Isobel,
Thanks for the reply. I feel this problem deserves more discussion.
I have found the message from: Gregoire Dubois, Date: Mon Mar 5, 2001,
Subject: AI-GEOSTATS: SUMMARY: Nscore transform & kriging of log normal
data sets (The original author couldn't be found, and s/he should be in the
list): "Most of geostatistics is "distribution free", i.e., the derivation
of the simple kriging, ordinary kriging and universal kriging equations do
not depend on a distributional assumption (contrary to what is sometimes
claimed)."
An example may be the "Indicator Kriging": It is impossible for the "0"s and
"1"s to follow the normal distribution.
The reason why I care about this issue is that there are at least two
problems related to data transformation (in order to follow the normal
distribution):
(1) The measurement scale is reduced. The orignal ratio/interval scale may
be reduced to the lower level of ordinal, even close to nominal, which
results in loss of raw information.
(2) Artificial relationship is introduced. We know that the lognormal
distribution is widely accepted. In correlation analysis, if the
log-transformed data are used, the correlation becomes the "log-log"
relationship, not the oginal linear relationship. In bivariate regression
analysis, the original function is:
y = a x + b
However, for the log-transformed data, the function becomes:
log(y) = a log(x) + b
or y = exp (a log(x) + b)
In many cases, it is not clear if the relationship should be linear or
"log-linear". However, the artificially introduced "log-linear" relationship
need to be proved.
The most difficult situation is that if scientifically the relationship
between x and y is linear, should the data transformation still be carried
out (just to satisfy the statistical requirement)?
Cheers,
Chaosheng
----- Original Message -----
From: "Isobel Clark" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Friday, May 17, 2002 7:39 PM
Subject: AI-GEOSTATS: Normal distributions
> Short answer is yes to everything.
>
> middle length answer is that Normality is not required
> for anything except where it is a basic assumption -
> such as in simulation. It is necessary that the
> distribution be well behaved (not skewed) and conform
> to the Central Limit Theorem.
>
> Having said that, I can't tell you where the join is
> between 'well behaved' and not. It is usually fairly
> obvious from probability plots and semi-variograms
> when things start to get hairy.
>
> Isobel Clark
> http://geoecosse.bizland.com/BYOGeostats.htm
>
>
>
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