There is one other very important assumption about these standard statiatical tests - namely that the samples are independent. This typically removes a large part of the usability of basic tests unless corrected for spatial variables. It is most likely the case that your samples within each horizon are not independent (unless the variogram has got zero range)- so your typical tests cannot be used. They will tend to give pessimistic results - in other words you will tend to find differences in means when none exists. So, these type of tests don't apply directly.
I don't know if there has been much work on trying to provide 'rigourous' methods (but given that it is impossible to give a statistical test that shows if a random function is stationary or not (Matheron - 'Estimating and choosing') then I guess the results would not be completely rigourous). You may be able to get an intuitive feel for the likely difference in means by trying to see how many quasi independent points you have got. You could guess-timate this by assuming that points separated by more than a variogram range are independent and see how many such 'range units' you have got and using this as the number of 'samples' (actually - you may be better by working with an integral range). But if you have any trends in the data then you will not reliable estimates of the two means and so cannot 'prove' that the samples come from the same random function - even if they do.
Regards
Colin Daly
-----Original Message-----
From: Glover, Tim [mailto:[EMAIL PROTECTED]]
Sent: Fri 12/3/2004 3:15 PM
To: Colin Badenhorst; [EMAIL PROTECTED]
Cc: [EMAIL PROTECTED]
Subject: RE: [ai-geostats] F and T-test for samples drawn from the same p
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 [EMAIL PROTECTED]
Web www.mactec.com
-----Original Message-----
From: Colin Badenhorst [mailto:[EMAIL PROTECTED]]
Sent: Friday, December 03, 2004 9:59 AM
To: '[EMAIL PROTECTED]'
Cc: '[EMAIL PROTECTED]'
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: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]]
Sent: 03 December 2004 14:15
To: Colin Badenhorst
Cc: [EMAIL PROTECTED]
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.
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E-Mail: (Ted Harding) <[EMAIL PROTECTED]>
Fax-to-email: +44 (0)870 094 0861 [NB: New number!]
Date: 03-Dec-04 Time: 14:15:09
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