- Dec 3, 2004Standard 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.

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E-Mail: (Ted Harding) <Ted.Harding@...>

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Date: 03-Dec-04 Time: 14:15:09

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