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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