[R-sig-ME] within-group averaging

David Duffy David.Duffy at qimr.edu.au
Thu Nov 29 11:01:39 CET 2012

On Thu, 29 Nov 2012, Jarrod Hadfield wrote:

> Hi Jonas,
> Thanks for your reply. Initially, I thought it was solely to do with 
> inhomogeneity too, and I agree that it plays a role. However, if you replace
> cuty<-cut(y,10) with cuty<-cut(x,10) (i.e. define groups by bins of x rather 
> than y) then the problems with bias and type-I error rate disappear despite 
> the same pattern of inhomogeneity existing.

If you plot your xbar2_cuty v. xbar and xbar2_cutx v. xbar you will see 
the latter is symmetrical around the line of identity, while the former is 
biased in the direction of the y~x regression line. The nonrandom 
coarsening of a subset apparently can affect inference

(A quick google obtained 

| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD at qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
| Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
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