Sampling design

In the most direct approach, plots are placed randomly or systematically over the entire area. However, such an approach may not be efficient in stands that are not uniform and where variation is high. In this case, stratified sampling is more efficient especially when the area has been logged at different times (temporal differences) and different intensities. For example, cutting intensities may vary among compartments. Also, there is a tendency to remove more trees closer to the road and to avoid removing trees in difficult terrain. Thus it is better to calculate separate estimates for each stratum. Overall estimates can still be made for the whole stand. Stratified estimates of the population mean and total produce smaller variance than non-stratified estimates. The practical implication is that stratified sampling produces more precise estimates (i.e. the standard error is smaller). Stratified sampling may also allow a reduction of the total sampling units. However, the advantage of this approach is realized only if the stratification is done properly. For surveying logged-over forests, the ability to stratify is very useful. In this study, the stratification is carried out with the help of satellite data and the strata are classified based on tree densities.

For the development of a rapid appraisal technique the stratified sampling design is the most practical. It minimizes costs by localizing inventory samples. The stratification of the forest area is undertaken based on recent satellite images. The timing of the last logging entry could also be used as a stratification criterion. This approach has been adopted for logged-over forests by the Forestry Department Peninsular Malaysia in its national forest inventory. In this study, the condition of the forest was highly variable and appeared to depend more on the quality of the logging operations than on the timing of the last logging entry.�

Figure 1. Location of study area

Accessibility within the logged-over forest is problematic. Therefore, a cluster sampling approach was adopted to reduce travelling time. In such an approach several plots are located close to each other to form a sampling unit. Each cluster forms a group of secondary plots at each location. The unit of observation is not the individual secondary plots but the entire cluster. In cluster sampling, the first stage is a selection of primary points rather than finite sampling unit areas. The second stage is a cluster of sample plots centered on the primary point, laid out in a pre-determined format.

Table 2. Compartments within the study area showing years after logging and extent

To overcome bias, plots are established at the intersection of 1-km grids. For a rapid appraisal the plots are located in the vicinity of accessible roads. Each cluster is considered a sampling unit and consists of five plots. The centre plot of the cluster is located at the grid intersection while the other four plots are located at a distance of 100 m to the north, east, south and west (Figure 2). Thus the effective size of the sampling unit is 100 x 100 m or 1 ha.

The number of plots depends on the desired level of accuracy. It is also influenced by the availability of funds, which in turn depends to some degree on the estimated value of the forest stand. Usually, more valuable stands are sampled more intensively. In most forest inventory operations the probability level is accepted at 95 percent. The accepted standard error (SE%) for volume estimates of production forests can vary from 10 to 20 percent depending on the forest types and stand conditions. For Peninsular Malaysia, the SE% for national and management unit inventories is 15 percent for areas logged more then 20 years ago. For areas logged less then 20 years ago, the SE% is 20 percent. Based on the formula below, the number of samples for various strata as adopted by the Forestry Department Peninsular Malaysia is shown in Table 3.

n_i = t² * (CV_i%²)/(SE_i%²)

n_i = total number of plots for stratum i

t = value on a confidence (probability) level of 95% �2

CV_i% = coefficient of variation of stratum i

SE_i% = standard error

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Figure 2.� Layout of the sampling unit and plot layout

Table 3. Number of sample units per stratum at state and national levels

Estimating the sample size required for estimating population based on a two-stage sampling design requires reliable estimates for both the primary sampling units (i.e. the forest strata) and the secondary units (i.e. plots within each stratum). In most situations, this information is unavailable before the inventory (Shiver and Borders 1996). It is possible to use the information from the previous national forest inventories as a guide but it may not be accurate because of the changes and variability between different logged-over forest stands. However, in general it is the variation between the forest strata (primary sampling units) that is much greater than the variation between plots of each stratum (secondary sampling units). Consequently, as the number of plots is limited, the aim should be to distribute the plots to all the strata proportionally.

The management unit for Peninsular Malaysia is the state. Following the stratification by years since logging, the study area has two strata, namely logged-over (11 to 10 years) and logged-over (21 to 30 years). The total number of sampling units required based on the CV for these classes obtained from the Third National Inventory undertaken in 1991/92 amounts to 48. This information could be used as a guide but would not be very accurate. However, the study area is much smaller and for a rapid appraisal the number of plots for each of the classes identified should be fewer. The calculation of the CV is based on the preliminary inventory samples and the number of plots is determined for each class. This is undertaken after the collection of data in the field. At the same time the stratification is not based on years after logging but on tree density of the residual stands (see �classification�, below).