Re: AI-GEOSTATS: Extreme values?

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• Dear Isobel, Thanks for your quick and helpful reply! (1) I would like to trust both the accuracy and precision of the dataset, and the real problem is how we
Message 1 of 10 , Dec 13, 2001
Dear Isobel,

(1) I would like to trust both the accuracy and precision of the dataset,
and the real problem is how we "play the computer game". The extreme values
may be from the samples which by chance contains many minerals.

(2) From the information of percentiles I provided in the message, you can
find that
the dataset is heavily skewed in deed. Logarithmic transformation can make
some of the variables follow the "normal distribution", but not all.
However, the extreme values still look extreme in the transformed dataset.

(3) There may be two populations: "background" and "mineralised". However,
there is really no way to "dichotomise" the two populations. Geographically
or mathematically? Geographically, there are three areas of high values.
Mathematically, we need some proof. Even though we could properly separate
the datasets into two "populations", the extreme values may still be extreme
in the "mineralised" population.

Since the really "bad" values are only <2% of the total number (such as 4 or
5 values out of the total number of 223, which can also be seen from the
percentiles), I am unwilling to use nonparametric methods until we cannot
find a way to use the parametric methods.

Another problem is when we carry out spatial interpolation, these values may
produce artificial contour lines around these sampling locations, even
though they can be smoothed. I don't think this is the realistic situation
in the field.

Well, I am still not very confident what the best way should be ... I know
the worst way is to discard these "outlying" values, and the second worst
way is to use non-parametric methods.

Cheers,

Chaosheng Zhang

----- Original Message -----
From: "Isobel Clark" <drisobelclark@...>
To: "Chaosheng Zhang" <Chaosheng.Zhang@...>
Cc: <ai-geostats@...>
Sent: Thursday, December 13, 2001 2:18 PM
Subject: Re: AI-GEOSTATS: Extreme values?

> > My question is: How to deal with the
> > extreme/outlying values in a data set?
> The real priority is to establish why you have extreme
> highs. For example:
>
> (1) is there a high imprecision in measuring the
> values, so that the sample observations are actually
> inaccurate? If so, is it relative to the value or a
> flat error?
>
> (2) do you have a skewed distribution of values?
>
> (3) do you have two (or more) populations, only one of
> which gives the high values?
>
> and there may be others. Once you determine the reason
> for extreme values, then you can more objectively know
> how to deal with them.
>
> For example, if you think (2) is most likely than look
> at transformations or distribution-free approaches to
> geostatistics. You can find some of my papers in
> dealing with positivel skewed distributions at:
>
> http://uk.geocities.com/drisobelclark/resume/Publications.html
>
> If (3) is more likely - as may be probable is your are
> looking at an area where samples may be 'background'
> or 'contaminated' - you really need to identify the
> populations first. Then you may be able to apply a
> mixture model together with indicator geostatistical
> approaches.
>
> If (1) is your problem, then you may be able to use a
> rough non-parametric approach to get to cross
> validation. The 'error statistics' in a cross
> validation exercise will often assist in identifying
> erroneous sample measurements.
>
> Hope this helps
> Isobel Clark
>
>
>
>
> __________________________________________________
> Do You Yahoo!?
> Everything you'll ever need on one web page
> from News and Sport to Email and Music Charts
> http://uk.my.yahoo.com

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• Dear Chaosheng Zang The sampling interval is so wide that the high values could easily be related to hot spots of higher grade contamination, i..e dumping
Message 2 of 10 , Dec 13, 2001
Dear Chaosheng Zang

The sampling interval is so wide that the high values could easily be related to "hot spots" of
higher grade contamination, i..e dumping areas for particular kinds of slags, mineralized
waste, etc. A property map might help.

Have you contoured the data? If so, the sampling interval is so wide that real hot spots of
environmental significance might not show 2D distribution on such a wide sampling grid,
however.

Regards

Marcel Vallée, Eng,, Geo.
Geoconseil Marcel Vallée Inc.
706 Routhier Ave
Québec, Québec G1X 3J9
Tel: (1) 418 652 3497
Fax: (1) 418 652 9148
Email: vallee.marcel@...

==============================================
13/12/01 08:01:48, Chaosheng Zhang <Chaosheng.Zhang@...> wrote:

>
> Date: Thu, 13 Dec 2001 13:01:48 +0000
>
> From: Chaosheng Zhang <Chaosheng.Zhang@...>
> Subject:AI-GEOSTATS: Extreme values?
> To: ai-geostats@...
>
>
>
> Dear all,
>
> My question is: How to deal with the extreme/outlying values in a data set?
>
> I am dealing with heavy metal concentrations in soils from a mine area. The
>
> sample number is 223, and the samples are spatially evenly distributed with
> the sampling interval of 400 metres. There are several samples with
> extremely high values, which makes me feel uncomfortable. The percentiles of
> the dataset are listed as follows (in mg/kg):
>
>
> Zn Cu Pb Cd As
> Min 4 1 25 0.0 2
> 5% 35 6 35 0.1 6
> 10% 40 7 41 0.2 7
>
> 25% 65 13 62 0.3 9
> 50% 122 18 168 0.6 15
> 75% 338 27 821 1.5 28
> 90% 907 56 2799 2.8 58
>
> 95% 1986 116 4490 4.2 80
> 96% 2462 151 4698 4.9 82
> 97% 3493 178 5413 6.2 91
> 98% 4697 207 7609 8.3 111
>
> 99% 6712 247 11750 12.4 184
> Max 11473 1293 16305 48.5 1060
> When doing geostatistical and statistical analyses, we need some confidence
> in dealing with the these very high extreme values which account for less
>
> than 2% of the total sample number.
>
> Any suggestions?
>
> Cheers,
>
> Chaosheng Zhang
> ===================================
> Dr. Chaosheng Zhang
> Department of Geography
> National University of Ireland
> Galway
> IRELAND
>
> Tel: +353-91-524411 ext. 2375
> Fax: +353-91-525700
> Email: Chaosheng.Zhang@...
> ===================================

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• Dear Marcel Vallée, Thanks. I think the sampling density is good enough to reveal the spatial structure, and the extreme samples are located within the hot
Message 3 of 10 , Dec 14, 2001
Dear Marcel Vallée,

Thanks. I think the sampling density is good enough to reveal the spatial
structure, and the extreme samples are located within the "hot spots". The
problem is that the few values are still extremely high within the "hot
spots". This may be what the "nugget effect" means.

I'm just wondering if these few extreme values should really be "discarded"/
"censored" or replaced. However, this could get some criticism as they may
be "real".

If it is hard to find the best way, I will have to "replace" all the extreme
values with 99% or 98% percentiles. But I'm not sure if it is appropriate to
do so.

Cheers,

Chaosheng Zhang

----- Original Message -----
From: "Marcel Vallée" <vallee.marcel@...>
To: <ai-geostats@...>; "Chaosheng Zhang" <Chaosheng.Zhang@...>
Sent: Thursday, December 13, 2001 10:40 PM
Subject: Re: AI-GEOSTATS: Extreme values?

>
> Dear Chaosheng Zang
>
> The sampling interval is so wide that the high values could easily be
related to "hot spots" of
> higher grade contamination, i..e dumping areas for particular kinds of
slags, mineralized
> waste, etc. A property map might help.
>
> Have you contoured the data? If so, the sampling interval is so wide that
real hot spots of
> environmental significance might not show 2D distribution on such a wide
sampling grid,
> however.
>
> Regards
>
> Marcel Vallée, Eng,, Geo.
> Geoconseil Marcel Vallée Inc.
> 706 Routhier Ave
> Québec, Québec G1X 3J9
> Tel: (1) 418 652 3497
> Fax: (1) 418 652 9148
> Email: vallee.marcel@...
>
> ==============================================
> 13/12/01 08:01:48, Chaosheng Zhang <Chaosheng.Zhang@...> wrote:
>
> >
> > Date: Thu, 13 Dec 2001 13:01:48 +0000
> >
> > From: Chaosheng Zhang <Chaosheng.Zhang@...>
> > Subject:AI-GEOSTATS: Extreme values?
> > To: ai-geostats@...
> >
> >
> >
> > Dear all,
> >
> > My question is: How to deal with the extreme/outlying values in a data
set?
> >
> > I am dealing with heavy metal concentrations in soils from a mine area.
The
> >
> > sample number is 223, and the samples are spatially evenly distributed
with
> > the sampling interval of 400 metres. There are several samples with
> > extremely high values, which makes me feel uncomfortable. The
percentiles of
> > the dataset are listed as follows (in mg/kg):
> >
> >
> > Zn Cu Pb Cd As
> > Min 4 1 25 0.0 2
> > 5% 35 6 35 0.1 6
> > 10% 40 7 41 0.2 7
> >
> > 25% 65 13 62 0.3 9
> > 50% 122 18 168 0.6 15
> > 75% 338 27 821 1.5 28
> > 90% 907 56 2799 2.8 58
> >
> > 95% 1986 116 4490 4.2 80
> > 96% 2462 151 4698 4.9 82
> > 97% 3493 178 5413 6.2 91
> > 98% 4697 207 7609 8.3 111
> >
> > 99% 6712 247 11750 12.4 184
> > Max 11473 1293 16305 48.5 1060
> > When doing geostatistical and statistical analyses, we need some
confidence
> > in dealing with the these very high extreme values which account for
less
> >
> > than 2% of the total sample number.
> >
> > Any suggestions?
> >
> > Cheers,
> >
> > Chaosheng Zhang
> > ===================================
> > Dr. Chaosheng Zhang
> > Department of Geography
> > National University of Ireland
> > Galway
> > IRELAND
> >
> > Tel: +353-91-524411 ext. 2375
> > Fax: +353-91-525700
> > Email: Chaosheng.Zhang@...
> > ===================================
>
>
>
>
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• Dear Chaosheng, ... Is it possible, in your opinion, to model your variogram excluding those few extremes data and after to krige all data, included the
Message 4 of 10 , Dec 14, 2001
Dear Chaosheng,

> Thanks. I think the sampling density is good enough to reveal the spatial
> structure, and the extreme samples are located within the "hot spots". The
> problem is that the few values are still extremely high within the "hot
> spots". This may be what the "nugget effect" means.
>
> I'm just wondering if these few extreme values should really be
> "censored" or replaced. However, this could get some criticism as they may
> be "real".

Is it possible, in your opinion, to model your variogram excluding those few
extremes data and after to krige all data, included the extremes values?
In this way, probably, you loose some spatial information concerning the
variability of your data but you could obtain a more reliable picture of the
"background" values. It depends from what you are asking to your data.
What you, or somebody else, think about?

regards
Claudio

----------------------------------------------------------------------------
-----------------------------

Claudio Cocheo
Fondazione Salvatore Maugeri - IRCCS
Centro di Ricerche Ambientali
via Svizzera, 16
ph. (39) 0498064511
fax (39) 0498064555
mailto:ccocheo@...
website: http://www.fsm.it

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• Chaosheng Zhang said Another problem is when we carry out spatial interpolation, these values may produce artificial contour lines around these sampling
Message 5 of 10 , Dec 14, 2001
Chaosheng Zhang said

"Another problem is when we carry out spatial interpolation, these values
may
produce artificial contour lines around these sampling locations, even
though they can be smoothed. I don't think this is the realistic situation
in the field."

This sounds like the crux of the problem. You sampled data and within it you
have discrete large values. You have confidence in the integrity of the data
but don't accept that for these values to be genuine you must have all these
'artificial' contour lines. This suggests to me that you are expecting the
data to behave so that these large values don't exist, yet you are saying
they should be regarded as valid. Is your sampling at a high enough spatial
resolution?

If you were to sample another point right next to one of these large values
would you expect another large value or a more 'normal' one? If you know the
answer to that then you should be able to decide whether the large values
are truly errors or simply unexpected but valid data. I would suggest the
problem here lies with understanding the underlying spatial variation of the
data set from which the samples were taken, rather than a problem of which
process to apply to the sampled data.

Just another way of looking at it!

regards,

Martin

______________________________________

ArchaeoPhysica Ltd.
Reconnaissance & Geophysics for Archaeology

Telephone: +44 (0) 7050 369789
E-mail: mail@...
Website: http://www.archaeophysica.co.uk
______________________________________

This e-mail is intended only for the addressee
named above and may contain confidential or
privileged information. If you receive this e-mail
it without further disclosure of its content.

Unless otherwise stated no opinions expressed in
this e-mail should be regarded as representative of
any policy of ArchaeoPhysica Ltd.

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• Hello, The crux of the problem is the smoothing effect of kriging. If you don t want to get artificial countour lines in your map, you have 2 choices: 1. use
Message 6 of 10 , Dec 14, 2001
Hello,

The crux of the problem is the smoothing effect of kriging.
If you don't want to get artificial countour lines in your
map, you have 2 choices:
1. use stochastic simulation which generates maps that
are consistent with (reproduce) the variability of your data.
2. use a non-exact interpolator, that is filter the
noise at data locations. An alternative is to slightly
shift the interpolation grid so that no interpolation
grid node coincides with a sampled location.

Pierre
<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

________ ________
| \ / | Pierre Goovaerts
|_ \ / _| Assistant professor
__|________\/________|__ Dept of Civil & Environmental Engineering
| | The University of Michigan
| M I C H I G A N | EWRE Building, Room 117
|________________________| Ann Arbor, Michigan, 48109-2125, U.S.A
_| |_\ /_| |_
| |\ /| | E-mail: goovaert@...
|________| \/ |________| Phone: (734) 936-0141
Fax: (734) 763-2275
http://www-personal.engin.umich.edu/~goovaert/

<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

On Fri, 14 Dec 2001, Martin Roseveare wrote:

> Chaosheng Zhang said
>
> "Another problem is when we carry out spatial interpolation, these values
> may
> produce artificial contour lines around these sampling locations, even
> though they can be smoothed. I don't think this is the realistic situation
> in the field."
>
> This sounds like the crux of the problem. You sampled data and within it you
> have discrete large values. You have confidence in the integrity of the data
> but don't accept that for these values to be genuine you must have all these
> 'artificial' contour lines. This suggests to me that you are expecting the
> data to behave so that these large values don't exist, yet you are saying
> they should be regarded as valid. Is your sampling at a high enough spatial
> resolution?
>
> If you were to sample another point right next to one of these large values
> would you expect another large value or a more 'normal' one? If you know the
> answer to that then you should be able to decide whether the large values
> are truly errors or simply unexpected but valid data. I would suggest the
> problem here lies with understanding the underlying spatial variation of the
> data set from which the samples were taken, rather than a problem of which
> process to apply to the sampled data.
>
> Just another way of looking at it!
>
> regards,
>
> Martin
>
> ______________________________________
>
> ArchaeoPhysica Ltd.
> Reconnaissance & Geophysics for Archaeology
>
> Telephone: +44 (0) 7050 369789
> E-mail: mail@...
> Website: http://www.archaeophysica.co.uk
> ______________________________________
>
> This e-mail is intended only for the addressee
> named above and may contain confidential or
> privileged information. If you receive this e-mail
> it without further disclosure of its content.
>
> Unless otherwise stated no opinions expressed in
> this e-mail should be regarded as representative of
> any policy of ArchaeoPhysica Ltd.
>
>
> --
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> * As a general service to the users, please remember to post a summary of any useful responses to your questions.
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• Dear Chaosheng Zhang This problem can be looked in various perspectives. You have to fit the data in the broader picture and objectives. First, what do your
Message 7 of 10 , Dec 14, 2001
Dear Chaosheng Zhang

This problem can be looked in various perspectives. You have to fit the data in the broader
picture and objectives.

First, what do your soil samples represent? How were they collected, what was their size? Are
they spot samples, multiple takes in a cross pattern with x metres between takes up to y
meters away from the centre? Etc.?

A significant part of nuggets effects when dealing with rock or soil materials may be sampling
and sample preparation generated. If these samples were assayed by AA, what was the size
of the portion used? If one gram, it is much more liable to generating a nugget effect than with 5
or 10 grams whenever pulverisation size was not fine enough and uniform.

Second, what is the purpose of your study. Academic work? Detection, remediation-
restoration, etc.? The high values might have physical significance in the later perspective
and smothing them may not be the ideal solution. Lead and Arsenic contamination cannot be
neglected or minimized.

In an industry or regulation perspective, the recommendation in that case might be to to carry
out additional sampling around the hot spots to delineate them better, say samples at 100 m
spacing, as well as checking the original hot spots, with a sampling method designed to be
representative. I am afraid I may not be easing you out of your problem, but such is physical
reality.

Chapter 8 in Jeff Myer's book "Geostatistical Error Management," deals with sampling and
Chapter 16 with sampling strategy. I published a text on "Sampling Quality Control" in a
mineral exploration and development perspective in Exploration and Mining Geology, Vol 7,
No 1-2, p. 107-116 (1998). This issue has several other papers on sampling. If it is not
available to you, I could send you a file copy of my paper.

Cheers

Marcel Vallée

Geoconseil Marcel Vallée Inc.
706 Routhier Ave
Québec, Québec G1X 3J9
Tel: (1) 418 652 3497
Fax: (1) 418 652 9148
Email: vallee.marcel@...

================================================

14/12/01 06:33:35, Chaosheng Zhang <Chaosheng.Zhang@...> wrote:

>Dear Marcel Vallée,
>
>Thanks. I think the sampling density is good enough to reveal the spatial
>structure, and the extreme samples are located within the "hot spots". The
>problem is that the few values are still extremely high within the "hot
>spots". This may be what the "nugget effect" means.
>
>I'm just wondering if these few extreme values should really be "discarded"/
>"censored" or replaced. However, this could get some criticism as they may
>be "real".
>
>If it is hard to find the best way, I will have to "replace" all the extreme
>values with 99% or 98% percentiles. But I'm not sure if it is appropriate to
>do so.
>
>Cheers,
>
>Chaosheng Zhang
>
>
>----- Original Message -----
>From: "Marcel Vallée" <vallee.marcel@...>
>To: <ai-geostats@...>; "Chaosheng Zhang" <Chaosheng.Zhang@...>
>Sent: Thursday, December 13, 2001 10:40 PM
>Subject: Re: AI-GEOSTATS: Extreme values?
>
>
>>
>> Dear Chaosheng Zang
>>
>> The sampling interval is so wide that the high values could easily be
>>related to "hot spots" of
>> higher grade contamination, i..e dumping areas for particular kinds of
>>slags, mineralized waste, etc. A property map might help.
>>
>> Have you contoured the data? If so, the sampling interval is so wide that
>>real hot spots of
>> environmental significance might not show 2D distribution on such a wide
>sampling grid, however.
>>
>> Regards
>>
>> Marcel Vallée, Eng,, Geo.
>> Geoconseil Marcel Vallée Inc.
>> 706 Routhier Ave
>> Québec, Québec G1X 3J9
>> Tel: (1) 418 652 3497
>> Fax: (1) 418 652 9148
>> Email: vallee.marcel@...
>>
>> ==============================================
>> 13/12/01 08:01:48, Chaosheng Zhang <Chaosheng.Zhang@...> wrote:
>> >
>> > Date: Thu, 13 Dec 2001 13:01:48 +0000
>> >
>> > From: Chaosheng Zhang <Chaosheng.Zhang@...>
>> > Subject:AI-GEOSTATS: Extreme values?
>> > To: ai-geostats@...
>> >
>> > Dear all,
>> >
>> > My question is: How to deal with the extreme/outlying values in a data
>>>set?
>>>
>> > I am dealing with heavy metal concentrations in soils from a mine area.
>>>The sample number is 223, and the samples are spatially evenly distributed
>>>with the sampling interval of 400 metres. There are several samples with
>>>extremely high values, which makes me feel uncomfortable. The
>>>percentiles of the dataset are listed as follows (in mg/kg):
>> >
>> >
>> > Zn Cu Pb Cd As
>> > Min 4 1 25 0.0 2
>> > 5% 35 6 35 0.1 6
>> > 10% 40 7 41 0.2 7
>> >
>> > 25% 65 13 62 0.3 9
>> > 50% 122 18 168 0.6 15
>> > 75% 338 27 821 1.5 28
>> > 90% 907 56 2799 2.8 58
>> >
>> > 95% 1986 116 4490 4.2 80
>> > 96% 2462 151 4698 4.9 82
>> > 97% 3493 178 5413 6.2 91
>> > 98% 4697 207 7609 8.3 111
>> >
>> > 99% 6712 247 11750 12.4 184
>> > Max 11473 1293 16305 48.5 1060

>> > When doing geostatistical and statistical analyses, we need some confidence
>> > in dealing with the these very high extreme values which account for less
>> > than 2% of the total sample number.
>> >
>> > Any suggestions?
>> >
>> > Cheers,
>> >
>> > Chaosheng Zhang
>> > ===================================
>> > Dr. Chaosheng Zhang
>> > Department of Geography
>> > National University of Ireland
>> > Galway
>> > IRELAND
>> >
>> > Tel: +353-91-524411 ext. 2375
>> > Fax: +353-91-525700
>> > Email: Chaosheng.Zhang@...
>> > ===================================
>>
>>
>>
>>
>> --
>> * To post a message to the list, send it to ai-geostats@...
>> * As a general service to the users, please remember to post a summary of
>any useful responses to your questions.
>> * To unsubscribe, send an email to majordomo@... with no subject and
>"unsubscribe ai-geostats" followed by "end" on the next line in the message
>body. DO NOT SEND Subscribe/Unsubscribe requests to the list
>> * Support to the list is provided at http://www.ai-geostats.org
>
>
>

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• Chaosheng Zhang - I think Marcel Vallee is headed in the right direction on your problem. There is a good chance that the problem is one of sample and or
Message 8 of 10 , Dec 14, 2001
Chaosheng Zhang -

I think Marcel Vallee is headed in the right direction on your problem.
There is a good chance that the problem is one of sample and or subsample
support. As mentioned, if you sampled within a foot or tow of a location
that displays an extreme or "outlier" value, you may find values an order of
magnitude or more below the outlier. Similarly, you may also have
"inliers", where a sample nearby a location with a low concentration may
contain a significantly higher value. Of course, no one gets excited about
the inliers that may be unrepresentative, but we get very excited about the
outliers!

The possibility of extreme values should be planned for in the initial stage
of the sampling program. Pierre Gy's work has revealed that the physical
size, volume, and orientation of a sample and subsample (i.e. the support)
are crucial to the concentration estimate obtained. You are asking a lot to
have a 10-g sample represent 400 meters between sample locations in any
case. Unless the support of the original sample and all subsampling stages
was sufficient, there is little chance that the samples are highly
representative of the true concentration. Mine areas typically are very
heterogeneous and proper sampling support when sampling is essential.
Perhaps you can provide some details. If the underlying data are not
representative due to improper suppoort, you are trying to "contour an
illusion", and typically the results are not pleasing.

The way in which the data are used in decision-making is also important.
For instance, if your purpose is to delineate hot spots for risk assessment,
extreme values do not pose a problem as they will be addressed. You may,
however, be very interested in getting your best information at an economic
cutoff value or risk threshold, since the decision for treatment of values
high above or way below the action level is easy.

Jeff Myers
Westinghouse Safety Management Solutions
2131 S. Centennial Ave., SE
Aiken, SC 29803
803.502.9747 (direct)
803.502.9767 (main)
803.502.2747 (fax)
jeff.myers@... <mailto:jeff.myers@...>
http://www.gemdqos.com <http://www.gemdqos.com>

-----Original Message-----
From: Chaosheng Zhang [mailto:Chaosheng.Zhang@...]
Sent: Thursday, December 13, 2001 8:02 AM
To: ai-geostats@...
Subject: AI-GEOSTATS: Extreme values?

Dear all,

My question is: How to deal with the extreme/outlying values in a data set?

I am dealing with heavy metal concentrations in soils from a mine area. The
sample number is 223, and the samples are spatially evenly distributed with
the sampling interval of 400 metres. There are several samples with
extremely high values, which makes me feel uncomfortable. The percentiles of
the dataset are listed as follows (in mg/kg):

Zn Cu Pb Cd As
Min 4 1 25 0.0 2
5% 35 6 35 0.1 6
10% 40 7 41 0.2 7
25% 65 13 62 0.3 9
50% 122 18 168 0.6 15
75% 338 27 821 1.5 28
90% 907 56 2799 2.8 58
95% 1986 116 4490 4.2 80
96% 2462 151 4698 4.9 82
97% 3493 178 5413 6.2 91
98% 4697 207 7609 8.3 111
99% 6712 247 11750 12.4 184
Max 11473 1293 16305 48.5 1060

When doing geostatistical and statistical analyses, we need some confidence
in dealing with the these very high extreme values which account for less
than 2% of the total sample number.

Any suggestions?

Cheers,

Chaosheng Zhang
===================================
Dr. Chaosheng Zhang
Department of Geography
National University of Ireland
Galway
IRELAND

Tel: +353-91-524411 ext. 2375
Fax: +353-91-525700
Email: Chaosheng.Zhang@...
===================================

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