- 1829 - 
RESULTS OF TWO-STAGE UNEQUAL 
PROBABILITY (PPS) SAMPLING FOR 
TIMBER VOLUME USING 
AN ORTHOPHOTO MOSAIC 
by 
* 
D.A. Stellingwerf 
General 
Assume a two-stage sampling design, in which the primary units (PU's) are 
of equal size and the number of secondary units (SU's) per PU are equal. 
Randomly selecting the PU's and the SU's in the sample with equal 
probability, the variance of the mean volume can be expressed by: 
B X r2 
"1. GO; - y) 
m.n, (m - 1) 
Re (-2 
2 vy =v 
= m (m - 1) 
in which y, 7 estimate of maán volume of PU, 
y = estimate of overall mean volume, 
m = number of PU's in sample, 
n, = number of SU's per PU, in sample. 
J 
It is also possible to consider the individual PU and SU components of the 
variance: 
  
  
Z. 4 
e = xm! 
J 
multiplying with m gives the standard deviation squared: 
2 
Vy = Vy = ef + — code doh Bl Bak). xD 
J 
or when using the reduction factors: 
  
s |: + 
  
  
* Ir D.A. Stellingwerf, Professor Forest Survey, Chairman Division of 
Natural Resources, Head Department of Forestry, International Institute 
for Aerial Survey and Earth Sciences, Enschede, The Netherlands.