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Sneaking in a few history lessons when teaching statistics Kirk Anderson Grand Valley State University
The big idea • We (statistics instructors) find the history behind the methodology interesting and important, so maybe our students will too • We’ll do anything to get our students’ attention (the lives of Fisher, Gosset, et al are likely more fascinating than ours) • Adding a short biography is one way to make our handouts/lectures better
The big idea, continued • Don’t be intimidated! A statistical consultant knows that he or she doesn’t need a medical degree to work on a research project with doctors. Likewise, a statistics instructor can teach a bit of history without rigorous training to be a historian. • It’s worth the (small amount of) class time
Personal history • What is the first “statistical tale” you remember hearing when you were in school? • For me, it was of the mysterious “Student.” That sealed the deal for me, since it established a firm connection between my two favorite things, statistics and beer.
Where to start? • Your favorite story/personality • The big hitters (Fisher, Pearson) • Can be driven by student questions (e.g. Why is alpha .05?) • Tailored to course (Business=Friedman, Psychology=Spearman, QC=Deming) • Pictures!
What a personality! • A natural approach is to give a short biography of a famous statistician at the appropriate time, e.g. • R. A. Fisher (ANOVA, etc.) • William Gosset (t-test) • Karl Pearson (chi-square, correlation) • John Tukey (post-hoc analysis, boxplots) • Many intro stat books have such bios as a feature in each chapter
An example In STA 215: Introductory Applied Statistics at GVSU, before introducing the t-test, I can’t help but give the background of why, when and where it was needed, who came up with it, and how it happened. How can you blame me? It not only involves the brewing of beer, but there is an added element of mystery regarding the pen name “Student.” An excerpt of the PowerPoint slides used for the t-test follows.
Who is this mysterious “Student?” Before we can construct confidence intervals for any of these three quantitative applications, we need to learn about a probability distribution that is quite similar to the normal – although it is different in one very important way.
As we move away from examples where we assume X follows a normal distribution into more realistic applications involving random samples (from any distribution), we have a problem. The random variable has standard deviation The goal is usually to estimate the unknown population mean (μ) using the sample mean ( ). If we don’t know the population mean, how would we know the population standard deviation?
It is much more practical to use both the sample mean and sample standard deviation, s. But this changes our methods somewhat. Specifically, instead of the normal, we need to use a distribution called Student’s t, or just simply the t distribution. follows the normal distribution, but does not.
History Lesson! At the turn of the 20th century, an Englishman named William Gosset went to work as a mathematician/chemist for a brewery in Dublin called Guinness. Gosset saw a need for scientific analysis of many factors in the brewing process, such as barley types, hop varieties, yeast activity, cooking temperature/duration, etc. To improve the quality of the beer, he experimented with the different factors, typically using small sample sizes. Realizing that does not follow the normal distribution, he developed a new distribution that is more appropriate for small sample sizes.
He published his findings under the pen name “Student,” per Guinness’ policy. Gosset’s achievement (and many others) has proven fundamental to statistical inference, and helped him become head brewer. William S. Gosset 1876-1937
The t distribution is very similar to the normal, but it depends on the sample size, and is more appropriate when we must estimate σ with s. There is a different t distribution for every sample size. We say that follows the t distribution with n – 1 degrees of freedom, or df.
Nonparametric Methods • You may (or may not) have the time to cover some nonparametric methods in your intro stat course • If so, it’s hard not to discuss the people behind the topic, since most of the methods are named after their inventors • I’m lucky to be able to teach a course on nonpar to our stat majors/minors…
Excerpts from typical handouts developed for STA 317, Nonparametric Statistical Analysis FRIEDMAN TWO-WAY ANALYSIS OF VARIANCE BY RANKS The title of Milton Friedman’s 1937 JASA paper, “The Use of Ranks to Avoid the Assumption of Normality Implicit in the Analysis of Variance,” clearly indicates a nonparametric alternative to ANOVA. Remarkably, it is a rank-based version of two-way ANOVA which appeared in the statistical literature years before similar results by Wilcoxon, Mann/Whitney, or Kruskal-Wallis. Friedman started his career as a mathematical statistician, but is mainly remembered for his work in economics. He believed in a free market economy, a “natural” rate of unemployment, and he opposed government regulation. As an economist, Friedman has many admirers, and many detractors. As a statistician, he worked on problems in many areas including experimental design and sampling inspection, but is mainly known for “Friedman’s Test.” (Sources: wikipedia (photo), and an obituary written by Stephen Stigler in 2006.)
Excerpts from STA 317 handouts, continued Correlation as we know it When we refer to the correlation between two quantitative variables, we usually have in mind a particular statistic: the Pearson product moment correlation coefficient, typically denoted by the letter r. This statistic was developed in 1895 by Karl Pearson, but it should be noted that the theory of regression and bivariate correlation was established by Francis Galton (pictured) a decade earlier. Sources: www.galton.org (photo), and Rogers, L. R., and Nicewander, W. A. (1988), “Thirteen Ways to Look at the Correlation Coefficient,” The American Statistician, 42, 59-66.) THE SPEARMAN RANK CORRELATION COEFFICIENT If we are not comfortable using Pearson’s r, we can simply replace the observed (x, y) pairs with (R(x), R(y)), where R denotes the rank of each x (or y) observation, and compute Pearson’s r using the ranks. This statistic, often called Spearman’s rho, was given by Charles Spearman in a 1904 American Journal of Psychology article titled “The Proof and Measurement of Association between Two Things.” Spearman was an English psychologist known for developing statistical methods. In addition to the rank correlation coefficient, he pioneered the use of factor analysis, and is sometimes given credit for inventing it. Sources: www.cps.nova.edu (photo), and wikipedia.
Assessment (if any) • Can be just for fun (don’t admit this) • Extra credit questions on HW or exams • Low-stakes (very few points) • Matching (pictures with names or methods, names with famous quotes, e.g. Who said An appropriate answer to the right problem is worth a good deal more than an exact answer to an approximate problem?)
Make history the main focus?! • History of statistics could be the focus of an optional seminar course • STA 430: History of Statistics is a one-credit hour course offered once a year at GVSU • We read David Salsburg’s The Lady Tasting Tea • Students participate in group discussions, are required to dig a little deeper into what is covered in the book each week, and write a paper (biography)
Other ideas • Tie in other important events for context (e.g. December 1945: Frank Wilcoxon publishes 3-page paper in Biometrics Bulletin covering both the 1-sample signed-rank and 2-sample rank-sum test, also in Dec 1945 Nazi SS personnel convicted of atrocities at Belsen and other holocaust concentration camps are hanged). • Study abroad theme?
Resources: History books • Salsburg, David. 2001. The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century. New York: W. H. Freeman and Company. • Stigler, Stephen. 1999. Statistics on the Table: The History of Statistical Concepts and Methods. Cambridge: Harvard University Press. • Johnson, N. L., and Kotz, S. (editors). 1997. Leading personalities in statistical sciences : from the 17th century to the present. New York : Wiley. • Box, Joan Fisher. 1978. R. A. Fisher, the life of a scientist. New York: Wiley. • Reid, Constance. 1997. Neyman. New York: Springer-Verlag.
Introductory statistics textbooks that contain short biographies of famous statisticians • Weiss, Neil A. 2008. Introductory Statistics. Boston: Pearson Education, Inc. • Ross, Sheldon M. 2005. Introductory Statistics. Burlington: Elsevier Inc. • Sullivan, Michael III. 2007. Statistics: Informed Decisions Using Data. New Jersey: Pearson Education, Inc. • De Veaux, R. D., Velleman, P. F., and Bock, D. E. 2006. Intro Stats. Boston: Pearson Education, Inc. • Agresti, Alan, and Franklin, Christine. 2007. Statistics: The Art and Science of Learning From Data. New Jersey: Pearson Education, Inc.
Websites • American Statistical Association’s Statisticians in History page https://www.amstat.org/about/statisticiansinhistory/index.cfm?fuseaction=main • The University of York’s Life and Work of Statisticians page http://www.york.ac.uk/depts/maths/histstat/lifework.htm • The University of Adelaide’s R. A. Fisher Digital Archive http://digital.library.adelaide.edu.au/coll/special//fisher/ • University of Southampton’s Figures from the History of Probability & Statistics page http://www.economics.soton.ac.uk/staff/aldrich/Figures.htm • University of Minnesota Morris’ History of Statistics & Probability page http://www.morris.umn.edu/~sungurea/introstat/history/indexhistory.shtml