Hi Chris, It depends on the inference space you wish to work in. If your hypothesis is justing testing for a difference in the population means of the three survey extents (fields), then any underlying autocorrelation in the population(s) is not really problematic - it is actually a bonus (i.e. you probably have better precision than you think). Geostatisticians are generally aware of this. They typically constrain inference about population means etc to the survey extent and are wary about extrapolation (after all it's generally considered unwise to think that one area has the same properties to other distant unsampled areas). By constraining inference to the survey extent, geostatistics (and other methods) can make use of autocorrelation to improve the precision of the parameter estimate.
In fact, if you're able to take a random sample from _any_ population, then your classical (Neyman) confidence intervals and hypotheses about the population parameters will be valid. Fisher knew what he was doing :-). The problems occur when you try to increase your inference to include unsampled extents [this would generally be considered 'pseudo-replication' in ecology and earth sciences]. If inference is extended beyond the range of the sample extent then by the sample can't be considered design-based (random), and autocorrelation has the opposite effect on your inference. i.e. its presence means that you have less information and fewer degree of freedom than classical tests assume. I am curious - this interaction between autocorrelation and inference space is never discussed by my ecology colleagues and rarely discussed in general and I am interested in finding out whether or not spatial scientists are well aware of this point? I thought the spatial inference scale in any spatial analysis should be something that is generally explicitly discussed since: (1) the scale of inference it is not always obvious when reading a paper, (2) it tends to have such profound effects. Perhaps I am being naïve in thinking this way? Feedback would be welcome. cheers, Mat -----Original Message----- From: C.J.Banks [mailto:[EMAIL PROTECTED] Sent: Wednesday, 1 March 2006 3:26 a.m. To: ai-geostats Subject: [ai-geostats] Comparison of sample areas Dear All I have sampled three rectangular fields within a larger area and measured a variable of interest at a lot of points in each of these fields. Values were taken from all over each of the sampled fields but are not necessarily over a systematic grid. I am interested in testing whether the three sampled fields come from the same population. However, an ANOVA (or other similar tests) assumes that there is no correlation between values within each of the sampled fields, which isn't true because of the spatial nature. I'm sure that similar studies have been done and would appreciate any pointers to useful sources or appropriate statistical tests. For those who are interested the data are depths of snow on different floes in the same area of the Antarctic. Many thanks Chris
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