11/4 Part 2 Estimating Effects 2
CLT - Central Limit Theorem
Analogy principle is to assume the actual value is equal to its analogy in the sample.
S3. Bootstrap Confidence Intervals
Question - what would happen if we observed JP’s career over and over again.
Bootstrap - we use the observed sample in place of the actual distribution.
Consider the Khan Academy data on emissions tests, then put in JP data
Khan Academy Data
What is the probability emissions > 20
15.6
16.2
22.5
20.5
16.4
19.4
16.6
17.9
12.7
13.9
Go to http://lock5stat.com/statkey/bootstrap_1_quant/bootstrap_1_quant.html
Go to "edit data" and copy in the data above.
Answer: JP is better than Babe Ruth!
S4 Bayesian Approach
Likelihood(JP’s BA = p | {1,1,1}) = p^3 (1 - p)^0 = p^3
Bayes’s Rule
Pr(JP’s BA = p | {1,1,1}, s(p)) = s(p) p^3 / (\sum_{q} s(q) q^3)
s(p) is “prior” distribution over p (JP’s actual batting average).
Assumption: s(p) could be the actual batting averages.
Answer: JP is better than Babe Ruth with 6.4% probability.
Assumption: s(p) is “similar” JP batters
Answer: JP is better than Babe Ruth with 0.01% probability