Transcript Slide 1

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 X has standard deviation n .
The goal is usually to estimate the unknown
population mean (μ) using the sample mean ( x ).
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.
Z
X 

follows the normal distribution, but
n
X 
t
s
n
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 X   does not follow the normal
s
distribution,
he developed a new
n
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.
X 
We say that t  s
n
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: SpringerVerlag.
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?fus
eaction=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/indexhisto
ry.shtml