1. Metode Sampling (Ekologi Kuantitatif)
CLUSTER SAMPLING
Dosen Pengampu:
Evellin D. Lusiana

2. Materi Cluster sampling Definisi cluster sampling
Perbandingan cluster sampling dan stratified random sampling
Contoh cluster sampling
Perhitungan cluster sampling

3. Referensi
Manly, B.F.J and Albert, J.A.N Introduction to Ecological Sampling. Florida: CRC Press
Zhang, Chunlong Fundamentals of Environmental Sampling and Analysis. New York: John Wiley and Sons
Poole, R. W An Introduction to Quantitative Ecology McGraw-Hill NY
Pielou, E. C An Introduction to Mathematical Ecology. Wiley Inter Science NY

4. Pendahuluan: Cluster Sampling
A cluster sample is a probability sample in which each sampling unit is a collection or a group of elements.
It is useful when:
(i) A list of elements of the population is not available but it is easy to obtain a list of clusters.
(ii) The cost of obtaining observations increases as the distance that separates the elements.

5. Pendahuluan: Cluster Sampling
In cluster sampling the population is partitioned into groups, called clusters. The clusters, which are composed of elements, are not necessarily of the same size. Each element should belong to one cluster only and none of the elements of the population should be left out.
The clusters, and not the elements, are the units to be sampled. Whenever a cluster is sampled, every element within it is observed.

6. Cluster vs Stratified

8. Cluster Sampling in Fisheries
In fisheries, cluster sampling has been used to estimate landings per trip in artisanal fisheries with a small number of vessels landing at many sites (beaches). Consider, for instance, a fishery with 100 small beaches, where a few vessels land at each beach. One is interested in the total catch per day of the vessels landing at these beaches, but one does not have the possibility to visit all of them. In this case each beach can be a cluster. If a beach is sampled, all its elements (vessel landings) should be observed.

9. Another example of cluster sampling in fisheries is the sampling of the length composition of an unsorted large catch of a species kept in fish boxes onboard a vessel. Let us assume that the catch in each box is as heterogeneous as possible. The fish boxes can then be looked upon as clusters, and when a box has been selected for sampling, all the elements (fish) inside the box have to be observed.

12. Cluster Sampling Calculation
Selection with equal probabilities
In this case, the probability of selecting any cluster i, in one extraction, is constant and equal to
An unbiased estimator of the population total value, Y, is:

13. Selection with unequal probabilities (proportional to cluster sizes)
Let us consider the special case where the selection probability is proportional to the size of the clusters
An unbiased estimator of the population total value, Y, is:

14. Procedure in Selection Proportional to Cluster Size
calculate the cumulative numbers of elements of the population in each cluster;
assign intervals of “selection numbers” to each cluster, based on these cumulative numbers;
use the “selection numbers” in order to choose the n clusters to be sampled, with a probability proportional to sizes. For this purpose, select (applying a simple random sampling design) one of the total number of the “selection numbers” to get the corresponding cluster;
repeat the selection of "selection numbers" to obtain the required number of clusters.

15. Example
Consider a situation where one wishes to select three out of five boats landing fish on a beach. The boats are considered as the clusters to be sampled. Each boat carries a different number of fish boxes to be landed. The percentages of the total number of fish boxes carried by each one of the five boats will be considered as the probabilities proportional to the sizes of the clusters.
Boat
Number of fish boxes
Cumulative numbers
Boat selection numbers
Selection probability 1 5 2 10 3 7 4 13 15