Re: Statistics or sadistics?

["James W. Wheeler" <jwheeler@eagle.lhup.edu>]

1.  The error in the result of A-B should be sqrt(145+41), which is 13.6.

2.  Using the well counted background, the expected background for one
minute is 35, but its uncertainty is sqrt(35) which is 5.9.  (Since
the distribution is Poisson!)  Thus the A-B result for one minute
would be 110 with an uncertainty of sqrt(145+35) which is 13.4. 

On Mon, 23 Mar 1998, LUDWIK KOWALSKI wrote:

> Questions generated by today's lab.
>
> A long-T radiactive sample was "counted" for one munute. The outcome 
> was A=145 -->st.dev.=12. Then the background was measured for one minute 
> yielding B=41 --> st.dev=6.4.
>
> 1) The estimated net A-B is 104. What error bar (st.dev.) should be
>    used for this result. I know it would be 18.4 if the result were
>    obtained from a multiplication, or from a division of A and B. But
>    what is the expected standard deviation of a differnce, or sum, in
>    terms of known sig_A and sig_B?
>
> 2) Subsequently the background, measured for 60 minutes, were 2110.
>    Thus B=35 --> st.dev.=sqrt(2110)/60=0.76. This is much better that
>    41 +/-6.4 . But the sample is no longer available for long counting. 
>    Can we really benefit from the long counting of the background? My 
>    answer is NO. We might know the long-term mean value of B very well 
>    but we have no way of knowing what fraction of the net count of
>    (145 +/-12) was actually due to the background. A very long 
>    counting of B does not help us to reduce the error bar around the
>    value of 104. Do you agree?