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1778Re: [ai-geostats] F and T-test for samples drawn from the same p

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  • Digby Millikan
    Dec 5, 2004
      Colin,

      Isn't a basic rule of geostatisitics that all populations must follow the
      intrinsic
      hypothesis, i.e. stationarity ,constant mean and variance, so you should
      split
      any populations that do not have the same mean and variance, introduced
      pp33 Mining Geostatistics A.G.Journel & Ch. J.Huijbregts.

      Regards Digby

      ----- Original Message -----
      From: "Colin Badenhorst" <CBadenhorst@...>
      To: <ted.harding@...>
      Cc: <ai-geostats@...>
      Sent: Saturday, December 04, 2004 1:28 AM
      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 ------------------------------
      >
      >
      >


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