5. Dellneatloa of Statistically Bbnogeneous Provinces 



General Philosophy 



The importance of defining statistically homogeneous provinces was 

 described In the previous chapter. The validity of frequency spectra, 

 and Indeed nearly all statistical measures, requires a stationary sample 

 space. Unfortunately, truly stationary phenomena are usually only 

 available to theoreticians and experimentalists. The statistics of most 

 natural phenomena vary In either time, space, or both. It Is therefore 

 essential In attempting to describe statistically non-stationary phenom- 

 ena, to delineate areas In which the statistic being generated varies 

 minimally and only within defined limits. In order to accomplish this 

 preliminary procedure of "province picking," it is necessary to design a 

 detection algorithm which takes account of the phenomenon being des- 

 cribed and the statistic being used. 



To illustrate this principle of matching the province detector to 

 the statistic being generated, we begin with an elementary statistic. 

 As an example, assume that it is necessary to describe the areal distri- 

 bution of height of the people of Africa. Assume for this discussion 

 that the desired significance of the mean requires samples of at least 

 10,000 Individuals. One approach might be simply to divide the conti- 

 nent into regular square areas and randomly select 10,000 heights from 

 each area to generate a mean. The means so generated should Indeed rep- 

 resent the populations of these arbitrary squares. 



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