Chaosheng
Some thoughts in response to your questions:
1: "Spatially correlated data provide redundant information for the
calculation of mean"
calculation of mean"
I would not say "redundant". Even if information is correlated, the correlation is not perfect (=1) which would be "redundant". If the data is spatially correlated, the correlations should be included in the choice of weight for each sample and in the calculation of the 'standard error' and confidence levels. An optimal weighted average of spatially correlated data will always give a better answer than a smaller subset on non-correlated data.
As an example, you might try kriging a large block with a set of (internal) samples spaced at the range of influence and then repeat the exercise with a handful of samples between these 'independent' ones.
2: "In the
presence of spatially correlated data, would a dispersion
variance . be the proper calculation for the measure of variance?"
variance . be the proper calculation for the measure of variance?"
The obvious answer is "yes and no". If by dispersion variance you mean the standard calculation of variance:
Sum(g_i - gbar)^2/(n-1) often calculated as
{Sum(g_i^2)/n - gbar^2}/(n-1)
where g_i represents each sample value and gbar the arithmetic mean of all samples, then No, it is not appropriate.
The proper calculation for dispersion variance of a spatially correlated data set includes all the cross-covariances, not just the squares of sample values. It also requires a better estimate of the population than gbar (see 1 above). If you are looking for descriptive statistics, then the dispersion variance can be calculated using the 'middle term' from the full estimation variance -- the
gamma-bar(S_i,S_j) term.
In prectice, the most appropriate (and probably simplest) estimate of the 'population' dispersion variance in the presence of spatially correlated data is the total sill on the semi-variogram model. This is, theoretically, the dispersion variance as calculated from samples which are non-correlated.
Isobel
Chaosheng Zhang <[EMAIL PROTECTED]> wrote:
Chaosheng Zhang <[EMAIL PROTECTED]> wrote:
AI-GEOSTATS
Move of the list to [EMAIL PROTECTED]Dear All,
I'm looking for answers to effects of spatial autocorrelation on
conventional descriptive statistics. More specifically, any comments on the
following statements?
1. "Spatially correlated data provide redundant information for the
calculation of mean";
2. "In the presence of spatially correlated data, would a dispersion
variance . be the proper calculation for the measure of variance?"
Best regards,
Chaosheng Zhang
------------------
Dr. Chaosheng Zhang
Lecturer in GIS
Department of Geography
National University of Ireland, Galway
IRELAND
Tel: +353-91-492375
Fax: +353-91-495505
E-mail: [EMAIL PROTECTED]
Web1: www.nuigalway.ie/geography/zhang.html
Web2: www.nuigalway.ie/geography/gis
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