Re: [R] regression towards the mean, AS paper November 2007

From: hadley wickham <h.wickham_at_gmail.com>
Date: Mon, 17 Dec 2007 15:10:32 -0600

> This has nothing to do really with the question that Troels asked,
> but the exposition quoted from the AA paper is unnecessarily confusing.
> The phrase ``Because X0 and X1 have identical marginal
> distributions ...''
> throws the reader off the track. The identical marginal distributions
> are irrelevant. All one needs is that the ***means*** of X0 and X1
> be the same, and then the null hypothesis tested by a paired t-test
> is true and so the p-values are (asymptotically) Uniform[0,1]. With
> a sample size of 100, the ``asymptotically'' bit can be safely ignored
> for any ``decent'' joint distribution of X0 and X1. If one further
> assumes that X0 - X1 is Gaussian (which has nothing to do with X0 and
> X1 having identical marginal distributions) then ``asymptotically''
> turns into ``exactly''.

Another related issue is that uniform distributions don't look very uniform:

hist(runif(100))
hist(runif(1000))
hist(runif(10000))

Be sure to calibrate your eyes (and your bin width) before rejecting the hypothesis that the distribution is uniform.

Hadley

-- 
http://had.co.nz/

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Received on Mon 17 Dec 2007 - 21:13:53 GMT

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