Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: Statistics or sadistics?



After reading my own message again I see an error. Let me coorect it.

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.

The last sentence is not correct. Suppose A and B are used to calculate
speed, for example, v=A/B=145/41=3.54, and that standard deviations are
as above. What is the standard deviation of v? It is 0.845 and not 18.4.

We add relative errors (dimensionless) and not absolute errors (meters
and seconds). In this case the relative error in A is 0.0827 and the
relative error in B is 0.1561. Thus the relative error in v must be
0.2388. The absolute error in v is the product of 0.24 and 3.54.

If A and B were used to calculate an area S=A*B=5945 then the relative
error of 0.2388 in S would correspond to the absolute error in S equal
to 0.2388*5945=1420 (rather than 18.4).

what is the expected standard deviation of a differnce, or sum, in
terms of known sig_A and sig_B?

John Trammell wrote:

OK, I'll have a go at it. Use 'd' for full derivative, 'D' for partial.

S = A - B

DS DS
dS = ---- * dA + ---- * dB
DA DB

= dA + dB [it was dA - dB, a typing error ?]

So, assuming gaussian statistics:

|dS| = sqrt((dA)^2 + (dB)^2)

Note that A and B are dimensionally identical (otherwise A-B would be
meaningless) and the sum of two squares is acceptable. This gives the
following absolute error (st. dev.) for the quantity S=A-B=104.

|dS|= sqrt(12^2+6.4^2)=13.6

Sort of strange. The error in A is 8.27%, the error in B is 15.61%
but the error in the A-B is only 13%. What is wrong?
Ludwik Kowalski