Introduction to the ideas involved in statistical thinking. We hear statistics every day related to political polls, the stock market and the economy, sports, and lots of other life where metrics of performance are useful in interpreting what's going on.

1. Statistics

2. There are three kinds of lies: lies,
damned lies, and statistics.

3. H.G. Wells
• Statistical thinking will
one day be as necessary
for efficient citizenship
as the ability to read
and write.

4. Artemus Ward
• It ain’t so much the
things we don’t know
that get us in trouble.
It’s the things we know
that just ain’t so.
Charles Farrar Browne
• This could be
considered unknown
knowns.

5. Evidence and Reality
• As we know, there are
known knowns, there are
things we know we know.
We also know there are
known unknowns, that is
to say we know there are
some things we do not
know. But there are also
unknown unknowns - the
ones we don’t know we
don’t know.
Donald Rumsfeld

6. Epistemology
• The branch of
philosophy concerned
with the nature and
scope of knowledge and
what distinguishes
justified belief from
opinion.

7. Samuel Johnson
• Round numbers are
always false.

8. Sir Francis Galton
• I have a great subject
(statistics) to write
upon, but feel keenly
my literary incapacity to
make it easily
intelligible without
sacrificing accuracy and
thoroughness.

9. Sir Francis Galton
Cousin of Charles Darwin
English polymath: anthropologist, eugenicist, tropical explorer, geographer, inventor,
meteorologist, proto-geneticist, and statistician. He was knighted in 1909.
Galton produced over 340 papers and books. He also created the statistical concept
of correlation and widely promoted regression toward the mean. He was the first to apply
statistical methods to the study of human differences and inheritance of intelligence, and
introduced the use of questionnaires and surveys .
He was a pioneer in eugenics, coining the term itself and the phrase "nature versus nurture".
His book Hereditary Genius (1869) was the first social scientific attempt to
study genius and greatness.
As an investigator of the human mind, he founded psychometrics (the science of measuring
mental faculties). He devised a method for classifying fingerprints that proved useful
in forensic science.
As the initiator of scientific meteorology, he devised the first weather map, and was the first
to establish a complete record of short-term climatic phenomena on a European scale. He
also invented the Galton Whistle for testing differential hearing ability.

10. Statistics
Is the study of the collection, organization,
analysis, interpretation and presentation
of data. It deals with all aspects of data,
including the planning of data collection in
terms of the design of
surveys and experiments.

11. Statistics is closely related
to probability theory
• probability theory starts
from the given
parameters of a total
population
to deduce probabilities
that pertain to samples.
• Statistical inference,
however, moves in the
opposite direction—
inductively
inferring from samples
to the parameters of a
larger or total
population.

12. Reasoning
Deductive
• http://www.youtube.com/watch?v
=ZTfVIMPV8KY
• Deductive reasoning, or,
informally, "top-down" logic, is the
process of reasoning from one or
more
general statements (premises) to
reach a logically certain conclusion.
• Deductive reasoning
links premises with conclusions. If
all premises are true, the terms
are clear, and the rules of
deductive logic are followed, then
the conclusion reached
is necessarily true.
Inductive
• http://www.youtube.com/watch?v=wg-
5LvwBnc4
• Inductive reasoning is reasoning in which the
premises seek to supply strong evidence for
(not absolute proof of) the truth of the
conclusion. While the conclusion of a
deductive argument is supposed to be
certain, the truth of an inductive argument is
supposed to be probable, based upon the
evidence given.
• It is a common fallacy to state that inductive
arguments reason from the specific to the
general, while deductive arguments reason
from the general to the specific. This is
sometimes true (as in inductive
generalizations), but this is not generally the
case, as in all of the other types of inductive
inference listed below (e.g. statistical
syllogisms and arguments by analogy).

13. Black Swan Theory
• The black swan theory or theory of black swan events is a metaphor that
describes an event that comes as a surprise, has a major effect, and is often
inappropriately rationalized after the fact with the benefit of hindsight.
• The theory was developed by Nassim Nicholas Taleb to explain:
• The disproportionate role of high-profile, hard-to-predict, and rare events that are
beyond the realm of normal expectations in history, science, finance, and
technology
• The non-computability of the probability of the consequential rare events using
scientific methods (owing to the very nature of small probabilities)
• The psychological biases that make people individually and collectively blind to
uncertainty and unaware of the massive role of the rare event in historical affairs
• Unlike the earlier philosophical "black swan problem," the "black swan theory"
refers only to unexpected events of large magnitude and consequence and their
dominant role in history. Such events, considered extreme outliers, collectively
play vastly larger roles than regular occurrences. More technically, in the scientific
monograph Lectures on Probability and Risk in the Real World: Fat Tails (Volume 1),
Taleb mathematically defines the black swan problem as "stemming from the use
of degenerate metaprobability"

14. Black Swan Theory
• http://www.npr.org/te
mplates/story/story.php
?storyId=10300687

15. From the Foot of Hercules
Ex pede Herculem, "from his foot, [we can measure] Hercules", is a maxim
of proportionality inspired by an experiment attributed to Pythagoras:
"The philosopher Pythagoras reasoned sagaciously and acutely in determining and
measuring the hero's superiority in size and stature. For since it was generally agreed that
Hercules paced off the racecourse of the stadium at Pisae, near the temple of Olympian Zeus,
and made it six hundred feet long, and since other courses in the land of Greece, constructed
later by other men, were indeed six hundred feet in length, but yet were somewhat shorter
than that at Olympia, he readily concluded by a process of comparison that the measured
length of Hercules' foot was greater than that of other men in the same proportion as the
course at Olympia was longer than the other stadia. Then, having ascertained the size of
Hercules' foot, he made a calculation of the bodily height suited to that measure, based upon
the natural proportion of all parts of the body, and thus arrived at the logical conclusion that
Hercules was as much taller than other men as the race course at Olympia exceeded the others
that had been constructed with the same number of feet." (translated by John C. Rolfe of the
University of Pennsylvania for the Loeb Classical Library, 1927)
In other words, one can extrapolate the whole from the part. Ex ungue leonem, "from its claw [we
can know] the lion," is a similar phrase.
The principle was raised to an axiom of biology ; it has found dependable use in paleontology,
where the measurements of a fossil jawbone or a single vertebra, offer a close approximation of
the size of a long-extinct animal, in cases where comparable animals are already known. The
studies of proportionality in biology are pursued in the fields
of morphogenesis, biophysics and biostatistics.

16. Big Data
• Statistics has many ties
to machine
learning and data
mining.

17. The Signal and the Noise

18. Signal and Noise

19. Curve fitting and over-fitting

20. Professor John Cousins
jjcousins@gmail.com
@jjcousins