Friday March 29 Class Notes

The Multi-World Metaphor

How to travel to the different worlds …

We've already done several examples using resampling — the idea is to see how much sampling variation there would be if the world were just like our sample.

Now to do shuffling.

Work with model coefficients and \( R^2 \) from a few models, with shuffling of an explanatory variable, or shuffling of the response.

Example: Sector of the economy and wages

mod = lm(wage ~ sector * sex + educ + exper, data = CPS85)
observedr2 = r.squared(mod)
## [1] 0.3113

Now go to Planet Null

s = do(1000) * lm(wage ~ shuffle(sector) * sex + educ + exper, data = CPS85)
densityplot(~r.squared, data = s)

plot of chunk unnamed-chunk-3

tally(~r.squared >= observedr2, data = s)
##  TRUE FALSE Total 
##     0  1000  1000

What's the p-value?

Do the same on a coefficient and look at the two-tailed test.

Stocks on Planet Null

## Retrieving from
## [1] TRUE
djia = getDJIAdata()  # djia-2011.csv is the basic file
## Retrieving from
xyplot(Close ~ Date, data = djia)

plot of chunk unnamed-chunk-4

Look at the day-to-day differences in log prices:

dd = with(djia, diff(log(Close)))
## [1] 0.000191

Subtract out the mean, shuffle, cumulative sum, and exponentiate to create a realization:

ddnull = dd - mean(dd)
sim = exp(cumsum(shuffle(ddnull)))
xyplot(sim ~ Date, data = djia)

plot of chunk unnamed-chunk-6

Drunk Driving Example

Planet Null:

Planet Alt

What's the decision threshold?

What's the

App for playing with Significance and Power

mHypTest()  # by default, a coefficient