Kathleen Z. Rooney
As we examine the growth of statistics in regulating and testing drugs, it is interesting and worthy to notice that the history of statistics itself is recent, and that the math co-evolved with the drug industry. Statistics is an infant among the ancient branches of mathematical study, yet it stands securely with its venerable peers among the four curriculum content strands in the state of Connecticut mathematics framework:
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Algebraic Reasoning (Al-Jabr was written in ancient Persia)
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Numerical and Proportional Reasoning (Incan and Mayan cultures explored the use of zero; there are ancient Arabic, Egyptian, Roman, and Hindu numerical systems.)
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Geometry and Measurement Working with Data (Geometry has roots in ancient Egypt; Pythagoras wrote theorems in ancient Greece)
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Probability and Statistics (The first time that statistics appeared in academia was the biostatistics program at John Hopkins University in 1918.
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Statistics developed from three disparate fields; political science, astronomy and gambling.
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From politics comes the name. This terminology persists in governmental bureaus of Vital Statistics. The name shares a Latin root with state, and is related to the notions of state as a condition of matter or body, state as in a body politic, and status. My 1947 edition of the Oxford English Dictionary gives the mid-century definition of statistic as "pertaining to status" and statistics as "that branch of political science dealing with the collection, classification, and discussion of facts bearing on the condition of a state or community. "
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The estimation of errors in measurement was an important pursuit in astronomy, and provided the basis for quantifying variability, which is the heart of statistical inference. Thirdly, the mathematical studies of chance in gambling throughout the 17th and 18th centuries provided the mathematical bases for many of the central theories in statistics. These fields began to come together as a recognized academic discipline in the earlier part of the 20th century.
The American Statistical Association (ASA) was founded in 1839, not as an academic pursuit, although erudite members of their Boston society founded it. The original members were graduates of Ivy League colleges and, as such, were all men. They had expertise in medicine, law and education. Their concerns were chiefly vital statistics, and their process was to generate and collect writings on statistical matters. These were articles concerned with public health issues, preventative medicine, and population and labor statistics.
As statistical study began to move into academia during the early twentieth century it was still considered vital statistics and focused on public health. During this period, mathematicians in the United States, Europe and Russia were building on theories of probability, and through the 1920s to '40s an expansion of these mathematical proofs led to a body of work in mathematical statistics with a focus on formal probability theory. Princeton University was a base for many mathematical statisticians and the theoretical frameworks developed in the middle of the 20
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century by these academics gave sound basis to the field as accepted math practice.
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Samuel Wilks and Henry Rietz split from the ASA to found the Institute of Mathematical Statistics and publish a separate journal, "Annals of Mathematical Statistics", to distinguish it from the practical application-oriented work. However, Wilks circled around to focus on practical applications. He influenced the great John Tukey, whose boxplot (first appearing in 1977) is one of the most familiar graphs to high school students today.
Current theory in statistics pedagogy emphasizes the applications of statistics and limits the focus on formal proof or derivation.
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This would not be possible without the formal mathematical proofs of the 1930s and 1940s. However, the fact that statistics no longer needs to "prove itself" is a result of the immense growth in the use of this math. Textbook author and distinguished professor of statistics at Purdue University, David S. Moore cites the 1996 joint recommendations of the MAA (Mathematical Association of America) and ASA in his argument for an application, process-based pedagogy for introductory statistics. That statement called for three basic reforms:
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Emphasize the elements of statistical thinking
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Incorporate more data and concepts, fewer recipes and derivations. Whenever possible, automate computations and graphics.
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Foster active learning
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Moore points out that the increase of computerized calculations and data organization allows a student to have less calculation skills while their exposure to a greater number of real world applications requires a higher level of inference and statistical analysis. There also needs to be a focus on ethics and a grasp of good experimental design and data production. He would replace the study of formal probability with these areas of content.
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It is important that our students learn through applications. This will prepare them best for the statistical questions that arise in their lives and studies. Many applications for statistics exist in the clinical trials and pharmaceutical industry, so it is a rich area to draw studies from. In addition, the notion of clinical trials has arisen within the political and scientific history of the United States pharmaceutical industry. This makes the immersion of statistical study in this area so rewarding.
