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