Hence my recommendation to use cross cross validation Isobel http://geoecosse.bizland.com/books.htm
--- Colin Daly <[EMAIL PROTECTED]> 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 === message truncated ===
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