An introduction to Statistical Consulting.

The purpose of this chapter is to motivate

the importance of statistical consulting in the context of the scientific process. That is, a statistical consultant should have a strong interest in science, and in particular, the art of scientific discovery.

Example 1: Is the population symmetric?

In a consulting meeting a question was posed about a machine filling bottles of pills.

Example 2: The Size of the Moon.
The moon is larger when viewed on the horizon versus directly above (???).

The examples show that theory alone does not always lead us to valid conclusions and it is crucial to look at data.

I. The scientific method.

This combination of both observational study and theoretical knowledge is called the Scientific Method and is the procedure followed in scientific discovery.

Scientific thinking before the Sixteenth century.

· Ancient Greeks scientific tradition.

· Learning from books.

· Mathematical theory for understanding nature. It was disconnected from experimentation.

o Orbits of planets where circular because circles are mathematically perfect. Spheres are perfect.

o Bodies fall at speeds proportional to their weights.

o Heat from the sun is different in nature from heat from fire.

· Applied knowledge acquired by craftsman was lost because they did not keep organized records and publications.

Sixteenth Century: End of the Middle Ages

· Copernicus cosmology.

· Galileo. Falling bodies experiment.

· Kepler.

Theory Proposed.

SEVENTEEN CENTURY: WILLIAM GILBERT, FRANCIS BACON, RENE DESCARTES.

· Important discoveries such as print, gun powder, magnetic compass showed that modern science was superior.

· Gilbert: Extensive work in Magnetism. "New tradition of men who look for knowledge not in books but in things themselves."

· Bacon: The scientific method. "The union of theoretical interpretation and the practical control of nature will produce a line and race of inventions that may in some degree subdue and overcome the necessities and miseries of humanity." For Bacon the scientific understanding and the theoretical control of nature went hand in hand, both were produced by the application of the scientific method.

· Descartes:

o Analysis: The way practical things are discovered.

o Synthesis: The theoretical way the same things can be deduced from first principles.

o "There is nothing more futile than to busy oneself with bare numbers and imaginary figures."

EIGHTEENTH CENTURY

· Newtonian Mechanics. Universal Gravitation.

· The problem of Navigation. Astronomy and the chronometer.

· Biology: Development of individual organisms. Circulation of the Blood. Cell theory.

· Chemistry: Lavoisier new Chemical theory. Composition of matter.

· Boyle-Mariotte.

NINETEENTH CENTURY

· Darwing and the theory of evolution.

· Development of Geology

· The atomic theory of matter

· The Wave theory of Light.

· Electricity and Magnetism.

· Mathematics: Geometry, Statistics/Probability.

· Engineering and Science.

TWENTIETH CENTURY: VERY SHORT LIST.

· Modern Biology.

· Relativity Theory.

· Quantum Mechanics.

· Data: Data Analysis and Statistics.

· Social Sciences.

The Development of Statistics

· Monte Carlo casino gamblers. Chevalier de Mere approached Pascal. Pascal and Fermat established some of the foundations of Probability (1654).

· Early developments in Data Collection and Processing in the Seventeenth Century. Tables of Mortality in England 1662.

· Tables of Annuities: Johan De Witt (1671).

· Normal distribution. Quetelet (1835).

· Poisson, The law of large numbers.

· Galton 1879. Introduced the concepts of correlation and regression (towards the mean). He used the Quetelet-Gaussian distribution.

· Pearson followed Galton and established the foundations of modern statistics.

· R A Fisher. The design of experiments, 95% confidence.

· The Polio trials.

· Connection between Lung Cancer and smoking.