Loading ...
Sorry, an error occurred while loading the content.

AI-GEOSTATS: summary: spatial stats for small data sets

Expand Messages
  • Raechel Waters
    Dear All, A sincere apology that it has taken be so long to post the responses to a query I sent earlier this year. The content of my posting and the replies I
    Message 1 of 2 , Aug 7, 2001
    • 0 Attachment
      Dear All,

      A sincere apology that it has taken be so long to post the responses to a
      query I sent earlier this year.

      The content of my posting and the replies I received are listed below.

      Thank you once again to those that responded, your input has been extremely
      helpful.

      Raechel Waters

      Original posting:
      Dear All,

      I am new to spatial statistics and am posting this query in the hope that
      someone may be able to point me in the right direction. I am a biological
      oceanographer and am interested in statistically describing the
      2-dimensional distribution of biological particles, primarily to define the
      'patchiness' of the distributions. I have two data sets which consist of
      7x7 and 9x9 point arrays, providing 49 and 81 samples respectively. Are
      there meaningful spatial statistics that can be applied to such small data
      sets?

      Thank you in advance,

      Raechel Waters

      Replies:
      1)
      If your data are actual point locations, as opposed to aggregations by
      grid cells, you can use my CrimeStat program. It has a variety of spatial
      statistics plus documentation on the use of them. Even though it was
      designed for crime analysis, many of these statistics may be appropriate
      for your purposes. The program is distributed by the Crime Mapping
      Research Center of the U.S. National Institute of Justice. You can find
      the program at either

      http://www.icpsr.umich.edu/NACJD/crimestat.html
      or

      http://www.ojp.usdoj.gov/cmrc/tools/welcome.html

      Ned Levine, PhD


      2)
      There are many routes you can take. The first thing you need to do is think
      long and hard about what you mean by patchiness. A lot of biologists use
      "patch" in a structural sense, i.e., they define a patch as something they
      can measure. Li and Reynolds have a paper in the later 90's about
      structural vs. functional spatial heterogeneity (Li, H. and J. F. Reynolds.
      1995. On the quantification of spatial heterogeneity. Oikos
      73: 280-284. ) that offers some excellent guidelines. Often a patch is
      defined as an area with discrete boundaries that is internally homogeneous
      and differs from the outside. I think the best definition of patch is an
      area beyond the perimeter of which there is no biolgical effect on the
      species or system of interest. You could have, for example, levels of some
      chemical radiating out from a spill where, below a certain concentration,
      say .005 ppm, there is no effect on plankton. So, the spatial interface
      between .005 and .006 ppm is the patch boundary.

      Indicator kriging (or just plain mapping) can allow you to make maps of
      biologically important levels of whatever it is you're measuring. There is
      a lot written on indicator kriging.

      If you want to calculate landscape statistics on your data, you have a few
      options: using "fragstats" or, for arcview gis, "patch analyst". Patch
      analyst is really slick, and is well worth using. You can interpolate
      between your sample points somehow, or draw discrete polygons around what
      you consider a patch, and then bring the data into arcview with spatial
      analyst (maybe one version of patch analyst works without spatial analyst)
      and generate about 3 gajillion landscape metrics. The PA manual is
      worthwhile having, because it gives you the equations for a lot of
      landscape metrics you might consider using. Leap2 is another program like
      fragstats/patch analyst for Windows NT. It works well, once you get it
      running.

      Good luck! I wouldn't yield to the temptation to use variography to
      describe the "patchiness". I'm currently working on a paper to decide how
      much about landscape pattern can be said using variography.

      Andrew

      3)
      Try a multiresponse permutation procedure (mrpp). It is particularly
      appropriate for small samples like you describe, is distribution-free, and
      the software is readily available. Search the web for BLOSSOM and
      mrpp. It is freely downloadable. Contact if you have any questions about
      it.

      Wayne Thogmartin

      4)
      7x7 and 9x9 are a bit sparse but randomization techniques could eek more
      out.
      however before metrics can be selected, two questions must be asked: what is
      the spatial extent of your point data relative to the expected patchiness?
      and what is the temporal resolution of the data relative to the processes
      thought to be forming the patchiness?
      tchau,
      geoff
      =+=+=+=+=+=+=+=+=+=+=+=+=+=
      Geoffrey M. Henebry, Ph.D.
      CALMIT (Center for Advanced Land Management Information Technologies)
      113 Nebraska Hall
      University of Nebraska
      Lincoln, NE 68588-0517 USA
      1-402-472-6158 (-4608 fax)
      ghenebry@...

      5)
      The answer to your question is a bit
      chicken-and-egg-ish.

      If your data is well behaved (simple distribution,
      pretty continuous) then you can get meaningful results
      from very few samples (probably not less than 20 or
      so!!)

      We have examples in the book with data sets of 27 and
      up. The 27 one is no good for geostatistics but this
      has more to do with the fact that the samples are 1km
      apart when the range of influence is probably about
      125 metres. The main tutorial set in the old book
      (available free at
      http://uk.geocities.com/drisobelclark/practica.html)
      which we now call "Page 95" has 50 samples very
      inefficiently placed which still yield good results
      for interpretation and estimation purposes. Even more
      so for simulation basis.

      So, I would say, go ahead and try it but look at your
      distribution before you go to geostatistics. Small
      data sets will give much better results if Normal
      (Gaussian) or normalised or transformed in some other
      way.

      If I can be of any more help, please let me know
      Isobel Clark


      6)
      May I suggest that rather than asking whether you can use spatial
      statistical methods you begin with asking what kind of information would
      you like to extract or confirm from your data sets. You do mention
      "patchiness", which intuitively is a pretty clear idea but maybe not so
      clear when it comes to choosing a statistical tool.

      One question, is your data "point data" nor "non-point data", if non-point
      what are the supports? all the same?

      Perhaps you want to simply try descriptive statistics first. For example, a
      bar chart in 3-d would give you a visual picture and perhaps a quick idea
      about patchiness. Try aggregating on subgroupings and look at
      the variance within vs the variance between. Begin with a uniform
      distribution (using the interval determined by the minimal and maximal data
      values), do a Chi-square test on goodness of fit. Although this does
      not capture the spatial context it can give you some information. Compute
      and plot sample variograms, the range of the sample variogram is some
      indication of the presence or absence of patchiness. You might also
      want to look at sample indicator variograms. Try Ripley's K test. I assume
      that you are looking for information from your data set, so try various
      things to see what they tell you.

      Donald E. Myers
      Department of Mathematics
      University of Arizona
      Tucson, AZ 85721
      http://www.u.arizona.edu/~donaldm



      --
      * 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

      --
      * 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
    Your message has been successfully submitted and would be delivered to recipients shortly.