Hello, I am currently principal investigator on a major NIH grant that aims to develop software for test of hypothesis using alternate hypothesis specified by the user and that differ from the omnibus "spatial independence"; we called them "spatial neutral models". For example, you can test for clusters of cancer rates "above and beyond" a regional background in exposure. The p-values are computed using randomization and I applied geostatistical simulation to generate multiple realizations that are then used to derive the empirical distribution of the test statistic.
I presented an example during the last GeoEnv conference and I put a PDF copy of the paper, which is in press for the moment, on my website. Cheers, Pierre <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><> Dr. Pierre Goovaerts President of PGeostat, LLC Chief Scientist with Biomedware Inc. 710 Ridgemont Lane Ann Arbor, Michigan, 48103-1535, U.S.A. E-mail: [EMAIL PROTECTED] Phone: (734) 668-9900 Fax: (734) 668-7788 http://alumni.engin.umich.edu/~goovaert/ <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><> On Sun, 5 Dec 2004, Colin Daly wrote: > > > Hi > > Sorry to repeat myself - but the samples are not independent. Independance > is a fundamental assumption of these types of tests - and you cannot > interpret the tests if this assumption is violated. In the situation where > spatial correlation exists, the true standard error is nothing like as small > as the (s/sqrt(n)) that Chaosheng discusses - because the sqrt(n) depends on > independence. > > Again, as I said before, if the data has any type of trend in it, then it is > completely meaningless to try and use these tests - and with no trend but > some 'ordinary' correlation, you must find a means of taking the data > redundancy into account or risk get hopelessly pessimistic results (in the > sense of rejecting the null hypothesis of equal means far too often) > > Consider a trivial example. A one dimensional random function which takes > constant values over intervals of lenght one - so, it takes the value a_0 in > the interval [0,1[ then the value a_1 in the interval [1,2[ and so on (let > us suppose that each a_n term is drawn at random from a gaussian distribution > with the same mean and variance for example). Next suppose you are given > samples on the interval [0,2]. You spot that there seems to be a jump between > [0,1[ and [1,2[ - so you test for the difference in the means. If you apply > an f test you will easily find that the mean differs (and more convincingly > the more samples you have drawn!). However by construction of the random > function, the mean is not different. We have been lulled into the false > conclusion of differing means by assuming that all our data are independent. > > Regards > > Colin Daly > > > -----Original Message----- > From: Chaosheng Zhang [mailto:[EMAIL PROTECTED] > Sent: Sun 12/5/2004 11:42 AM > To: [EMAIL PROTECTED] > Cc: Colin Badenhorst; Isobel Clark; Donald E. Myers > Subject: Re: [ai-geostats] F and T-test for samples drawn from the same p > Dear all, > > > > I'm wondering if sample size (number of samples, n) is playing a role here. > > > > Since Colin is using Excel to analyse several thousand samples, I have > checked the functions of t-tests in Excel. In the Data Analysis Tools help, a > function is provided for "t-Test: Two-Sample Assuming Unequal Variances > analysis". This function is the same as those from many text books (There are > other forms of the function). Unfortunately, I cannot find the function for > "assuming equal variances" in Excel, but I assume they are similar, and > should be the same as those from some text books. > > > > From the function, you can find that when the sample size is large you always > get a large t value. When sample size is large enough, even slight > differences between the mean values of two data sets (x bar and y bar) can be > detected, and this will result in rejection of the null hypothesis. This is > in fact quite reasonable. When the sample size is large, you are confident > with the mean values (Central Limit Theorem), with a very small stand error > (s/(sqrt(n)). Therefore, you are confident to detect the differences between > the two data sets. Even though there is only a slight difference, you can > still say, yes, they are "significantly" different. > > > > If you still remember some time ago, we had a discussion on large sample size > problem for tests for normality. When the sample size is large enough, the > result can always be expected (for real data sets), that is, rejection of the > null hypothesis. > > > > Cheers, > > > > Chaosheng > > -------------------------------------------------------------------------- > > Dr. Chaosheng Zhang > > Lecturer in GIS > > Department of Geography > > National University of Ireland, Galway > > IRELAND > > Tel: +353-91-524411 x 2375 > > Direct Tel: +353-91-49 2375 > > Fax: +353-91-525700 > > E-mail: [EMAIL PROTECTED] > > Web 1: www.nuigalway.ie/geography/zhang.html > > Web 2: www.nuigalway.ie/geography/gis/index.htm > > ---------------------------------------------------------------------------- > > > > > > ----- Original Message ----- > > From: "Isobel Clark" <[EMAIL PROTECTED]> > > To: "Donald E. Myers" <[EMAIL PROTECTED]> > > Cc: "Colin Badenhorst" <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> > > Sent: Saturday, December 04, 2004 11:49 AM > > Subject: [ai-geostats] F and T-test for samples drawn from the same p > > > > > > > Don > > > > > > Thank you for the extended clarification of F and t > > > hypothesis test. For those unfamiliar with the > > > concept, it is worth noting that the F test for > > > multiple means may be more familiar under the title > > > "Analysis of variance". > > > > > > My own brief answer was in the context of Colin's > > > question, where it was quite clear that he was talking > > > aboutthe simplest F variance-ratio and t comparison of > > > means test. > > > > > > Isobel > > > > > > > > > > > > -------------------------------------------------------------------------------- > > > > > > > * By using the ai-geostats mailing list you agree to follow its rules > > > ( see http://www.ai-geostats.org/help_ai-geostats.htm ) > > > > > > * To unsubscribe to ai-geostats, send the following in the subject or in > > the body (plain text format) of an email message to [EMAIL PROTECTED] > > > > > > Signoff ai-geostats > > > > > > > > DISCLAIMER: > This message contains information that may be privileged or confidential and > is the property of the Roxar Group. It is intended only for the person to > whom it is addressed. If you are not the intended recipient, you are not > authorised to read, print, retain, copy, disseminate, distribute, or use this > message or any part thereof. If you receive this message in error, please > notify the sender immediately and delete all copies of this message.
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