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. -------------------------------------------------------------------- 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 ------------------------------ XFMail ------------------------------
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