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

1773RE: [ai-geostats] F and T-test for samples drawn from the same p

Expand Messages
  • Glover, Tim
    Dec 3, 2004
    • 0 Attachment
      Standard t-tests make two assumptions: 1. both data sets are normally
      distributed; 2. they have approximately equal variance. Test these
      assumptions before applying a t-test. Violate these assumptions at your
      own risk. If you fail either assumption, you need to consider your
      options, but probably should not use a plain-vanilla t-test. You could
      possibly use a data transform to "fix" the first assumption. You might
      have to use a modified t-test (such as Satterthwaite's modification) Or
      you might consider a non-parametric approach, such as Mann-Whitney
      U-test.


      Tim Glover
      Senior Environmental Scientist - Geochemistry
      Geoenvironmental Department
      MACTEC Engineering and Consulting, Inc.
      Kennesaw, Georgia, USA
      Office 770-421-3310
      Fax 770-421-3486
      Email ntglover@...
      Web www.mactec.com

      -----Original Message-----
      From: Colin Badenhorst [mailto:CBadenhorst@...]
      Sent: Friday, December 03, 2004 9:59 AM
      To: 'ted.harding@...'
      Cc: 'ai-geostats@...'
      Subject: RE: [ai-geostats] F and T-test for samples drawn from the same
      p

      Hi Ted,

      Thanks for your reply. I suspect my original query was too vague, so I
      will
      illustrate it with a practical example here.

      I have an ore horizon that splits into two separate horizons. One of
      these
      split horizons has a lower average grade, and the other has a higher
      average
      grade. I need to determine whether I should treat these two horizons as
      separate entities during grade estimation. My geological observations
      tell
      me that these two horizons derive from the same source, and on the face
      of
      it are not different from one another in terms of mineral content and
      genesis. I aim to back it up by proving, or attempting to prove, that
      statistically these two horizons are the same, and can be treated as
      such as
      far as grade estimation goes. Because the mean grades vary between the
      two,
      I suspect that the T-test might fail, but I also suspect that the
      variance
      in grade between the two might be very similar, and thus the F-test will
      pass. Now I have a problem : a T-test tells me the populations differ
      statistically, and but the F-test tells me they don't.

      The confidence limit I refer to in (2) by the way is the Alpha value
      used to
      determine the confidence level for the test - I am using Excel to do the
      test.

      Thanks,
      Colin


      -----Original Message-----
      From: Ted.Harding@... [mailto:Ted.Harding@...]
      Sent: 03 December 2004 14:15
      To: Colin Badenhorst
      Cc: ai-geostats@...
      Subject: RE: [ai-geostats] F and T-test for samples drawn from the same
      p


      On 03-Dec-04 Colin Badenhorst wrote:
      > Hello everyone,
      >
      > I have two groups of several thousand samples analysed
      > for various elements, and wish to determine if these
      > samples are drawn from the same statistical population
      > for later variography studies. I propose to test the two
      > groups by using a F-test to test the sample variances,
      > and a T-test to test the group means, at a given confidence limit.
      >
      > Before I do this, I wonder how I would interpret the results
      > of the test if, for example:
      >
      > 1. The F-test suggests no significant statistical difference
      > between the variances at a 90% confidence limit, BUT
      > 2. The T-test suggests a significant statistical difference
      > between the means at the same, or lower confidence limit.
      >
      > Has anyone come across this scenario before and how are they
      > interpreted?

      On the face of it, the scenario you describe corresponds to
      a standard t-test (which involves an assumption that the
      variances of the two populations do not differ), though I'm
      not sure what you mean in (2) by significant "at the same,
      or lower confidence limit." (Do I take it that in (1) you
      mean that the P-value for the F test is 0.1 or less?)

      However, if you get significant difference between the variances
      in (1), then it may not be very good to use the standard
      t test (depending on how different they are). A modified
      version, such as the Welch test, should be used instead.

      There is an issue with interpreting the results where the
      samples have initially been screened by one test, before
      another one is applied, since the sampling distribution
      of the second test, conditional on the outcome of the
      first, may not be the same as the sampling distribution of
      the second test on its own. However, I feel inclined to
      guess that this may not make any important difference
      in your case.

      Hoping this helps,
      Ted.


      --------------------------------------------------------------------
      E-Mail: (Ted Harding) <Ted.Harding@...>
      Fax-to-email: +44 (0)870 094 0861 [NB: New number!]
      Date: 03-Dec-04 Time: 14:15:09
      ------------------------------ XFMail ------------------------------
    • Show all 16 messages in this topic