To Illustrate the effect of non-statlonarlty on the validity of the 

 measured statistic, assume that in a particular sample square, the 

 southern region is inhabited exclusively by Pygmies, averaging only 4 

 feet tall, while the northern region is inhabited by Uatusis, averaging 

 7 feet tall. The method just described would predict a single popula- 

 tion, averaging 5*6" height, inhabiting the area. In fact, very few of 

 the individuals in the population are near this height and our statistic 

 has failed to perform its intended function; to describe the areal dis- 

 tribution of heights of the population. 



In order to confine our sampling to relatively homogeneous sample 

 spaces, it is necessary to detect the boundary between independent pop- 

 ulations prior to final sampling. The best method for accomplishing 

 this "province picking" is to measure the mean crudely with much smaller 

 samples, say ten individuals or even one individual over smaller areas. 

 Even these crude measures could be sufficient to define the large gra- 

 dient in population mean across the boundary. Notice that the same sta- 

 tistical measure (the mean) is used to describe the population and to 

 define the province boundary. After the provinces are delineated, sam- 

 pling within homogeneous provinces ensures statistical validity, at 

 least to the degree that stationarity was confined in the province pick- 

 ing procedure. An additional operational advantage of the province 

 picking procedure is that very large areas of stationary means might be 

 detected which would require only one random sample of 10,000 individ- 

 uals to describe a large area, rather than conducting several repetitive 

 samplings using the arbitrary grid technique. 



When one uses more advanced statistical measures to describe the 

 earth, it becomes necessary to design more complex procedures for homo- 



46 



