lot of detours along the way, but I eventually graduated from NKU with a major in mathematics and a minor in physics in 2008. The graduation was momentous as my parents were able to attend and it was an opportunity for them to visit my newfound country, America.
AR: How did your university experience in the U.S. compare to that in Ghana? What adjustments did you need to make, both academically and socially?
PA: They were very different in many ways. Academically, everything was fast-paced in the entirety of my first semester at NKU. I was consistently overwhelmed with homework, projects, quizzes, and exams. Every week at NKU felt like a final exam week at KNUST. In a sense, I had to mutate and adapt aptly—with the help of planning and good time management—to the speed in the ensuing semesters. However, I felt like I was really learning the course materials in every detail, which was refreshing. At last, I had access to textbooks, computers, reliable internet, office hours, tutoring, and every possible resource was readily available to help me learn and succeed. Also, the barrier between students and professors at NKU seemed relatively porous compared to my experiences at KNUST.
For the most part, social adaptation was an easy transition for me because of my communal upbringing in Ghana. Ghanaians are generally known for their friendliness and hospitality. It took some learning, but I managed to say and do more culturally appropriate things than inappropriate to elude culture clash. I had to come to terms with the oppositeness of some aspects of the two cultures. For instance, in Ghanaian culture, it is a compliment to call someone old because older adults are revered for the wisdom they have amassed through aging. Further, Ghanaians are very relaxed about time; being several hours late to an event is excusable (this is commonly referred to as “Ghanaian time”). Obviously, these are very opposite in the U.S. culture. Fortunately, establishing a good rapport with most people I have met in the U.S. has been uncomplicated, despite my cultural background.
AR: How did you decide on your next move after graduating from NKU?
PA: I was determined to further my education after my bachelor’s degree. Although my ultimate goal was a doctorate degree in mathematics, applying to a master’s program in mathematics made sense at the time. Upon research, Ball State University (BSU) was very appealing because of its proximity to Cincinnati, where I lived then. Most importantly, BSU had funding opportunities for their master’s program in mathematics in the form of graduate assistantship. I was fortunate to get into the program with assistantship. An exciting layer, and perhaps the deal-breaker, of my assistantship offer from BSU involved teaching undergraduate math and statistics courses.
AR: How much statistics had you studied at that point? Were you introduced to statistics at KNUST? Did you take (m)any statistics courses at NKU? Did you have much interest in statistics when you began graduate school?
PA: I was briefly introduced to statistics in high school, but I had no idea it was a discipline to pursue because it was taught as part of the math curriculum. I recall calculating statistical summaries (including mean, median, mode, and standard deviation) by hand and drawing graphs (bar graphs, pie-charts, histograms, and scatterplots) by hand. The only formal statistics courses I had taken were introductory sequence courses at KNUST, but they were taught rather theoretically. Regretfully, I did not have the opportunity to take any statistics courses at NKU. Like many statisticians, my attraction to statistics began in graduate school when I took the mathematical statistics sequence courses at BSU. Although the course sequence was very theoretical in nature, they made so much sense to me and I could clearly see the applicability of statistics, unlike my graduate school courses in math. However, through statistics I developed a greater appreciation for mathematics because it was pertinent in all the derivations.
The unveiling of statistics and thus the spark of my interest began when I was assigned to teach an introductory course in statistics to undergraduates at BSU. I really believe in the saying: If you want to master something, teach it. Teaching it brought lucidity of the concepts from my introductory courses at KNUST. I would also be remiss if I did not commend my teaching mentor then, Dr. Rebecca Pierce, and the textbook assigned for the course. The simplified instructor edition of the textbook was very clear, thorough, interesting and had lots of example to drive home statistical concepts. Coincidentally, the textbook, which I still own a copy of, is Workshop Statistics, by Allan Rossman, Beth Chance, and Robin Lock. Little did I know that this book was foreshadowing the opportunity that I would have to work with Allan and Beth—two of the most highly respected names in statistics education—at Cal Poly in San Luis Obispo.
AR: You earned a master’s degree in mathematics at Ball State, right? How did you decide about what to do next?
PA: I graduated from Ball State with a master’s of art degree in Mathematics. I was still set on keeping the torch of education and knowledge burning to the highest level. Taking the theory sequence courses and teaching an introductory statistics course at BSU converted me from mathematics to statistics, so I applied to statistics Ph.D. programs afterward. The next chapter of my education took me to Temple University’s Ph.D. program in Statistics. I was again fortunate to be awarded a graduate assistantship with a role in teaching undergraduate courses in business statistics and calculus.
AR: That must have been a big change—from mathematics to statistics, from master’s to doctorate level, from rural to urban setting. How challenging were those adjustments?
PA: Indeed, those were life-altering changes. My mathematical background was suitable for a doctorate program in statistics and helped in making the transition, especially for my theoretical coursework. The statistical methods courses required different thinking and swift adjustment, which I embraced. For instance, understanding the underlying mathematics for logistic regression was unexacting, but communicating the model was a new skill to master. I appreciated both the theoretical and methodological courses as well as the connections between all courses. One of the most enjoyable projects during my first semester at Temple University was using data from the surveillance, epidemiology, and end results database to build a model to predict one’s proclivity for cancer based on several predictor variables. This project connected most of the facets of statistics—methodology, theory, computing, and communication. Additionally, I was able to supplement my computing proficiency with statistical software languages such as R and SAS.
Moving from Muncie, Indiana, to Philadelphia required some adjustments, ranging from palatable food trucks to setting a reminder to lock my car doors. Like every major city, Philadelphia is busy, densely populated, and diverse. The variety of restaurants (including Ghanaian restaurants), rich history, art museums, and beautiful parks made Philadelphia livable. Thankfully, the adjustments to schoolwork and lifestyle were smoother with a collaborative Ph.D. cohort. The entire cohort got along from the outset, as most of us collaborated on coursework and explored our new city together.
AR: Did you continue to have a teaching-focused career in mind throughout your Ph.D. studies? How did your teaching develop over these years?
PA: Yes, I had teaching-focused academic jobs in mind throughout my studies. At the beginning of my teaching career, I spent all my preparation time on the content of the lesson. As I developed as a teacher, I became cognizant of the importance of delivery and accessibility of the course material as a supplement to content preparation. With larger class sizes at Temple University, my goal was to make the material accessible to a majority of, hopefully all, students regardless of the content. I found that designing a lesson plan while identifying with the students helps in making the lesson interesting, fun, and accessible. Accordingly, my teaching philosophy became focused around accessibility and clarity.
To bolster my teaching experience, I worked part-time as an adjunct instructor at nearby La Salle University in addition to teaching at Temple and working on my dissertation. I was also involved in teaching for the academic discovery program (ADP) at La Salle. The ADP helped disadvantaged students gain admission to La Salle University after successfully passing courses offered in a special summer session. I taught a course on math myths and realities (primarily based on topics in introductory statistics) for the program. This program was very impactful for the students, but having the opportunity to teach these students from broad backgrounds was in turn impactful for me personally and my development as a teacher.
AR: Please tell us about your Ph.D. research.
PA: I worked with Dr. Sanat Sarkar and Dr. Karthik Devarajan (Fox Chase Cancer Research Center, Philadelphia) as advisors for my dissertation: application of procedures controlling the tail probability of the false discovery proportion (FDP). Controlling the tail probability of the FDP is a new focus of research under multiple hypotheses testing (multiplicity). The classical approach to tackling multiplicity is to control the probability of at least one Type I error among all hypotheses, known as the familywise error rate (FWER). However, the FWER is often conservative, especially when the number of hypothesis to be tested is large. The false discovery rate (FDR), which is the expected proportion of Type I errors among all rejected hypotheses, was introduced by Benjamini and Hochberg (Citation1995) as a more liberal error rate metric in multiplicity. However, procedures that control the FDR are usually affected by dependence among the p-values.
A proven solution to the problem of dependence among the p-values is to control the probability of the FDP exceeding a fixed threshold γ∈[0,1), the γ-FDP. This recent error rate metric was introduced independently by van der Laan (Citation2004) and Genovese and Wasserman (Citation2006) as less-stringent alternatives to the FWER and the FDR. The pertinence of the control of this error rate metric is apparent in most application areas like microarray experiments and digital gene expression experiments, where massive numbers of hypotheses are tested simultaneously to elicit the number of differentially expressed genes among many genes which are highly dependent on each other.
We developed four new step-up procedures controlling the γ-FDP. The first of these procedures is developed by modifying the critical constants of the BH procedure to suit the γ-FDP control under both independent and positively dependent test statistics. The three others are step-up and adaptive procedures implemented in two stages with tasks of estimation and incorporation of the number of true null hypotheses in the first and second stages, respectively. Inspired by the fact that adaptive FDR controlling procedures like Benjamini, Kreiger, and Yekutieli (Citation2006) are more powerful than their nonadaptive counterpart the BH method, our two-stage procedures provides an improvement and offer alternatives to existing procedures that control the γ-FDP. Moreover, our new procedures are easy to implement and computationally inexpensive, regardless of the number of hypotheses to be tested, making them easily applicable to high-dimensional data. In collaboration with the statistics department at Fox Chase Cancer Research Center, we were able to apply and investigate the performance of several multiple testing procedures (along with our new procedures) on microarray and digital gene expression data to find differentially expressed genes among thousands of genes.
AR: You earned your Ph.D. at Temple and embarked on a job search. I know very well how your search turned out, because I chaired the Statistics Department at Cal Poly—San Luis Obispo when you accepted the offer to join our faculty. What kind of positions did you apply for, and what did you think of the hiring process from the applicant’s perspective?
PA: I applied to both tenure-track and nontenure-track teaching-focused academic positions across the U.S. It was the most auspicious job search I have embarked on, which was comforting because it was my first real job search as a professor. I received offers from everywhere I interviewed, including an informal offer from Temple University’s Fox School of Business. The interview process was taxing since I agreed to so many interviews around similar time frames. Nonetheless, I enjoyed meeting multitudes of statisticians of various specializations, sightseeing various campuses and cities, and, of course, the nice meals. I particularly enjoyed sharing ideas on effective teaching. One main tenet of the teaching profession is repetition to ensure better understanding of the material. This came into play during the interview process, as I answered and asked similar questions with every department.
As you pointed out, Allan, Cal Poly was the best choice for me in the end. I made this choice for several reasons: it was the top school for undergraduate statistics, the statistics department was very organized, all the faculty seemed to enjoy teaching, and faculty members seemed collegial. I could discern the established rapport between students and faculty as I walked down a hallway of open doors overhearing lively discussions. The prospects of working alongside notable statistics education researchers were also alluring. Across the board, it was truly a great department to be part of. The added bonuses were the natural beauty and weather of the area. I enjoyed the contrast of the ocean, mountains, and the uniqueness of various surrounding cities, combined with the most desirable weather all year round. After the interview, I couldn’t wait to tell my wife all about the department and the area’s beauty. It was an obvious yes upon receiving the offer, and I am glad that materialized nicely.
AR: What questions do you recommend for other interviewees to ask?
PA: Let me begin by quoting you, Allan. Ask good questions. Academic job seekers should keep in mind that the interview process goes both ways: Departments interview applicants to find the best candidate to hire, and applicants in turn interview departments to find the best fit. Therefore, preparing good questions to ask is essential. I would recommend asking questions that depict your keen interest in working at the department/university. For example, “I noticed on your website that tenured professors tend to teach the more advanced courses offered by the department. Are there opportunities for new faculty members to teach advanced courses, like STAT xxx?” I would also recommend asking questions that aim to elicit a consensus answer by faculty members in the department. For example, “what do you like (and dislike) about working at this department/university?” Further, steering away from questions with answers that are readily available on the department’s website is perhaps a good idea. I would also refrain from financially related questions, at least initially.
AR: Having been a student for so many years, in two different continents and three different states, what was the most challenging aspect of adapting to the life and work of a university professor?
PA: I have been privileged to hold the title of a university professor. In my mind, being a university professor is one of most prestigious positions in society. This status comes with immense responsibility—both inside and beyond the walls of the classroom. Constantly striving to be my best self to fit my role is probably the most challenging aspect of my job. This includes being an effective teacher, setting a good example through my actions, remembering to encourage students to pursue their dreams, and being aware that every word uttered to a student has an impact. My experiences as a student guide me on this journey to help make our society better through education and empowerment of students, our future leaders. Whenever I can, it is my hope to pay forward the benefits I have enjoyed from the most influential teachers who have helped shape my future to be who I am today.
AR: What has surprised you about students at American universities? Perhaps you can identify one pleasant surprise and a less pleasant one.
PA: That is a great question, Allan. This might come as a surprise to most instructors, but one pleasant impression is that I find a majority of students at American universities to be honest. In my experience teaching at various universities, most students abide by the expectations set in the course syllabus and uphold academic integrity standards. Let me explain with an example. In grading exams, I tend to round total scores to the nearest whole number. Over the years, I have had a good number students approach me at the end of class to acknowledge the extra half a point as a miscount of their total points on the exam. I am yet to gather more data on this with the current and abrupt shift to online teaching, but I trust that most students will continue to uphold academic honesty standards.
This might not surprise most instructors but a less pleasant request—it feels like a demand sometimes—by students at American universities is a practice test as a means of preparing for every exam. I have succumbed to giving a practice test on a few occasions and found that some students ignore the rest of the material and only study the practice test. I think a more exhaustive preparation is studying the course material—in-class notes and previous assignments. I should point out that I am not completely against practice tests. They are absolutely necessary for asynchronous web-based courses when the instructor is somewhat removed. Also, a practice test is necessary when the test covers a broad range of topics. I was very grateful for all the available practice tests when preparing for the graduate record examination (GRE).
Teaching Statistics and Data Science
AR: At Cal Poly you taught two different course sequences—an introductory sequence for business majors and a sequence in mathematical statistics for statistics majors. For each of those course sequences, please tell us the topic that your students found to be the most challenging, and describe how you tried to help them with understanding that topic.
PA: Like all introductory statistics courses, the most challenging topic for students in my business statistics sequence courses was sampling distributions—a fundamental background for statistical inference. Sampling distributions is perhaps the hardest concept for many students in introductory courses to wrap their minds around since there are literally so many moving parts to it. Without loss of generality, I will focus on sampling distribution of the proportion. I try to help students understand the sampling distribution of the proportion by using the classic Reese’s pieces class activity. I provide a bulk amount of Reese’s pieces to the class and ask every student to take a random (thoroughly mixing and blindly selecting the candies) sample of 25 candies and note the color. I then ask each student to calculate the proportion of orange candies among the 25 candies and then make a dotplot of all the sample proportions on the black/white board. With small class sizes at Cal Poly, it was sometimes difficult to observe the convergence of the sampling distribution of the sample proportion to a normal distribution. To observe the convergence, I combined all the proportions from all the students across my sections of the course. Afterward, I showed them the elaborate simulation from the Reese’s pieces applet at rossmanchance.com to bring it home (thanks to you, Allan and Beth!). Recently, in my attempt to be frugal, I have been illustrating the same concept with playing cards and looking at the distribution of the proportion of red cards in a sample of 25 cards. The main difference between the two activities is that the parameter—proportion of orange candies among all Reese’s pieces—is unknown (at least by students) in the Reese’s pieces activity, whereas the parameter—proportion of red cards among all playing cards—in the playing card activity is known. There are advantages to both approaches. The Reese’s pieces activity helps students understand the broader topic of parameter estimation (via confidence intervals), while the playing cards activity helps students understand the sampling distribution formula since the parameter is assumed to be known.
The mathematical statistics sequence is perhaps the most challenging for statistics majors. These courses utilize a strong mathematical background on algebraic manipulations, calculus, and a proof-based math course such as real analysis or abstract algebra. The chapters covered in the two-part sequence that I taught include special probability distributions, estimation, hypotheses testing, and nonparametric methods. I find the collection of topics under estimation to be the most challenging for students. Finding estimators using methods like maximum likelihood, method of moments, and the Bayesian approach is typically routine and students get it. However, evaluating estimators—using unbiasedness and the squared error loss function—and the subsequent topics are not as straightforward for students. To help students understand these concepts, I start by giving an intuitive definition of both concepts. Let me start from unbiasedness. An estimator is said to be unbiased if it does not over-estimate or under-estimate a parameter, on average. In other words, an unbiased estimator has no bias—the long-run average of the estimator is equal to the parameter itself. Next, using the squared error loss function, we can evaluate an estimator by taking the long-run average of the squared difference of the parameter and its estimator—this is known as the mean square error (MSE). Using this metric, the estimator with the smaller MSE is a better one. For unbiased estimators, the MSE is equivalent to the variance of the estimator. With a concrete understanding of these two aforementioned concepts, it is easy for students to understand the meaning of the best unbiased estimator (or efficient estimator)—among the class of all unbiased estimators. The efficient estimator is the unbiased estimator with the least variance. Consequently, these concepts provide a background to help students understand and see the motivation behind the Fisher information, Cramer–Rao lower bound, and the need to improve a crude unbiased estimator through Rao–Blackwell-ization.
AR: Last summer you moved from Cal Poly to the University of Virginia (so now you have lived in five different states). I understand that you have taught an introduction to data science course. Please tell us about that course and how it differs from an introductory statistics course.
PA: The emergence of the field of data science is exciting for many students. The definition and constituents of data science are still fluid, as it is dependent on whom you ask. I will attempt to give my definition at the end. Indeed, I have been teaching an introduction to data science with R course since the fall semester of 2019, when I moved to University of Virginia (UVA). In my first semester, I taught the course as an introductory statistics course with emphasis on coding in R, borrowing ideas from the notable Data 8 course at UC Berkeley which is taught in Python. Since then, I have made some revisions to the course to include even more coding while keeping intact the statistical principles. First, let me talk about the backgrounds of the students who take this course. The course has no prerequisites and it is required to declare a major in Psychology but it is open to every student to enroll. The distribution of students’ year at UVA in the class is about uniform and the course attracts students from all majors by virtue of its popularity. These diverse attributes makes it a fun course to teach, since there is no limitation on areas of statistical application to extract examples, but challenging at the same time, since it is difficult to target a suitable level to teach the course.
I start the course by collecting data on the students via Google spreadsheet. With a big class size, I get a decent size dataset with several variables. The hope is to motivate every lesson with relatable data to help students understand the course concepts. In addition, I use many big datasets from diverse application areas throughout the course. The first week of the course is spent on guiding students to install R (and RStudio Desktop) and explore the basics of R, as well as showing them how to use R Markdown for authoring their homework. Next, we cover more basic topics in R—data structures, installing and loading R packages, importing and exporting data, and finding summary measures. I use this opportunity to talk extensively about measures of center and spread. We then move on to traditional coding approach to data wrangling and manipulation in R. We proceed with more data wrangling techniques but with a more intuitive approach to coding in R using the dplyr/tidyverse package (I typically wear a t-shirt with the dplyr logo for this lesson). The next lesson is spent on data collection and cleaning, which involves web scraping. We then move on to data visualization. My principle on data visualization is borrowed from the adage that “a picture is worth a thousand words.” We talk about the named graphs in statistics and then create elaborate graphs such as density plots, violin plots, bubble plots, and moving bubble plots using the gganimate package. Throughout data visualization, we focus a lot on communicating what the graph reveals.
Following data exploration through wrangling, summarizing, and visualization is drawing robust conclusions beyond the data—modeling and statistical inference. The lessons on modeling—simple linear, multiple, and logistic regression—focus on coding the regression model, model selection, finding a correlation matrix to address multicollinearity, interpreting the regression output, and making predictions. We then spend time on one-sample and two-sample inference with focus on coding and interpretation. I leave out the underlying formulas utilized in a typical introductory statistics course but emphasize coding and interpretation of outputs. Thus, the working definition of data science in mind throughout the course is the extension of statistics by taking full advantage of computing (extensive coding in R in our case), which I find to be in concordance with many definitions of data science.
AR: How many students were in this class? For how many hours per week did it meet? Did you use a textbook? I ask these things because your description sounds like a very full and ambitious course. It seems to include much of what we typically cover in “Stat 101” plus more—such as multiple and logistic regression—in addition to all of the coding and visualization. Did you leave out more than just formulas in order to introduce students to all of these topics?
PA: I typically teach three sections of the course with about 100 students in each section. It is a three credit-hours course that meets two days a week for 75 min each day. I provide students with all course materials, including R Scripts, handouts, and slides. Hence, there is no required textbook for the course, but the suggested resources are Learning R by Cotton, R Cookbook by Teetor, and Statistics, 4th edition by Freeman, Pisani, and Purves. The first half of the 16-week semester is spent on introduction to R, data wrangling, summarizing data and data visualization. The second half is spent on regression and inference. There is usually enough time to cover all these topics. A typical class introduces the main idea with a motivating example, live coding with student participation, communicating results, and a class activity at the end. Sometimes students are put in groups to work on the class activities. If there is enough time, we go over the class activity together or the solution is posted for students after class. During the live coding session, I pause to answer questions and help with error messages in R. Of course, I also pause to ask and answer questions throughout the class duration.
AR: You mentioned earlier that understanding sampling distributions is the key to learning concepts of statistical inference and that this is the most challenging topic for students in an introductory statistics course. In an introduction to data science course, do you have time to allow students to explore sampling distributions to prepare them for learning concepts of inference?
PA: Yes, I do, but my approach to showing the concept of sampling distributions is slightly different in my introduction to data science course. At this juncture in the semester, students are comfortable with coding and creating visualizations in R, and this helps with simulating and visualizing of sampling distributions. I begin with an extra credit activity assignment outside of class. I ask students to flip a coin 25 times, calculate the proportion of heads in the 25 flips and submit their answers in a shared Google spreadsheet. We graph their sample proportions in a histogram and find the summary measures. It is very helpful with a large class size, since it is easy to observe the approximate normal distribution of the sampling distribution. I use this opportunity to briefly introduce the binomial distribution, which comes up again in logistic regression. In particular, I show them how to generate random samples from the binomial distribution and use it to simulate the sampling distribution of the proportion. From here they can iteratively see the convergence to normality as the number of samples increases. We also find the summary measures for the simulated distributions, which alludes to the sampling distribution formula without stating it explicitly. I use this concept as a reference throughout statistical inference.
AR: How do you assess student learning in your data science course—primarily with exams or projects or what? What kinds of questions do you ask?
PA: Students’ understanding is assessed through weekly homework, two midterm exams, and a culminating final project. Every homework assignment involves using a dataset and gives students further practice on the week’s content. For instance, after covering data wrangling, there is an assignment on how to use some the techniques to transform a messy dataset into tidy data (observational units on the rows and variables on the columns). The content of the first midterm is based on the material covered in the first half of the semester, which is mostly on coding in R. The exam tests students on the use of R functions by exploring a small dataset. The second midterm is based on regression and inference. The exam tests students’ conceptual understanding of the topics as well as interpreting results and outputs. The final project gives the students a culminating experience of data science by applying techniques and ideas from the course on a dataset and communicating findings in a report. They can find the final project dataset online (e.g., kaggle) or by scraping the web or by collecting data on their own. I also make several datasets available to choose from if needed.
AR: I’m sure that your teaching environment changed as a result of COVID-19. Please describe how you made the transition to remote teaching. What impact do you think this disruption had on student learning?
PA: The undisputed and unfavorable impact of COVID-19 will be felt in educational institutions across the world for many years to come, unfortunately. For most students and educators in the U.S., the switch to online due to the upsurge of COVID-19 cases was abrupt with only a week to transition. At UVA, we were a few days into spring break when we received the message to migrate all classes online for the foreseeable future. Without a doubt, the abruptness of the switch to online was very disruptive to student learning. Dealing with the devastation of COVID-19 and making abrupt life changes, just to list a few, are singular and unfortunate events that are affecting all of us. Couple that with the unsuitable home learning environment for many students, I presume made it very difficult to learn.
Another area of disruption to student learning, at least some students, is online learning itself. For a similar reason why people enjoy live and in-person shows/performances rather than watching on TV, most students and educators succeed and highly prefer in-person classes. However, I don’t want to minimize the fact that some students and educators thrive in online learning and instruction, respectively. Nonetheless, I applaud all students and educators for adapting and persisting through the tasking educational obligations amidst the extraordinary circumstances.
Like many educators, I deliberated both synchronous and asynchronous delivery methods for my courses in the spring. Synchronous delivery mimicked “live” class sessions, and asynchronous delivery allowed flexibility for both faculty and students (in particular, international students). I settled on a hybrid approach. I recorded and posted all my lectures as well as holding a live Zoom session during class times to answer questions on the lecture videos and any general questions for that matter. I recorded my lectures using the Screencast-O-Matic application. It was easier to just capture my computer screen with the app because most of my lectures involved coding and showing slides along with annotated notes. Recording the lectures was very time-consuming because I strived to be clear, succinct, and perfect. Well, I got better with sufficient practice, but along the way I had to adopt the philosophy of not letting the perfect be the enemy of the good. I also assumed that students’ attention span is probably very good when watching a good movie or playing video games but is probably very low for educational videos. Presumably, I could have their attention for about 15–20 min at a time, but compressing a 75-min lecture into 20 min was a challenge. A good balance was to compress my lectures into a maximum of 50 min and make it a point to remind them during the video to take a break at every time frame of 20 min. Most students noted that this was very helpful to help them digest the material.
AR: As we conduct this interview in June of 2020, COVID-19 is not the only current event in the news. The country has seen massive protests about racial injustice. Moreover, I know that Cal Poly experienced an incident in which a student wore blackface while you were there, and your current residence of Charlottesville was the site of considerable racial tensions a few years ago. Let me start with a very open-ended question: As an African who immigrated to the United States, what is your perspective on the topic of racial injustice in the U.S.?
PA: One of the courses throughout grade school in Ghana focuses on Ghanaian history, which is heavily intertwined with slave trade and slavery. We were taught about the horrendous slave trade and how our leaders aided and abetted the process. Sadly, it was taught without a trace to the ongoing realities on the trail of slave trade and slavery. Before moving to the U.S., I had no inkling of the aftermath of slavery and how our brothers and sisters, all around the world, are still living with the repercussions. I was awakened and appalled when I moved to the U.S., as I was able to solve the puzzle and put everything in perspective. I could see the aftermath of the devastation due to slavery in African-American communities everywhere I lived and visited in the U.S., including New York City, Newark, Cincinnati, and Philadelphia. I also took a history course at NKU where I learnt about the history and the journey of African-Americans when they arrived on U.S. soil. To be honest, I was very outraged to learn about Jim Crow-ism and maltreatments of people of color. I am not known to skip out on anything, but I skipped this class on several occasions because I couldn’t bear listening and reading about the horror due to the cruelty and abuse of people.
Unfortunately, some parts of the dark history resurface in African-American communities today, as we witnessed the brutal murder of George Floyd and hence the reliving and re-ignition of anger that is reverberating all around the world. The reality of the disparity in terms of education, opportunities, and the injustices for African-Americans and black people around the world is so black-and-white and needs rectification. I endorse the current Ghanaian president and his team on their initiative to host black people from all around the world in Ghana. Last year, Ghana hosted multitudes of people of African descent by branding the year as Year of Return in an effort to defy the Door of No Return sign in the Cape Coast castle where slaves embarked on their harrowing journey to the western world. I think this was a good step to begin healing and mending of our painful wound in our joint history.
Saying that I have lived the African-American life would be disingenuous. Nevertheless, I am able to enjoy life in the U.S. because of the fight by African-Americans led by heroic figures like Dr. Martin Luther King. As a result, I have not personally experienced any unfair treatments in the U.S. by virtue of my color. Although, I might have but I lack the context for discernment. Throughout my 16-year period of living in the U.S., I have felt different emotions on a spectrum about race—spanning from indifference to embrace of my societal binning and categorization—which is probably dependent of the stage on my journey. I have often cited my uncommon life trajectory and said that race has nothing to do with someone’s path to living a fulfilled life and referenced my upbringing in Ghana where race was not something I thought about on a daily basis. My conspicuous complexion did not play a conscious part of my track to achieving any goals in life, for which I am glad. (Don’t get me wrong, we have our own injustices relating to tribalism and ethnicity.) I now realize my blindness to the regretful and unbreakable vicious cycle of inequities and lack of opportunities in communities of people of color. I have a son who will be experiencing a completely different life than mine, and it is my fervent hope that he lives a fulfilled life regardless of his societal categorization and race.
I hope the silver lining of the recent racial tensions is mindfulness on race. We as a people need to transform our mindsets, both consciously and unconsciously, about race. We can change the laws to make things better, but what can really make a difference in our daily lives is changing our mindsets and treating everyone as we want to be treated. We are all in this together. Changing laws, transforming mindsets, and tackling issues of injustices squarely today will help create a better world tomorrow. Our goal for a better future should surround the fact that someone’s complexion (and for that matter gender, sexual/gender orientation, creed, disability, etc.) is not, and should not be, a good predictor of who they become. We should not deprive our world of the next Einstein (or any great scientist) because of a mere societal categorization. Life is very brief. Everyone should be accorded with dignity and respect that we all yearn for and deserve as humans in our shared brief moment in life.
AR: Thanks very much for your thoughts on this, Prince. What do you think can be done to increase participation by under-represented groups in STEM fields, particularly in our discipline of statistics?
PA: Great question, Allan. I agree with the general solution that has been hypothesized by many researchers in education, which is increasing the number of under-represented teachers. However, this circles back to breaking the vicious cycle I talked about earlier, especially when it comes to recruiting teachers of color. Allow me to revisit Ghana, my exclusive point of reference, again on this topic. Students’ accessibility to all levels of education in Ghana is boundless by geographical location. For example, I attended high school about 8 hr away (about 257 miles but on bad roads) from my hometown where I did my primary education. I was able to get into one of the best high schools in Ghana by merit. Also, a couple of my siblings attended primary school far away from home in a boarding school. My point is that one can grow up in an underprivileged neighborhood/town but can attend K-12 (as well as tertiary) schools all across Ghana purely based on merit and probably affordability. This is very similar to the charter school model in the U.S. but it is accessible by every qualified student in Ghana. Such a system can help with equity and increase the number of under-represented students and teachers in STEM fields. The under-represented teachers can be role models and a source of inspiration to the under-represented students and thereby help to create a new and positive cycle.
Additionally, under-represented college professors (including me) should reach out to local schools to showcase a cool project/activity about our disciplines and interact with students. This could help inspire under-represented students to get interested in STEM by projection. Specifically to statistics, apart from the aforementioned points, we have an advantage over other STEM disciplines because we are in the coolest and hottest field. I think we need teachers to help promote the awesomeness of our discipline to all students and thereby capture students from under-represented groups. Statistics teachers at various levels should use interesting and current data examples to illustrate how statistics can be used to draw robust conclusions, see patterns in data, and make predictions about our world using incomplete data. For instance, Amazon and Netflix can make recommendations to customers on what they might like based on available data. We should also emphasize the need for statisticians in almost every industry and highlight the innumerable career options for statisticians.
AR: I know that you worked one-on-one with some students from under-represented groups at Cal Poly. Have you had a chance to do the same in Virginia? What have you learned from those students about their experiences and challenges? What are the keys to providing mentorship for them?
PA: Good point, Allan. Faculty mentorship for under-represented students should be an addendum to my previous response. Faculty mentors can help coach these students academically and personally. Mentorship can also provide students with the opportunity to socialize with professors, which is unlikely in most settings. The keys to providing good mentorship to students is listening, sharing experiences, and offering advice if needed. My assigned mentees through Cal Poly’s mentoring program were in STEM areas, which was helpful. I met with them almost every week. The first conversation topic is sharing how our week went. If they had any quizzes or exams, I asked them how they prepared and how it went without any judgment and condescension. If warranted, I shared with them a related experience when I was a student. I also made it a point to give them a useful tip of some sort every week to help them academically and personally. I relished being a mentor and building friendship with these students at Cal Poly, and we have continued to stay in touch. The positive experience also provided me the impetus to sign up to be a mentor for graduate students through the UVA mentoring institute program for this upcoming year.
One of the pillars to finding meaning in life is belongingness. A heightened sense of belonging can inspire someone to pursue a goal and aim for the best in all endeavors. Belongingness can allow peer pressure (I mean positive peer pressure) to work. Being similar to others helps us create a sense of belonging. In my experience, my mentees from under-represented groups lack this sense in college, unfortunately. Oftentimes this manifests in lack of interest and consequently makes academics challenging. I wish under-represented students felt similarity with other students and hence a sense of belonging through common goals, courses, fields of study, and general interests rather than race, gender, sexual/gender orientation, creed, or disability. Having good mentors and role models can help under-represented students transcend beyond these dissimilarities.
AR: Let’s move on to the “pop quiz” portion of this interview, where I’ll ask several questions, many of which will move beyond the teaching of statistics, and I’ll ask that you keep your responses brief. First, please tell us about your family, back in Ghana and also in the U.S.
PA: I am lucky to be married to my best friend and the most incredible person alive. Together we have an eight-month-old son, who is just perfect! We are very fond of him and we can’t wait to show him how beautiful life is. Through marriage, I have been extremely lucky to join the most amazing family here in the U.S. My wife’s entire family represents the best of America—they are the most loving, caring, woke, and compassionate family I have ever seen. In Ghana, I have an extra-large family. My nuclear family consists of my parents and my two younger brothers. My parents, whom I owe everything to, are still instrumental in my life. My mother is the best mother anyone could ask for. She effortlessly raised three recalcitrant boys. My dad, who recently became a sub-king in my hometown, is a visionary businessman. My middle brother also graduated from Ball State University and studied statistics. He is currently teaching at Ivy Tech Community College in Indiana. My youngest brother recently graduated from college in Ghana with a major in history and is hoping to join us in the U.S. for his graduate studies.
AR: I have to follow up by asking: What does being a sub-king entail?
PA: Ghana is a chieftaincy-based society. Every village, town, city, and constituency has a queen, king, and sub-kings who report to them. My dad was installed as the king among all the sub-kings in my hometown. This is comparable to the chief of staff in the White House setting. This comes with a lot of pride for my dad. I have to address him as a King when I talk to him now. I guess that makes my name unintentionally befitting, in a sense.
AR: What are some of your hobbies?
PA: I like to enjoy and appreciate nature in any way I can. Besides that, I like playing soccer and racquetball. I also enjoy watching professional tennis and play-off games for most sports, including football and basketball. I am more involved in watching college basketball now because I walk on the same grounds with the national champions, UVA Cavaliers.
AR: Please recommend a book (not a textbook), a movie, a musical selection, and a place to visit. To make this more fun, I’ll ask you to recommend one item in one of these categories, two items in a second category, three in a third, and four in a fourth.
PA: Unlike my wife, I am not a big nontechnical reader. However, the last enjoyable book I read was Sapiens: A Brief History of Humankind by Yuval Noah Harari.
Movies: Pursuit of Happyness starring Will Smith and Antwone Fisher starring Denzel Washington.
Musical selections: Ghanaian highlife music (K. Frimpong and his Cubano fiestas) and hiplife music (Sarkodie).
Places to visit: Dotonbori area in Osaka, Japan; Cambria, CA; Yellowstone National Park, WY; and Coconut Grove Resort, Cape Coast area, Ghana.
AR: That will be a long trip, as you’ve included three continents there. Here is a fanciful question: You can travel in time to observe what’s going on in the world for one day. What time would you travel to—in the past or the future—and why?
PA: That is fanciful, Allan. I would definitely travel to the future. I would like to witness how far (and fast) we, as a species, can travel through the cosmos and our discoveries about the universe. I would also like to see the realization of my ideal future of humanity: being in tune with each other (as well as our planet) and coexisting in harmony.
AR: Here’s another silly one: You can have dinner anywhere in the world (all expenses paid) with three companions, but the dinner conversation must revolve around teaching and statistics. Who would you invite, and where would you eat?
PA: I would invite David Blackwell (as a frequentist), Andrew Gelman (as a Bayesian), and Hadley Wickham (as an expert in statistical computing) to reflect on the past, present, and future of statistics and how it should be taught. I hope they all like steak because I am thinking a top steakhouse restaurant, probably in Kobe, Japan.
AR: Let’s collect some data: Do you consider yourself an early bird or night owl? On what day of the week were you born? How many of the 50 states have you set foot in? How many miles do you live from your birthplace?
PA: I was a deep night owl during my graduate school days, but I am now an early bird (with strong coffee). It is easy for a Ghanaian to answer a question on what day of the week they are born. My middle name, Kwame, is the name for all males born on Saturday. I have been in 24 states. I currently live 5619 miles from my birthplace, according to Google maps.
AR: What are you most proud of with regard to your teaching? What aspect of your teaching do you think needs the most improvement?
PA: As an instructor, I aim to be very clear and concise, in terms of breaking down complex concepts to simpler terms, to reach students at all levels. In fact, I learnt this philosophy from one of my best and most impactful teachers at NKU—Dr. Chris Christensen, whom I had for a course in cryptology. Fortunately, I regularly get a lot of positive feedback from students on my course evaluations about how accessible my courses are. Thus, a prideful accomplishment. I think an area of my teaching that needs improvement is to bolster participation by involving students during class, especially for my larger classes. I typically teach my courses in a lecture style setting. I think most of my students are engaged during class, but I need to think of creative ways to enhance their participation. Student participation is even more challenging for me to foster in virtual class settings, which has been common of late due to our current predicament. Perhaps, I should borrow ideas for you, Allan, and invest in teaching my courses in an activity-based setting and/or using simulation-based methods.
AR: Thanks very much for agreeing to this interview, Prince, and for providing such thoughtful answers to my questions. I realize that I should have asked more specifically about your position at UVA. I believe that it’s a teaching-focused position within a research university. Do I have that right? What are your teaching responsibilities, and what are the other expectations for those in your position? Perhaps you could also tell us what prompted your move from Cal Poly to UVA.
PA: Good discovery, Allan. This would have been the missing piece in the interview. One key reason for leaving my tenure-track position at Cal Poly was to move closer to my wife’s family—this became even more important when we decided to start a family. That is correct, Allan, my position at UVA is teaching-track (namely, General Faculty), and I am currently at the assistant professor level. The position entails a 90% teaching role—with a teaching load of three courses per semester—and a 10% service requirement. My department has been very kind and nice with only one course preparation so far. I have taught three sections of the same course (introduction to data science with R) in my first year here.
AR: I always close by asking what advice the interviewee has for those just starting a career in teaching statistics. I will ask that of you next, but because you’re fairly new to this career yourself, I want to ask if you have any advice for more experienced faculty. What would you recommend to us in order to help newer teachers to a good start in their career?
PA: A commendable feature of both Cal Poly and UVA departments of statistics is allowing and valuing the opinions of newer faculty, including assistant professors and lecturers. I think that is a good step to helping newer faculty feel welcome and be comfortable in the department. Also, promoting a supportive departmental atmosphere where newer faculty can ask questions and seek mentorship (or advice) from experienced faculty is always helpful. This could be informal chats to share ideas on effective teaching strategies, research, and any general topics.
AR: What advice do you offer to those who are just starting out in a career of teaching statistics?
PA: Well done, Allan, on a good interview and thanks again for this opportunity. The best advice comes with lots of experience but I will do my best with my brief experience in teaching. Let me begin with an analogy. I learnt how to drive with a stick shift on bad roads. I remember the arduousness of learning the new skill and the abrupt engine stops. Like most people, with persistence and practice, I got better and driving became second nature over time. As a new teacher, there might be force starts and missteps, but these are essential part of practice and learning. We are able to be a teacher by virtue of our persistence through years of education; our persistence will carry us to be better teachers as well. With persistence, we can invest time into developing and fine-tuning our teaching to find a suitable philosophy. With persistence, we can seek advice and mentorship from established faculty members whom we admire in teaching and research. The other side of the analogy is of paramount importance: teaching someone how to drive. Just as the student driver’s safety (and success) is inter-connected with the teacher, our success as educators is always tied with our students’ success. A good daily reminder for us as educators should be as follows: We are here because some of our teachers put us first and were very influential on our lives. It is time to reciprocate. In my mind, being a teacher is like being a parent. In the moment, we might be incognizant of the fact that our patience, care, and step-by-step guidance can revolutionize a student’s life.
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Sharaf Mahama celebrates 26th birthday with a donation and reading session with kids
Sharaf Mahama, the son of former President John Mahama, celebrated his 26th birthday with a donation and a reading session with the children at the Chance for Children Orphanage Home in Nsawam, located in the Eastern Region.
On his 26th birthday, which was celebrated yesterday, Sharaf, accompanied by some of his close friends, paid a visit to the orphanage and donated food, household items, and books to the children. Also, they spent the day reading a variety of children’s books with the kids and shared a meal together.
Items donated included 20 bags of rice, 5 bags of sugar, 4 large packs of toilet paper, 5 boxes of tomato paste, 2 boxes of cooking oil, 2 cartons each of Nido and Milo, 24 packs of beverages, 28 packs of biscuits, and 20 packs of water.
Among the books read with the children were ‘Ananse and the Sticky Gum’, ‘The Widow of Nain’, ‘101 Favourite Stories from the Bible’, ‘Courtesy for Boys and Girls’, ‘Better Late Than Never’, ‘Make Hay while the Sun Shines’, ‘Treasure Hunt’, ‘Animal Friends’, and several others.
The management of the orphanage thanked Mr. Mahama for spending his birthday reading with the children and his generous donations.
On his part, Mr. Mahama said: “I am humbled and touched by the work the management is doing to provide for the basic needs of these children, and coming here today on my birthday is to say thank you. For the children, I encourage you to learn hard, continue reading your books always, and continue to dream big.”