Philosophy Exam 2

(Bayesian Thinking) Evidence supports H if

P(E|H)>P(E~H)

(Bayesian Thinking) Bigger difference =

Stronger evidence

P(E|H)

How likely the evidence is if H is true

P(E|~H)

How likely the evidence is if H is false

If P(E|H)>P(E|~H)

The evidence supports H, doesn't mean H is true, should increase confidence in H

Bayesian Thinking example

H = "This pill works", E = "Pain goes away quickly". If pill works -> pain goes away often -> P(E|H) is high. If pill doesn't work -> pain goes away rarely -> P(E~H) is low. So P(E|H) > P(E|~H), meaning the evidence (the pain goes away) supports the idea that the pill works, and we can increase our confidence that the pill works.

P(E|H) < P(E|~H)

Evidence supports ~H, should decrease confidence in H

Correlation does not equal

causation

Reverse causation

You think A causes B, but really B causes A

Reverse causation example

You think drinking beer causes watching beer commercials, but watching beer commercials causes drinking beer.

Common cause

A third factor causes A and B to occur

Common cause example

A study finds that people who carry lighters are more likely to get lung cancer. Common cause would be smoking.

Regression to the Mean

Extreme outcomes naturally return to average, causes false casual beliefs

Regression to the mean example

bad performers improve and great performers decline slightly

Selection effects

Biased sample

Example of selection effects

Only surveying your dorm

Probability range

0 to 1

Mutually exclusive events

Two events that cant happen at the same time P(A&B)=0

mutually exclusive event example

Flipping a coin and getting heads and tails at the same time

Independent effects

Two events where one does not effect the other

Independent effects example

Flip a coin twice: first flip does not effect second

Independent effects rule

P(A&B) = P(A) * P(B)

Independent effects rule example

P(heads first) = 1/2, P (heads second) = 1/2. So, P(both heads) = 1/2*1/2=1/4

P(at least one)=

1-P(none)

survivor bias

only see successes. not counting for failures

response bias

People lie/skew answers in a study

Whats the probability of getting at least one tail in 3 coin flips?

Step 1: find "none" "no tails" = all heads, P(all heads)=(1/2)^3=1/8. Step 2: subtract from 1, 1-1/8=7/8

Good experiment

random assignment, control group, double blind, only difference is variable tested

Selection bias

Bad sample in a study

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