e = people died after being visited
H= Oscar, the cat, is magical
Example of which one Sagan's Laws?
If one is strongly skeptical H, they shouldn't become believer unless given strong evidence for H
What are Sagan's Laws?
1. One equally surprised to find e whether or not H, then e neither confirms nor rejects H
2. One surprised to find e if H were false, e confirms H
3. One surprised to find e if H were true, e rejects H
4. One strongly skeptical about H, then one shouldn'
What is the Hypothetico Deductive Method?
Derive predictions and hypotheses, if one is wrong than entire hypothesis is wrong - not used by scientists - too black and white
Pr(A)= Rational Level of Confidence
Problems? Advantages?
Personalist Interpretation - problems: makes probabilities on us, rather than world; causes constraints - advantages: can handle all examples given
Pr(A)= # Observed Cases of Where A Occurs/# Total Observed Cases
Problems?
Statistical Interpretation - problems: certain observations haven't been properly conducted; certain probabilistic judgments not observable (like Iran statement)
Pr(A)= #'s of A's in n-many trials/n
Problems?
Frequency Interpretation - problems: some probabilities not trial specific; never in position to know what happens when n goes to infinity; knowing value, doesn't help understand what might happen next
e=Phil 1520 has over 120 seats
H= Force = Mass x Acceleration
Example of which Sagan Law?
e neither confirms or rejects H
What are basic principles of Bayesian confirmation?
1. Evidence e rejects H iff Pr(H|e) < Pr(H) i.e if confidence in H lower after considering e
2. Evidence e confirms H iff Pr(H|e) > Pr(H) i.e if confidence in H higher after considering e
3. Evidence e neither confirms or rejects if Pr(H)=Pr(H|e)
Pr(A) = Equally probable cases such that A/# Totally Equally Probable Cases
Problems? PI?
Classical Interpretation - PI= Principle of Indifference: A & B equally probable iff one has no more reason to expect A than B - problems: PI contradictory; deep conceptual problems; doesn't make sense with probabilistic statements past
e = Universe Law-Governed
H = There is Creator?
Which of Sagan's Laws?
Surprised to find e if H is false, e confirms H
What is Confirmation Theory?
Philosophical theory provides us with mathematical model at how humans OUGHT to update beliefs in life of new evidence
e = Muslim-Americans dominantly voted for Bush in 2000
H = Minorities vote for Democrats
Which of Sagan's Laws?
Surprised to find e if H were true, e rejects H
Probability of getting heads on THIS coin is 1/2
Which interpretation?
Frequency
What is a Stratified Random Sample?
Definition & uses?
Forces representation into sample - definition: sample carefully paritioned into every combo of relevant factors and filled accordingly; Factor
relevant iff likelihood that F is a G depends on whether or not F has
; perfect for heterogeneous population
What happens in a retrospective study?
1. Researchers notice difference between two groups before same point t0
2. At t0 the study begins
3. Researchers investigate same point before, to discover cause that distinguishes two groups
Researchers calculated that underage drinkers (12-20) consume about 18% of alcoholic drinks - more than 20 million drinks per year
Which of Best's ideas?
numbers that are too high or too low - numbers that seem hard to produce; how would someone calculate that
Underage college student dies from acute poisoning - links with number of underage students drink
Which of Best's ideas?
Dramatic examples coupled to big numbers
Know that regular exposure to second-hand smoke increases chances of developing heart disease by around 25% - for every non-smoker who works in smoky environment one of them will suffer disability and die from prematurely from heart condition from second-
Explanations that convert statistic into simpler language have surprising implications
Website claims "4 million women battered to death by husbands or boyfriends each year" - this number cannot be correct because there are only about 17,000 homicides annually.
Which of Best's ideas?
Numbers inconsistent with benchmark figures
9/11: Worst Disaster in US History
Which of Best's ideas?
Superlatives; 'biggest', 'worst' etc.
Women are only paid $.72 to every $1 a man is paid
Example of what type of suspicious data?
Masquerading numbers
The murder rate of states with capital punishment higher than states without capital punishment.
Example of what type of suspicious data?
Confusing correlation with causation
In 1980's Gorbachev suspected rise in alcoholism in USSR and announced crackdown on drinking - Soviet officials blamed drinking for declining industrial production
What fallacy?
Confusing cause and effect
Young man was fine before reading Fear and Trembling - week later he can't sleep and emits awful moans; Fear and Trembling is a dangerous book
What fallacy?
Post Hoc
Today, a young person, 14-26, kills themselves every 13 minutes in the U.S
Which of Best's ideas?
Numbers that seem surprisingly large or small
What happens in a prospective study?
1. Exposure to cause happens before study begins
2. At t0, study begins
3. Researchers look to see if any interesting differences appear in two groups
What is the fallacy of Biased Statistics?
When one tried to make basic inference and sample lacks sufficient variety
What does it mean if you get a negative correlation?
Hypothesis reverses; F's tend not to go with G's
What is Confusing Cause and Effect?
Two events occur at the same time, we commit the fallacy when we take cause for effect and effect for cause
What is a homogeneous population? Big or small?
Everyone there is the same; small
We've created 1,000,000 new jobs this year!
Example of what type of suspicious data?
Beware of what is not said
What is heterogeneous population? Big or small?
Cannot find a consensus among all - things may be more fine-grained than that; big
What is a Self-Selecting sample? Problems with this type of sample?
People invited to contribute and any participant is counted
Problems: tend to be unrepresentative; not everyone has access to way surveys collected (phone, email, etc.); customer service: people only give feedback when angry; no control to number of respo
What are requirements for a good sample?
Size and Representation
Studying effects of new drug on patients
What sample?
Self-Selecting
Studying musical taste of college students
What sample?
Stratified Random
Quality control on assembly line of same toy
What sample?
Random
Bible Code, Necker Cube and Spinning Woman examples of which cognitive failure?
Attached significance to patterns when there are none
Aquarius/Libra bad drivers, Harvard grads & jobs, Low SAT scores are examples of which cognitive failure?
Eager to infer causation from correlation
iPod shuffle function and Special Relativity Experiment are examples of which cognitive failure?
How we interpret data influenced by preconceptions - believed evidence that agrees and ignores evidence that contradicts
What is the fallacy of Misleading Vividness?
Ascribe undue importance to vivid evidence in face of non-vivid evidence
.75 < CC < 1 = ?
Good or bad?
Strong positive correlation; good
.4 < CC < .75 = ?
good or bad?
Medium positive correlation; good
People with larger feet tend to be better readers. Either big feet improve reading skills or improved reading skills cause feet to grow
Which fallacy?
Ignoring Common Cause
Tooth decay cause of bad dental hygiene. Think about it .. people give up after working so hard and still get cavities.
Which fallacy?
Confusing Cause and Effect
Connection between finger length and SAT scores. Apparently, if ones ring finger is longer than index finger likely score better on math portion of SAT - I'm bad at math, so I'm just going to cut off tips of my index fingers! 800 math here I come!
Which f
Ignoring Common Cause
Before TV came along, we didn't have much of a problem with illegal drugs. People learn about drugs on TV and want them, so TV is ruining the country
Which fallacy?
Ignoring Common Cause
According to latest poll 56% of registered voters in Ohio would vote for Bush if election held today - has margin of error of +/- 3%
Example of what type of suspicious data?
Margin of Error Talk
Last month, unemployment dropped from 5.7% to 5.6%
Example of what type of suspicious data?
Mathematical Hocus Pocus
Average starting salary of our financial planners is $56,000
Example of what type of suspicious data?
Suspiciously Specific Numbers
Last year, American pet owners spent $30,652,875,327 on pet food
Example of what type of suspicious data?
Suspiciously Round Numbers
What is Post Hoc fallacy?
One event occurs after another, so one concludes on that basis alone that the one caused the other
Saturns are great! I've had mine for 5 years with no issues!"
Which fallacy?
Anecdotal Evidence
Revenue form opening weekend of Dark Knight Rises less than expected because of Aurora shooting
Which fallacy?
Misleading Vividness
What is anecdotal evidence?
Relying on others stories
What is the fallacy of Hasty Generalization?
When one tries to make basic inference with too small a sample
What is the Method of Agreement?
Identify common factor among range of cases where effect occurred
What is the Method of Difference?
Compare cases where effect is present and ones where it is not
Joe weighing cargo on trucks - truck pulls onto scale and Joe records 6,000 lb - subtracts weight of truck to determine cargo weight
Which of Mill's Methods?
Method of Residues
Dick and Jane did bad on test - both had studied, but pulled all-nighters - conducted lack of sleep caused poor test scores
Which of Mill's Methods?
Method of Agreement
What is the Method of Residues?
After verifying certain causes, one removes those from casual picture to determine whether there are further causes
What is the Method of Concomitant Variation?
Check to see if greater or lesser proportions of putative cause result in greater or lesser proportion of effect
What is the Joint Method?
Find both cases where cause present and effect occurs and where cause is not present and effect does not occur
By third shot of whiskey, Rob noticed he was feeling drunk- drank another, feeling increased- curious, he drank another and room began to spin- concluded whiskey was making him drunk
Which of Mill's Methods?
Concomitant Variation
0 < CC <.4 = ?
good or bad?
Weak positive correlation; bad
CC = 0 = ?
good or bad?
No correlation; BAD
-.4 < CC < 0 = ?
good or bad?
Weak negative correlation; bad
-.75 < CC < .4 = ?
good or bad?
Medium negative correlation; good
-1 < CC < -.75 = ?
good or bad?
Strong negative correlation; good
Formula for Correlation Coefficient?
CC = Agreement - Disagreement/Total
What is a Double Blinded Study?
Why is double blindness important?
Subjects do not know whether in control or experimental group - researchers do not know which of subjects are in experimental or control group; psychosomatic effects, "tipping off", researcher bias (personal success, monetary of investment of company, etc
Under what conditions is Double Blindness possible? What type of studies?
Experimental is BEST!; Prospective is possible depending on study; Retrospective is IMPOSSIBLE - effects already present - data in case casual history of subject - very hard to discover that without first starting with what group person is in
What are two groups are in controlled studies?
Experimental group and Control group
What happens in an experimental study?
1. Study begins t0
2. Researchers separate group into experimental and control group
3. Researchers expose experimental group to cause and control group is left alone
4. Researchers wait and see if expected effect occurs
What are the types of controlled studies?
Experimental, prospective and retrospective
What is the experimental group? Control group?
Experimental exposed to putative cause; Control group not exposed to putative cause - groups alike: no correlation=no cause, groups different: correlation=very likely causation
COnstellations, Tortilla Jesus, Hot Hands are examples of what cognitive failure?
Look for and find patterns in everything
What is fallacy of Ignoring Common Cause?
Two events may always be correlated and one might happen just after the other - but it doesn't follow that are caused the other, they exist both be caused by something else!
Studying opinion of local voters on issue of school vouchers. What sample?
Self-selection: may content with all problems of self-selecting but it is a starting point
Studying anatomical features of bird in Amazonian rain forest?
Random if both male and female look alike; Stratified random if male and female drastically different
Issues for Controlled Studies? Retrospective? Prospective? Experimental?
Retrospective & Prospective: causal inference between time of beginning of study and introduction of putative cause leads us to doubt reliability of conclusion; Experimental: artificiality and ethical worries
e = Scanlon owned pengun
H = James Dixon shot police officer Scanlon
Example of which of Sagan's Laws?
Strong believer in H, then one shouldn't become skeptic unless strong evidence against H found
What is the Basic Inference?
X% of F's are G's in sample; Therefore, X% of the F's are G's in the population
What is a Random Sample? Definition and Practical Concern?
Every member of population has equal chance of ending up in sample; Practical concern: employing truly random sample nearly impossible in heterogeneous population - perfect for homogeneous
I warned those boys not to stand on Prince's grave, when he was buried his mother put a curse on the grave - but, those boys would not listen and now look at them! - all broken up from car crash! - tell you, that curse worked!
What fallacy?
Post Hoc
Probability of United States engaging Iran by 2014 is 40%
Example of which interpretation?
Personalist
Probability of getting heads on FAIR coin is 1/2
Example of which interpretation?
Classical