R help - Nov 2005 - OT: Statistics question

I apologise for asking this question here but I am hoping that someone
can either give me direct guidance and/or point me to a better group for
this type of disucssion.

I have what I feel should be a fairly simple problem but which my
limited stats knowledge can't answer. I have two overlapping
distributions (both normal) and I want to answer the question how do I
calculate the cut-off value so I can be 95% sure that samples => than
the cut off fall in the right hand distribution?

A while ago I did a bayesian statistics course that I think answered
this very question but in the absence of any course notes or recent
practice Ihave forgotten how to go about this.

Many thanks for your time
Tom

tom wright <tom at maladmin.com> writes:
> I apologise for asking this question here but I am hoping that someone
> can either give me direct guidance and/or point me to a better group for
> this type of disucssion.
> 
> I have what I feel should be a fairly simple problem but which my
> limited stats knowledge can't answer. I have two overlapping
> distributions (both normal) and I want to answer the question how do I
> calculate the cut-off value so I can be 95% sure that samples => than
> the cut off fall in the right hand distribution?
> 
> A while ago I did a bayesian statistics course that I think answered
> this very question but in the absence of any course notes or recent
> practice Ihave forgotten how to go about this.
The ratio of the tail probabilities should be bigger than 19
(.95/.05), *if* there is a 50/50 chance of belonging to either group.
Otherwise, you have to weight the tails according to the group
probability. Beware that this ratio is not necessarily a monotone
function of the cutoff if the variances differ.

-- 
   O__  ---- Peter Dalgaard             ??ster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907

What if the distributions are not normal etc? You might want to try a
simulation to get an answer. Draw random samples from each
distribution (without assuming normality etc - one way to do this is
to get the quantiles, then draw a sample of quantiles, then draw a
value from each quantile), throw them into a grid and get the % of
As/Bs in each bin. After several iterations it should become
reasonably clear where the 95% B bins start.

> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Peter Dalgaard
> Sent: Wednesday, November 30, 2005 12:26 PM
> To: tom wright
> Cc: r-help at stat.math.ethz.ch
> Subject: Re: [R] OT: Statistics question
>
>
> tom wright <tom at maladmin.com> writes:
>
> > I apologise for asking this question here but I am hoping
> that someone
> > can either give me direct guidance and/or point me to a
> better group for
> > this type of disucssion.
> >
> > I have what I feel should be a fairly simple problem but which my
> > limited stats knowledge can't answer. I have two overlapping
> > distributions (both normal) and I want to answer the
> question how do I
> > calculate the cut-off value so I can be 95% sure that
> samples => than
> > the cut off fall in the right hand distribution?
> >
> > A while ago I did a bayesian statistics course that I think answered
> > this very question but in the absence of any course notes or recent
> > practice Ihave forgotten how to go about this.
>
> The ratio of the tail probabilities should be bigger than 19
> (.95/.05), *if* there is a 50/50 chance of belonging to either group.
> Otherwise, you have to weight the tails according to the group
> probability. Beware that this ratio is not necessarily a monotone
> function of the cutoff if the variances differ.
>
> --
>    O__  ---- Peter Dalgaard             ??ster Farimagsgade 5, Entr.B
>   c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
>  (*) \(*) -- University of Copenhagen   Denmark          Ph:
> (+45) 35327918
> ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX:
> (+45) 35327907
>
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