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References in periodicals archive ?
This function considers as null hypothesis ([H.sub.0]) the complete spatial randomness (CSR) of a series of points.
From 700 m up to 5000 m, the [L.sub.12] curve was less than 0 indicating repulsion, notably; the repulsion was weak and near complete spatial randomness ([L.sub.12] = 0) (Figure 3(a)).
The deviation of the observed spatial relationship ([L.sub.12] curve) from complete spatial randomness (CSR) was greatest in PGA followed by TRL and least in PR, suggesting that "randomness" was relatively higher in PR followed by TRL and finally the PGA, a phenomenon which is thought to correlate well with relative forage resources abundance across the different land-use types.
Therefore, we graphically evaluated the compatibility of the sampling pattern with respect to the Complete Spatial Randomness (CSR), which assumes that there are no particular regions in the study area where events are more likely to occur and that the occurrence of one event does not modify the probability of occurrence of another one in the vicinity, comparing the empiric against the expected function (Bivand et al., 2008).
The spatial patterns for the total population and for each sample represented by the tree diametric class (class 1 = 1-2 cm, class 2 > 2-4 cm, class 3 > 4-8 cm, class 4 > 8-16 cm and class 5 > 16 cm) was analysed using Ripley K-function, also known as the reduced second order moment, where confidence envelope intervals were created through 500 permutation of complete spatial randomness using the total number of individuals sampled (Ripley, 1981; Camara et al., 2001).
Descriptive spatial techniques can be used to generate hypotheses about whether data collected from different areas exhibit "complete spatial randomness" or "spatial dependence" (Bailey & Gatrell, 1995).
The weighted K function indicated that the parasite density distribution pattern was significantly different than expected under complete spatial randomness for age groups 0.6-9 (Figure 5A) and 10-19 years (Figure 5B), but was random in adults (Figure 5C).
When the x- and y-distances are randomly (and thus independently) sampled, the Hopkins statistic under complete spatial randomness follows an F-distribution, namely [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].
It is also possible that ESDA may reveal that none of the characteristics of the data differ from what might be expected to result from a pure chance process (i.e., complete spatial randomness), in which case the analyst may decide that spatial pattern analysis is inappropriate.
The sample distribution is compared to complete spatial randomness (CSR), using a Monte Carlo technique to generate the CSR distribution (Diggle 1983).
The estimated function is compared to the theoretical function under the null hypothesis, [H.sub.0] (complete spatial randomness for spatial pattern tests or spatial independence for spatial association tests), through a test statistic whose expected null-hypothesis value is zero at all distances.
An appropriate simulation process is the two-dimensional Poisson process, which produces patterns exhibiting complete spatial randomness (CSR sensu Diggle 1983).
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