Week 3: The Reign of Statistics (19 C) Flashcards
How did statistics change in the 19th C? Why?
Statistics began wielding great political and scientific power
o Applications such as eugenics, criminology, epidemiology, and demography
• Statistics were no long just about reasoning/understanding the world – but used directly for its actual administration (for both business and politics - “Biopolitics”)
• Context: This was during the churn of the French Revolution
o Gave rise to the modern state and business state
o Government began taking responsibility for managing details of the people’s lives
E.g. providing healthcare and managing living conditions
• This was enabled by the introduction of government surveys
o To help understand AND to help administer the populace
Actively sought to modern, enlightened society and unshackle it from problems of the past through
Biopolitics
o Idea of biopolitics: that a government’s management and administration of its population must directly reflect the population itself
Associated with thinkers such as Foucault
Pierre- Simon Laplace’s work on Jury Duty?
• 1814: Laplace publishes his calculations on the subject
o Discusses potential jury systems, and their chances of error
o Worked on the concept of a juror’s “reliability”; uniformly distributed in range [0.5, 1]
o An example of SUBJECTIVE PROBABILITY
o i.e. based entirely on his personal judgement, with no relation to empirical data
Would need refinement by his pupil, Poisson
Siméon Denis Poisson’s work on Jury duty?
Just a few years (~1820) after Laplace’s headway, Poisson refines the work:
o Unlike Laplace, who was working without data to pioneer a new system following the French Revolution, Poisson had French Judicial data to study
o Analysis of this data revealed that year to year, the jury always convicted the same percentage of the cases they were presented
Refined Bernoulli’s Theorem (frequency of x approaches p(x) as n->inf) to Poisson’s Theorem
- model jury selection as drawing jurors from bins
- Sn approaches p; p = (#red balls in all bins)/(# balls in all bins)
Of course he didn’t have mathematical proof that this modeled the judicial system - but it was a scientist’s reasoning given the rate is stable and N is large
Law of Large Numbers? Importance?
Arises from question of Jury duty
- Laplace performs initial foray, finding the probability of mistrial for different jury set ups
- Poisson extends it using data, realized conviction rate is constant yearly, developing Poisson’s Theorem
This gives us the Law of Large Numbers
o With enough samples, the average will converge on a stable value
o This is true despite large individual variance
o Data can be anything – birth, mortality rates, ship wrecks…
o Poisson conflates a mathematical theorem with empirical regularity
o a powerful tool as it allows analysis on any data set providing adequate sample size
Adolphe Quetelet?
o Belgian astronomer, he was familiar with the theory of errors and distributions
o Sought to apply similar techniques to society in the 19th century
o Took the view of “Social Physics”
Social phenomena can be studied just as astronomical phenomena is, using mathematical tools
1835: Introduces The Average Man
- all parameters average of population
- reflects population’s deep, innate regularities
1844: Biometric study
- Realizes humans are Gaussian
The Average Man
1835: Adolphe Quetelet introduces the Average Man in A Treatise on Man & the Development of his Faculties
o A conceptual construct, who is the average of his population
Average height, intelligence, income…
o These mean values are real quantities, not simply theoretical calculations or mathematical constructs
Accepted because they are very stable (thanks to the law of large numbers)
o The average man reflects the population’s deep, innate regularities
Can reveal common core of population
o The average man was the first hallmark of Statistical Reasoning
o The idea that you can ignore uncertainty and randomness at the micro level, but attain regularity, determinism, and law at a macro level by averaging out the variations
C.f. Laplace’s 18th century deterministic worldview: Laplace believed determinism of the micro level yielded macroscopic stability
o Probabilities provided a limit for empirical frequencies (recall Sn)
Bell Curves in Society?
Adolphe Quetelet’s Biometric Study (1844)
Using data from a medical journal, he analyzed the chest sizes of Scottish soldiers
-biological traits follow distributions much like astronomical error curves
Bodies are Gaussian - ties back to CLM
- Biology is aggreggate of unrelated random factors
- so bell curve is reality of population
Gives idea of normal vs pathological
What is the “normal” vs “pathological” shift?
- Idea of bell curve adopted throgh 19th C
- by Late 19th C, conceptual transformation
o “Mean” went from being the population’s representation, to be the society’s norm
o Bell went from being an index of deviations, to showing “pathological” conditions
• This didn’t just mean that the “normal” was good and “pathological” was an illness
o They’re different in degree – but they are of the same kind
Taken further by Emile Durkheim & suicide rates
Émile Durkheim
French Sociologist - one of the architects of modern social science.
Ties into normal vs pathological in late 19th C.
Analyzed Suicide in 1897 at a population level
Realized rates are constant – they reflect that society’s environment and pressures, not of the individual’s human nature
o Proposed that suicide was a statistical phenomenon; it was representative of the people at the tail ends of the bell curve
Two implications:
• Suicide is not a pathological illness, just a position on the distribution
• Suicide is unavoidable, as the tail of the distribution always exists
o Further, he believed that suicide could have a function – you need the tails of the bell curve to have a full representation of the population’s spectrum
