“ Adolphe Quetelet: Statistics and Social Science in the Early 19 th Century”

1. “Adolphe Quetelet:Statistics and Social Science in the Early 19th Century” Evan Brott February 3, 2003

2. Quetelet: 1796-1874 • Today, Quetelet is nearly unknown • But, he made major contributions to statistics • Also one of his era’s greatest social scientists

3. Main Works • 1835- Publishes Physique Sociale: A Treatise on Man, and the Development of His Faculties which introduces the concept of the ‘Average Man,’ a basic concept in the Social Sciences. (That’s him on the right) • 1846 – Is the first to fit a normal curve to a distribution of human traits

4. Outline • Science in the 1830’s • The Early Life of Quetelet • The Average Man: a Study of Mortality • Comparisons of Average Men: a Look at European Sex Ratios • Statistical Morality and Early ANOVA: Crime and Punishment in 1820’s France • Fitting a Normal Curve: the Chest Size of a Scotsman • Quetelet’s Legacy

5. Part I: Science in the 1830’s or: They Thought WHAT!?

6. State of the Arts • Quetelet’s research was from 1820-1850. • MANY theories we take for granted were not yet developed.

7. Biology • 1859 – Darwin publishes The Origin of Species • 1860s – Pasteur develops Germ Theory of Disease • 1865 – Mendel discovers basics of Genetics

8. Quetelet’s Environment • Spontaneous Generation not disproved • Quetelet believes Miasmic Theory of Disease • Many results seemed strange without understanding heredity

9. Social Science • Quetelet one of the first mathematical social scientists • 1830’s beliefs seem very strange today • Ex: Phrenology: Personality read by the shape of the skull

10. Early Statistical History • Beginnings in 17th century • Studied Laws of Probability through Gambling

11. More Proto-Statistics • 1680s: Newton and Leibniz independently develop Theory of Calculus • 1689: Bernoulli first states the Law of Large Numbers

12. Normal Distribution • 1733: De Moivre finds Normal Distribution arises as a limit of the Binomial • 1778-1812: Laplace develops the Central Limit Theorem • 1809: Gauss finds that most random errors are distributed normally

13. Future Statistical Knowledge • 1890s: Pearson develops his correlation coefficient • 1904: Gosset (a.k.a. ‘Student’) develops the t-distribution • 1920s: Fischer’s work starts the modern era of statistics

14. Part II: The Early Life of Quetelet or: how to build an observatory without really trying

15. Origins • Born on 2/22/1796 in Ghent, Belgium • Doctorate in conic sections from University of Ghent in 1819

16. Astronomy • Initial post-doctoral work in astronomy under Arago and Bouvard • Famous story about founding Belgium’s first observatory: traveled to France at age 26, and got funding despite having NO experience at all.

17. Astronomical Statistics • Galileo first showed astronomical measurement errors were: - random - symmetric - small errors occur more often than large errors.

18. Hypothesized Error Distributions • Thomas Simpson (1756) • Daniel Bernoulli (1777) • Karl Freidrich Gauss (1809)

19. More Statistical Exposure • Met the 75-year old Laplace while getting funding for his observatory • Post-doctoral mathematical work with Fourier

20. The Census • 1826: began work with the Belgian Department of the Census- was in charge by 1829. • All censuses at that time were total population counts; Laplace thought of a simpler method • Count the number of births in several regions; then multiply by ratio of births/population

21. Quetelet’s Plan • Quetelet was interested in Laplace’s method • Received a letter from Baron de Keverberg • Letter said far too many variables in social science for random sampling • Quetelet was convinced- conducted full census anyway

22. PART III:THE AVERAGE MAN

23. Physique Sociale • Newton’s mechanical physics was highly esteemed in Quetelet’s time • Quetelet envisioned a similar Social Physics • Central to this was the idea of The Average Man – which was likened to a social ‘center of gravity’

24. What is the Average Man? • It’s exactly what you think it is • Consider human size: Small AVERAGE Large

25. Influential • Quetelet was obviously not the first to think of this sort of thing • He popularized it, and as we will see carried the concept much further though • It is a VERY common concept today

26. Nutritional Example “The average man needs 250g of carbohydrates each day”

27. Common Example • “The Average Family has 2.4 Children” (Here, we see the Average man doesn’t necessarily exist)

28. Political Example • “The Average American will save $278 dollars with my tax plan” • “But 50% goes to the top 1% of Americans” • “The bottom 20% pays no taxes” • “The top 1% makes over $300,000 already” - And so on . . .

29. Silly Example • “The Average Man has less than 2 legs” (Out of the worlds 6 billion people at least 10,000 have only 1 leg . . .)

30. What Quetelet Thought “If an individual at any given epoch of society possessed all the qualities of the average man, he would represent all that is great, good, or beautiful.”

31. Cournot’s Critique • “A totally average man, if forced to exist, would be an unviable monstrosity: just as the averages of several different right triangles will not be a right triangle.”

32. Quetelet’s First Example • The beginnings of Survival Analysis came from Mortality Tables • These listed the expected times of death • In short, the Age of the Average Man

34. Quetelet’s Work • Mortality- P(dying this year)*10,000 • Viability- 1/P(dying this year)

35. Part IV: Many Average Men Or:Where Male Babies Come From

36. Categories • Quetelet did not only envision the Average Man as a ‘global average’ • Rather, there was: An Average Man – and Woman – for every “race, location, age, and epoch – and all combinations of these” • Allowed between group comparisons

37. Categories • This was also understood before his time • The mortality tables were divided by gender, location, and occupation • Still, Quetelet popularized and greatly refined the notion

38. The Sex Ratio • It is a biological fact that 1.06 male babies are born for every female baby. • Known as early as the 17th Century • Why? 1.06 : 1.00

39. Current Thought • Evolutionary: men are more expendable • Sources of variation: - Prenatal diseases disproportionately effect boys - First birth, younger women have more boys - Effects of family planning • Quetelet noticed most of these!

40. The Mind of God • 1710: John Aurbuthnot believes probability evidences the Divine Mind: • Sees sex ratio as evidence – more men die in war, but still enough left to evenly match with women • One of the first applications of probability outside of pure math / gaming

41. Quetelet: by Country • Shows global average; evidence of variation

42. Sources of Variation • Tried to explain why different countries had different ratios • Decided on racial differences (e.g. Russians naturally have more boys than Swedes) • Showed many other possible causes

43. South Africa • Climate, Race, Lifestyle, Small Samples

44. Legitimacy • The following page shows a table of births by marital status • Quetelet never said WHY this effect was there – surely he didn’t think church sanction ‘blessed’ the couple with more boys? • Proxy for age? Or social status?

45. Legitimacy

46. Age • Quetelet presented other theories, this one from Hofacker: • Overstates effect

47. Other Theories • Dismisses Bicke’s family planning theory • Shows first marriages (not births) lead to more boys • Town vs. Country also considered • Decides on Race

48. Still Births • Several Chapters later, demonstrates that Stillbirths are predominately male • Does not realize that differing levels of healthcare can exaggerate this effect- accounting for variation

49. Part V: Analysis of Crime or: “If you must murder, try to be a well-educated woman over 30”

50. Victorian STAT 410 • Ordinary Least Squares had been known for centuries • ‘Regression’ would not be called such until Galton in the 1870’s • Hypothesis Testing, ANOVA still in extremely vague state