Variancestabilizingtransformations
Whenthe standard
deviation Y is a
of
function(p) of themean
valuep - E(Y),
we cantransform to h(Y) by
Y
dh(Y)/dY: ktl/(Y)l
1.e.
h(Y): I/rff) dY.
The standard
deviationof h(Y) no longer
depends p.
on
q
e
u\
irp
238
MORE C
N,
cfw_r
Distributions:
Normal
let
1);
Chi-square: ZbeN(O,
ThenZz is chi-square
with 1 df:
21, Z u . o .) Z n Z
(0,
normalindependent 1);
ThenZ(Zr)'is chi-square
with n df.
t: iet ZbeN(0,l);
Let W be chi-square,
independent Z;
of
Then
zl.1ryn)
hasat-distr
The proportionalreductionin the varrance
of
Y accounted by its regression X is
for
on
known as K-'.
n'is knownasthecoefficient
of
determination.It is alsothe squareof the
correlation coefficientbetween andY.
X
x
UI
R ec al l :!:- - - c r + p x t + e 1
whe