Statistics education

Summary: Statistics education has grown and adapted since the nineteenth century.

At the start of the twentieth century, science fiction author H. G. Wells asserted, “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write.” While use of statistical methods dates to earlier times, the first college statistics departments were founded in the early twentieth century, and many textbooks were written on statistical subjects like the design of experiments. A century after Wells’s prediction, the notion of statistical thinking permeates all levels of education from kindergarten through college. In the early twenty-first century, there are increasing calls for statistical literacy in the United States and abroad in order to help people manage an increasingly complex and data-driven world.

Etymology

The word “statistics” derives from the term “state arithmetic,” which refers to the various counting and calculating operations necessary for governments to operate effectively. The ancient Babylonians, Egyptians, Greeks, Romans, Chinese, and others appear to have used various kinds of mathematics for activities like partitioning land and determining army sizes. The eleventh-century Domesday Book, a survey of England ordered by William the Conquerer, is another example of such state arithmetic. Statistician Maurice Kendall cites the first possible occurrence of the term “statistics” in the sixteenth-century work of Italian historian Girolamo Ghilini, who wrote about “civile, politica, [and] statistica e militare scienza.” However, he also traces the conceptual beginnings of the field to the “political arithmetic” of the seventeenth century and the work of researchers like pioneer demographers John Graunt and William Petty, who examined population growth and commerce in London versus Rome and Paris; and mathematician Edmond Halley, who some consider to be the founder of actuarial science for his work on life expectancy tables and insurance calculations. German historian and economist Gottfried Achenwall is frequently credited with inventing the German form of the word “statistics” in the eighteenth century and the related term Staatswissenschaft for political science. Their shared root staats means “state.” Scottish politician John Sinclair appears to have been the first to use the term “statistics” in English in his Statistical Accounts of Scotland, a late eighteenth-century work addressing people, geography, and economics. He said: “I thought a new word might attract more public attention, I resolved to use it.”

Historical Applications

In the nineteenth century, the ideas of statistical counting and calculating began to spread into a wider variety of political, social, scientific, and financial applications. For example, British physician William Farr received statistical training in France and applied statistics to medicine and models of epidemic diseases, calling his methods “hygiology” after the word “hygiene.” He is credited as the founder of the field of epidemiology. Another pioneering epidemiologist was physician John Snow, who famously used statistical methods to trace the source of an 1854 cholera outbreak in London. His conclusions were politically controversial. In approximately the same period in the United States, self-taught statistician Lemuel Shattuck was appointed to plan a census of Boston in 1845 and later helped plan national census activities. He ultimately helped implement many local and state public health measures. Governments, businesses, and academic institutions increasingly used data and statistical methods to inform decisions. During this period, countless mathematicians, statisticians, economists, scientists, and others contributed to the development of statistical methods and the mathematical foundations of statistics, as well as the related field of probability. Many of them addressed both the theory and application of statistics.

Historical Education

Universities had existed in Europe since the Middle Ages. In other parts of the world, there were centers of learning at which scholars gathered to exchange ideas and teach. However, education in many academic subjects was often accomplished through mentorships or private tutoring. For example, nineteenth-century statistician and nurse Florence Nightingale was tutored in arithmetic, algebra, and geometry. She, in turn, tutored others before becoming involved in nursing. One of her tutors was the well-known mathematician of the period, James Sylvester. She was also influenced by the work of Farr and corresponded with mathematician Adolphe Quetelet, who was a pioneer in the use of statistics for anthropometry and criminology. She called him “the founder of the most important science in the world.”

Other statisticians formed relationships with universities for research. For example, Karl Pearson, Francis Galton, and Walter Weldon worked at University College London. Pearson gave statistics lectures starting in 1894, and the trio founded the journal Biometrika in 1901 “as a means not only of collecting or publishing under one title biological data of a kind not systematically collected or published elsewhere in any other periodical, but also of spreading a knowledge of such statistical theory as may be requisite for their scientific treatment.” Upon his death in 1911, Galton bequeathed the university a large endowment. Pearson became the first Galton Professor of Eugenics, sometimes called Galton Professor of Applied Statistics, perhaps because of the controversial nature of eugenics. That same year, Pearson was instrumental in creating the university’s Applied Statistics department, now the Department of Statistical Science, which was recognized as the world’s first college statistics department. It merged biometrics and eugenics (genetics) laboratories that had been founded by Pearson and Galton—though the Galton Laboratory later moved to the Department of Biology. Some other statisticians who worked or studied at University College London in the early nineteenth century include William “Student” Gossett, who is credited with the development of the Student’s t distribution; Karl Pearson’s son, Egon Pearson, who became the head of the Applied Statistics department when it split with the Department of Eugenics; Ronald Fisher, who was the first head of the Department of Eugenics and is referred to by some as the “father of modern statistics;” and Jerzy Neyman, who co-developed what is often called “Fisher–Neyman–Pearson inferential methods” or “classical” methods of statistical inference. These techniques typically use what is known as the “frequentist approach” to statistical analysis, which is based on defining probabilities of events as the limits of their relative frequencies over a large number of trials or experiments. It is perceived by many as being wholly objective and therefore “scientific.” This approach is in contrast to Bayesian methods (or Bayesian analysis), named for mathematician Thomas Bayes. Bayesian statistical methods allow for subjective or belief-driven probabilities that may or may not be derived from observation or experimentation. The Applied Statistics department at University College London temporarily relocated during World War II; the war was to have a broad impact on mathematics and statistics in Europe and the United States.

Education in the United States

The Unites States was also developing its own college-level education programs at the beginning of the twentieth century. Similar to the department at University College London, many programs and other efforts started with individuals offering courses and partnerships between researchers and universities. One often-cited example is Iowa State University. George Snedecor, a professor in the Department of Mathematics, taught courses that included statistics content starting in 1914. He often focused on agriculture problems, a significant research area at the university. In 1924, he co-wrote a worldwide publication about computational statistical methods with Henry Wallace, who would later become Secretary of Agriculture and vice president of the United States. Iowa State created a statistical consulting and computing service in 1927, which was available to researchers in many disciplines. This service led to Iowa State’s creation of the first recognized statistical laboratory in the United States, in 1933, and its Department of Statistics, in 1947. However, statistics degrees were offered before that time, beginning with Gertrude Cox’s master’s degree in 1931. Cox went on to help found the Department of Statistics at North Carolina State University, one of the oldest statistics departments in the United States. She was the first female full professor and first female department head at the school and went on to start other college programs as well. An anecdote about her hiring at North Carolina State reports that, when Snedecor was asked to recommended five men for the job, he added to his letter: “. . . if you would consider a woman for this position I would recommend Gertrude Cox.”

European statisticians also proved influential on U.S. statistics education and, in some cases, on government policy. Fisher visited Iowa State in the 1930s, and his agricultural work at the Rothamsted Experimental Station made a great impact on Snedecor. William Cochran, who was born in Scotland, also worked at the Rothamsted Experimental Station and taught at Iowa State. He went on to help create many statistics departments, including the one at Harvard, and he served on the committee that produced the 1960 Surgeon General’s Report on Smoking and Health. Statistics proliferated, and similar efforts took place elsewhere, such as at the University of California, Berkeley. Jerzy Neyman, who was born in Poland and also studied in England, France, and Russia, started working at Berkeley in 1938. Like many mathematicians and statisticians of the time, he was fleeing the growing Nazi influence in Europe. Prior to World War II, colleges sometimes offered a few undergraduate and graduate statistics courses but entire departments were still fairly rare. Thanks largely to Neyman’s efforts, Berkeley had a department by 1955. He would also contribute significantly to experimental design, including some methods used by the United States Food and Drug Administration to test new medicines. Berkeley would become a center for mathematical statistics and was chaired for a time by statistician and mathematician David Blackwell, the first tenured African-American professor at Berkeley.

Post–World War II Statistics Education

Statistics and statistics education exploded after World War II, influenced by developments that occurred during the war and the subsequent Cold War. Statisticians had contributed significantly to the war effort in both the United States and Europe. For example, Hungarian mathematician and statistician Abraham Wald, who had suffered persecution for being Jewish, helped solve the problem of where to armor British bombers against antiaircraft fire. Others, like French-German Wolfgang Doeblin, would die as a result of the war. Later studies of Doeblin’s works showed that he was an early pioneer of Markov chains, named for Andrei Markov. John Tukey was one of the most influential statisticians working in the mid- and later twentieth century. According to statistician Frederick Mosteller, the first chair of Harvard’s statistics department and an influential force in statistics education: “He probably made more original contributions to statistics than anyone else since World War II.” Tukey worked at the government’s Fire Control Research Office during World War II, among his many roles. At the same time, he was often praised for his teaching. Mathematician Robert Gunning called him a “very lively presence on campus” and “a good and energetic teacher,” who also helped schedule class and exam times in his head. As a member of Princeton’s mathematics department, Tukey helped found the school’s Department of Statistics in 1966, following earlier work by statistician Samuel Wilks, who had worked for the Office of Naval Research and profoundly influenced the application of statistics to military planning. The American Statistical Association’s Samuel S. Wilks Award was named in his honor. Later, the department became the Committee for Statistical Studies, which encourages cross-disciplinary study of statistics and coordinates courses in many departments and programs.

The post-war extension of statistics into areas like clinical trials (pioneered by statistician Austin Bradford Hill), business, manufacturing (influenced by statisticians like W. Edwards Deming), and financial economics (for which economists Harry Markowitz, Merton Miller, and William Sharpe won a Nobel Prize), as well as the revival of Bayesian methods, meant that statistics was reaching a broader audience. It also meant that, more often, statistics courses were taught outside traditional mathematics and statistics departments. The debate over who should teach statistics was not new. Given that the discipline had been developed within so many fields—agriculture, psychology, biology, sociology, business, just to name a few—it was only natural that teaching would occur within these fields. Statistician John Wishart, who had worked with Pearson at University College London and with Fisher at Rothamsted, asserted that non-statisticians were not equipped to teach statistics or supervise statistical research. Fisher took a different approach, citing statistics’ basis in research and applications and arguing for focused statistics offerings in departments in which statistics were often used, like psychology and biology. Around 1940, Harold Hotelling, who taught at Stanford University, Columbia University, and the University of North Carolina Chapel Hill, presented the idea that being a strong mathematician is not sufficient for teaching statistics, so mathematicians and statisticians were not always superior instructors versus individuals in other disciplines. He asserted that a statistics teacher must meld quantitative skills with “a really intimate acquaintance with the problems of one or more empirical subjects in which statistical methods are taught.” Hotelling recognized that in typical academic structures, there might be some reluctance among faculty to teach courses that lay outside their specialty areas and that keeping current with statistics might be a daunting task for non-specialists. These issues remain matters of debate at the start of the twenty-first century. A study published in 2000, funded by the National Science Foundation, suggested that students were more likely to receive statistics education from instructors outside mathematics or statistics departments.

Employment

Through the 1970s, universities in the United States and elsewhere produced many statisticians or statistically trained practitioners in other disciplines, many of them to meet growing industry demands. However, employers were showing increasing concern that their new employees did not know how to practice statistics on the job, even if they had been instructed in current applied methods and practices in their academic programs. The American Statistical Association (ASA), which was founded in 1839, created a committee in the late 1940s to consider matters related to the training of statisticians. In 1980, the ASA Committee on the Training of Statisticians for Industry presented guidelines for programs that train industrial statisticians. One conclusion that spurred further debate stated: “. . . it is generally agreed that the MS degree is a minimum requirement for the professional statistician… it is recommended that someone interested in statistics as a profession obtain solid foundations in science or engineering and mathematics.” Some discussion centered on balancing theory, applications, and employer-desired skills such as communication and teamwork. In Great Britain, the 1986 report Supply of and Demand for Statisticians cited both teaching factors and unrealistic expectations on the part of employers. Overall, in the 1980s, there were many general calls from statisticians to increase both the number and quality of programs, with mixed success. In the 1990s, there were also calls to increase the quality of undergraduate education and provide more interdisciplinary opportunities to graduate-level statisticians to “modernize” statistics for the twenty-first century. This call hearkened back to statistics’ inherently interdisciplinary roots in previous centuries.

New Emphasis

The hallmarks of statistics education in the latter twentieth century and into the twenty-first century would be an increased focus on concepts over computation, statistical literacy, statistical thinking, use of real data, use of technology for both data analysis and conceptual understanding, and assessment to gauge student learning and understanding. Reports by several professional mathematical and statistical organizations contributed to this shifting educational emphasis. For example, the 1991 Focus Group on Statistics Education, part of the Curriculum Action Project of the Mathematical Association of America, produced Heeding the Call for Change. Later, the ASA Undergraduate Statistics Education Initiative (1999) focused on many aspects of education. One concern they noted was that many students were having a negative first experience in introductory statistics. In 2005, the Guidelines for Assessment and Instruction in Statistics Education (GAISE) committee, sponsored by ASA, produced K–12 and undergraduate reports focusing on instructional practice and assessment. There have also been recurring meetings, such as the International Conference on Teaching Statistics (ICOTS), which allow statistics instructors to address and debate issues, including the place of “classical” statistical methods versus Bayesian or computationally intensive exact methods in introductory classrooms; how best to meet the needs of non-majors taking statistics courses in mathematics and statistics departments; the “best” structure for introductory statistics textbooks; or the role of online tools and distance education.

The 2000 edition of the National Council of Teachers of Mathematics Principles and Standards for School Mathematics outlined standards for mathematics education that included statistics threaded from kindergarten through the last year of high school. Previously, statistics had been offered in various forms in high schools, though it presented some difficulty because many did not think it fit neatly into the traditional algebra, geometry, trigonometry, calculus sequencing used by many schools. The Advanced Placement (AP) Statistics exam was first offered in 1997. More than 7000 students took the exam, the most for a first offering of any AP exam as of 2010, and between 1996 and 2010 the rate of enrollment increased more quickly than any other course offered by AP.

Bibliography

Aliaga, Martha, Carolyn Cuff, Joan Garfield, Robin Lock, Jessica Utts, and Jeff Whitmer. “Guidelines for Assessment and Instruction in Statistics Education (GAISE) College Report.” Washington, DC: American Statistical Association, 2005. http://www.amstat.org/education/gaise/.

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Fienberg, Steinberg. “When did Bayesian Inference Become ‘Bayesian?’” Bayesian Analysis 1, no. 1 (2006).

Gargield, Joan, ed. Innovations in Teaching Statistics (MAA Notes #65). Washington, DC: The Mathematical Association of America, 2005.

Hulsizer, Michael, and Linda M. Woolf. A Guide to Teaching Statistics: Innovations and Best Practices. Hoboken, NJ: Wiley-Blackwell, 2009.

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