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Re: AI-GEOSTATS: Extreme values?

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  • Chaosheng Zhang
    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,

      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 "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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    • Marcel Vallée
      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
        Canada
        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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      • Chaosheng Zhang
        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
          > Canada
          > 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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        • claudio.cocheo
          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
            > "discarded"/
            > "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
            I 35127 - Padova
            ph. (39) 0498064511
            fax (39) 0498064555
            mailto:ccocheo@...
            website: http://www.fsm.it


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          • Martin Roseveare
            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
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              by mistake please advise the sender and destroy
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              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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            • Pierre Goovaerts
              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
                > by mistake please advise the sender and destroy
                > 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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                >


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              • Marcel Vallée
                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
                  Canada
                  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
                  >> Canada
                  >> 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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                  --
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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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                • Myers, Jeff
                  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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