onal 
ume 
and for its variance: 
2 
M 2 mn y 
E15 pp 25 
NE > paf — 300 uuihefeur (3) 
à cH gl - sis du da 
When all (-M) PU's are taken, as is done in the test, a weighting of the 
quotients by the corresponding size variable x must be introduced. 
For the calculation of the variance and the totd1 volume 
  
y 
= of, v2 Sy 
(y = J = i. is used, and therefore: 
x 2x 2x, 
J J 
M 
L 7, À 
Ye ® M (22g eu. e. 4. o. 9m. aito X4 
Y x 
M 
; M y Sy M = M 
and Vy = zZ yy i S: y, and Vy, * t 2x, viduus pat se ou D) 
(Loetsch, Zóher, Haller, 1973). 
Also here the variance can be split up into a / and a } component. 
Application 
The two-stage unequal probability sampling with PU's of unequal size was 
applied to a forest area in Austria. The area comprises 10,000 hectares on 
which conifers (mainly spruce, with fir and some pine and larch) mixed 
with broadleaves (mainly beech) occur. An orthophoto mosiac, scale 
1:10,000, was constructed from black and white infra-red aerial photographs, 
scale 1:30,000. Grids with 675 (M-29), 450 (M=34) and 225 (M=62) hectares 
each were superimposed on the mosaic.Property boundaries, boundaries between 
forest - non-forest, between one hundred per cent broadleaves and the rest 
of the forest (a mixture of small groups and individual trees of conifers 
and broadleaves and furthermore pure conifers), and between forest up to 
and older than 41 years, and younger than 41 years, were drawn.