The calculation of the
sample size depends on the CV and allowable error. In theory, point sampling
occurs on an infinite population. Since a point has no area, there can be an
infinite number of points even in the smallest area. Based on preliminary
sampling, sample size can be estimated as:
n = 4(CV)2/(AE%)2 [13]
where: n is
the sample size of characteristics of interest
4
is the approximate Z2 value for 95 percent confidence
CV
is the coefficient of variation in percent
AE%
is the allowable error in percent
For example, for FCD Class 1 with a CV of basal area
per hectare of 34 percent (Table 11) and with and allowable error of 10 percent:
n =
4(33.5)2/102 = 44.89 sample points
In other words, a minimum of 45 sample points is required to estimate the basal area of trees greater than 15 cm dbh with 95 percent confidence and a 10 percent allowable error.
Table 11 shows the number of
samples required for the study area based on the CV for the
different FCD classes at different accuracy levels for trees with a dbh above
15 cm for different allowable errors. A higher allowable error reduces the
number of samples required. Forest managers will have to decide on the
desirable level of accuracy to determine the number of sampling plots.
For a
rapid assessment of forest conditions, an allowable error of 15 percent is recommended. At this
level, the total number of samples required for all the FCD classes within the
study area calculated based on volume/ha amounts to 121 plots. The variation is
higher for the higher density forest classes. However, the number of samples
required for FCD Class 2 is very small (12 samples) because of the
significantly lower CV for
that class. The CV for each FCD class will be different if calculations are
based on different dbh classes and subsequently, the number of samples required
will also differ. Thus if managers are only interested in the large trees (e.g.
trees with dbh >45 cm), the number of samples required should be calculated
based on the CV of large trees.
Table 11.
Number of samples for trees > 15cm dbh
|
FCD class |
CV |
No. of samples at 10 % A.E |
No. of samples at 15% A.E |
No. of samples at 20% A.E |
||||
|
bah |
volh |
bah |
volh |
bah |
volh |
bah |
volh |
|
|
1 |
33.5 |
32.4 |
45 |
42 |
20 |
19 |
12 |
11 |
|
2 |
12.9 |
26.0 |
7 |
27 |
3 |
12 |
2 |
7 |
|
3 |
28.1 |
46.8 |
32 |
88 |
14 |
39 |
8 |
22 |
|
4 |
51.7 |
53.3 |
107 |
114 |
48 |
51 |
27 |
29 |
|
Total
no. of samples |
191 |
271 |
85 |
121 |
49 |
69 |
||
Note:
bah: average
basal area per hectare (m2/ha)
volh: average
volume per hectare (m3/ha)
CV: Coefficient
of variation (%)
A.E: Allowable
error
Once
the number of samples required for each FCD class has been determined, the
sampling points can be systematically distributed across the study area. A
system of computer-generated grids is on the map based on the existing RSO
grids to avoid bias (Figure 14). Sampling points need to be established at the
grid intersections. The sampling points required are then distributed randomly
for each FCD class (Figure 14). For example, for FCD Class 1 the 19 samples
required are distributed randomly within the 200-m grid intersections for that
class.
For
practical reasons, the distribution of the sampling points could also be based
on their distance from existing roads. In this approach, preference is given to
samples that are located closer to roads. Although this may generate a bias, it
is more cost effective, as accessibility can be a major constraint in making an
inventory of logged-over forests.
Figure 14. Sample points on FCD classification image
