The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
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Counting the frequency: Counting and marking the number of 
sampling units of each group at PGT, which is called frequency 
listed in the third column on the left side of table 2, signed with 
f(y)- 
Accumulating the frequency: A new column omitted in table 
2 was correspondingly produced, which was used to store the 
data of accumulating frequency when the frequency of each 
group was accumulated and then marked at each PGT from top 
to bottom of this data array, the data of accumulating frequency 
was signed with ^ . 
Accumulating^^: 
A new data array was calculated and 
marked by accumulating the square root of the data of 
accumulating frequency at each PGT, which is listed in the 
fourth column on the left side of table 2. 
Thresholds of layers: The distance datum between two layers 
can be calculated using the last accumulating data of the square 
root of the data of accumulating frequency which was shown at 
the bottom of the third column on the right side of table 2 
divided by layer amount such as six. This distance datum which 
is 9288.83 in table 2 was used to partition the data array of the 
third column on the right side of table 2 and mark at six PGT 
listed in the second column on the right side of table 2. 
Marking layers: Every sampling unit can be marked with the 
sign of layers when the thresholds of layers are confirmed. In 
the above table, total sampling units were partitioned to six 
regions according to the thresholds of layers, and every region 
was marked with numerals as codes of layers. These signs of 
layers were listed in the first column on the right side of table 2. 
SYSTEMATIC CLUSTERING MEANS (SCM) 
where y h = the average value of the collectivity of the 
h layer 
N = the amount of the collectivity 
N h = the amount of the collectivity of the h layer 
Y h . = the total crop area of the / unit of the h layer 
S 2 - the summation of variable error of the h layer 
±y u 
4= rZ(T W - 
«„“It? 
(3) 
(4) 
where y - the average value of the samples of the h layer 
n = the total amount of the samples 
n h = the amount of samples of the h layer 
y hj = the crop area of the i unit of the h layer 
s 2 h = the variable error of the samples of the h layer 
So, the least samples amount of stratified sampling is 
determined by the follow formula: 
(5) 
It is reasonable to stratify sampling units using systematic 
clustering for reference. The result of clustering is similar to 
that processed by FAM although there is only one parameter 
used to cluster, that is crop area such as paddy rice of sampling 
units. The main steps will be introduced corresponding to the 
process of stratified sampling of early rice of 2007 in China. 
Where n = the total amount of samples 
L = the amount of layers 
V = the variable error of estimating value 
The others are as same as the above 
Preparing data: The data used to cluster need not to be sorted 
ascending or descending. It only needs to be transformed into 
appropriate format for statistical software such as SPSS. 
Clustering: It is easy to cluster when the background data is 
imported using statistical software. RSAC also selects the 
number of six as the number of clustering in stratified sampling 
of early rice of 2007 in China. The clusters of six were used as 
layers of six. 
3.1.4 Calculating the least samples: The following 
equations should be used to calculate the least samples when 
the job of stratified sampling has been done (Chen, etc., 2000). 
Distribution according to proportion: 
Where 
The others are as same as the above 
(6) 
The surveying accuracy signed 5 is set to a certain value such 
as 0.95, and the reliability signed (1-a) is also set to 0.95 or 
other value, the value of V should be calculated according to 
(2) the follow formula: 
V = {d! t) 1 
(7)