Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

Example: n = 12 and @ = 95%:
1
n = 12 and @ = 99%: I/-- G = ~'1003 - 1 = ~43 = 1.22
11- 2 1 ' -
2
5
n = 12 and B = 50%: 4 - - G =
11- 2
42 - 1 = a = 0.39
1
For large n and n; >> lny (y = -1, the following approxiinations are
1-F
valid :
- 2 - 2
G - - lny
n-2 n
This approximation. exemplifies the general propaga-ti-on-of-error law,
namely that the errors are reduced proportional. to the square root
of the number of observations.
Ln the more general case that Z depends on X and Y with a non-zero
coherence between X and Y confidence limits can be obtained in a
similar way: Let
z = a x + boyo + 6zo,
0 0
assuming that now X -- and Y are real-ized error free. Then the Fisher-
distributed ratio, involving the deviation of A and B from a and
0
b ; turns out to be
which has a f (4, n-4) dis.tri.buti.on. The confidence limi-ts for A and
F
R cannot be calculated individuall.y, unless of course S is taken
"jr
to be zero. On the other hand, if we assume that I~-a,l and I R-boI
are equal, Chen