RE: Type II Poisson Errors (REPOSTED)

["Christoph Hofmeyr" <chofmeyr@nnr.co.za>]

James,Radsafers,

I think you are posing a very interesting question.  Poisson statistics

are applicable when we are dealing with a counting problem.  When one

mentions 'background' to any HP person, or, for that matter to most

physicists, their immediate urge is to want to subtract it somewhere.

Now, the Poisson distribution has the fairly unique and valuable

property that the variance is equal to the average.  Futher, the sum of

two Poisson distributions (say, background and say, source) is again a

Poisson distribution. But, and this is a big BUT, the difference is in

general NOT a Poisson distribution.  So, having lovingly subtracted the

background, you have destroyed the Poisson distribution of your data.

Makes one think, doesn't it.

One redeeming feature is that the equivalent Normal gaussian

distribution is very similar for anything above about 20 'events' (with

SD = square root of 'mean') in a given time, but obviously the main

difference lies in the tails (Poisson stops at 0), if one is willing to

overlook the continuous nature of the Gaussian.  But here one must also

remember that variances ADD, so subtraction should be avoided, if

possible.  Hope these pointers are useful.  Own thoughts.

Chris Hofmeyr

chofmeyr@nnr.co.za   



-----Original Message-----

From: james.g.barnes@att.net [mailto:james.g.barnes@att.net]

Sent: Friday, September 21, 2001 7:45 PM

To: RadSafe Bulletin Board

Cc: james.g.barnes@boeing.com

Subject: Type II Poisson Errors (REPOSTED)





PLease forgive me if this is a repost.  I am in the 

process of shifting email accounts, and the first posting 

may have been lost in the shuffle. . . .



Folks,



We have been working with determining detection levels in 

some low background count situations, and have been 

examining the counter behavior using Poisson statistics.  

Poisson statistics will basically allow one to calculate 

a cumulative probability of the number of counts a person 

would see for a given count with an expected background 

for that count period.  This approach appears to 

calculate a value that could be considered (I suppose) 

equivalent to a "Type 1" scenario (i.e., roughly 

equivalent to the Decision Level; prone to "false 

positive" detections).



Is there an approach using a poisson distribution that 

calculates something akin to the Type II error (i.e, the 

LLD value that anticipates and corrects for false 

positive events).  I have looked at all the usual 

references, but haven't seen any treatment of this.  Is 

"LLD" even a meaningful concept in a Poisson 

distribution?



Thanks,



Jim Barnes, CHP

Radiation Safety Officer

Rocketdyne/Boeing

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