Stats 155 Class Notes 2012-11-05

Election-Eve Activities

• 512 paths to the White House
• A prediction contest — fill this in and hand it back. We'll analyze the results on Wednesday.

Hypothesis testing framework review

The Ivory Billed woodpecker from a hypothesis testing perspective second page.

Reminder about confidence intervals

Confidence intervals are computed on Planet Samp.

1. What fraction of the earth is covered by water? Toss the globe around.
2. How much of the US is within one mile of a road?
   
   • Use google maps with a location specified like this (100.342 W, 35.873 N) and look for the green arrow rather than the “push-pin” (which gives the nearest address, which is typically near a road). *Pick a random longitude between 65 and 125 degrees W, and a latitude between 25 and 50 degrees N. If you get water, pick a new point. (Here's a map that can be used to justify this range of locations.) !
   • Tally up how many yesses and no's.
   • Resample these to get a standard error. Also do the regression report.

Shuffling

A proof for the existence of Extra-Sensory Perception! If I can get you to focus on a number, I can predict, to some extent, your thought process.

Your birthday is a number that plays an important part in your thought process. Generate a random number between 0 and your birday.

Permutation test by hand

Spreadsheet reading command:

esp = fetchGoogle("https://docs.google.com/spreadsheet/pub?key=0Am13enSalO74dE5iMjZrcGFjTUtJSjg0T05NLW84Mmc&single=true&gid=0&output=csv")

## Loading required package: RCurl

## Loading required package: bitops

Power

How did I know that I could reject the Null in the shuffling problem? I did a little simulation.

mysim <- function(n = 15) {
    days = resample(1:31, size = n)
    nums = ceiling(runif(n, min = 0, max = days))
    mod = lm(nums ~ days)
    list(r2 = r.squared(mod), p = summary(mod)$coef[2, 4])
}
s15 = do(1000) * mysim(24)  # typical R^2 is about 0.4
mean(~r2, data = s15)

## [1] 0.06933

tally(~p < 0.05, data = s15, format = "proportion")

## 
##  TRUE FALSE Total 
## 0.961 0.039 1.000

Do mHypTest(TRUE) setting the “effect size” to about 0.4