Metode Sampling (Ekologi Kuantitatif)

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

2. Materi Multi-stage sampling • Definisi multistage sampling • Perbandingan cluster sampling dan multistage sampling • Contoh multistage sampling • Perhitungan multistage sampling

3. Referensi • Manly, B.F.J and Albert, J.A.N. 2015. Introduction to Ecological Sampling. Florida: CRC Press • Zhang, Chunlong. 2007. Fundamentals of Environmental Sampling and Analysis. New York: John Wiley and Sons • Poole, R. W. 1974 An Introduction to Quantitative Ecology McGraw-Hill NY • Pielou, E. C. 1969 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. Multi-Stage Cluster Sampling • Multistage sampling refers to sampling plans where the samplingis carried out in stagesusing smaller and smaller sampling units at each stage. • Take random sample of clusters (stage 1) • From this sample take random sample of individuals (stage 2)

6. Multi-Stage Cluster Sampling – Terms and Examples • Primary Sampling Unit (PSU) • The first set of clusters identified and sampled • Secondary Sampling Unit (SSU) • The second or sub-set of clusters identified and sampled • Example: Population is the entire adult U.S. population • PSU’s may be all U.S. counties • SSU’s may be ZIP codes within selected counties • A sample of individuals from within selected ZIP codes of selected counties from within the U.S. is taken as the final sampling unit (FSU)

7. Stratified Multi-Stage Cluster Sampling • Same as multi-stage cluster sampling, except… • Stratify PSU’s prior to initial sampling • In last Example: Stratifying counties into three strata – Urban, Suburban and Rural

8. Multistage Sampling • Refers to the process of sampling within a previous selected sample • Used to decrease data collection cost • Used when a sampling frame is not available • Often one would stratify within stage depending on known information

9. Two-stage Sampling • In the two-stage sampling design the population is partitioned into groups, like cluster sampling, but in this design new samples are taken from each cluster sampled. The clusters are the first stage units to be sampled, called primary or first sampling units and denoted by SU1 or (PSU). The second-stage units are the elements of those clusters, called sub-units, secondary or second sampling units and will be denoted by SU2 or SSU.

10. Example of Two Stage Sampling • Two-stage sampling is used when the sizes of the clusters are large, making it difficult or expensive to observe all the units inside them. This is, for example, the situation when one wishes to estimate total landing per trip of a fishery with many landing sites and also with a large number of vessels. • Sometimes, in order to decrease the sizes of the primary sampling units, one can previously stratify the population and apply two-stage sampling to each stratum. • It is possible to extend the two-stage sampling design to three or more stages. A short reference will be made to a three-stage sampling design, using a case where the procedure to estimate errors is simple.

15. Sampling World: Two Stage Sampling • Simple random sampling at both stages • Random sampling with different probabilities at the first stage, and simplerandom sampling at the second stage.

16. Simple random sampling at both stages In this two-stage sampling design, an unbiased estimator of the total value of the population is: where Ŷi is an estimator of the total value of the characteristic in cluster (SU1) i. Taking into consideration that simple random sampling is adopted in the second sampling stage, the estimator Ŷi would be:

17. Both selection are with equal probabilities • 1st stage : 1/N • 2nd stage: 1/M • Mean per element

18. Random sampling with different probabilities at the first stage, and simplerandom sampling at the second stage. To analyse this design, let Pi be the known probability of selecting the ith cluster(SU1i) in one extraction An unbiased estimator of the population total, Y, is: with with

19. Example: SRS at both stages • A two-stage sampling has been carried out in order to estimate the total landings fromthe demersallongline fleet. During the first stage 5 vessels out of 58 have beensampled. During the second stagea sample of 50 fish boxes was drawn from each selected vessel. Estimate: The total and mean weight of fish landed.

20. Estimate total weight landing • Estimate mean weight

21. Example: Unequal probabilities at first stage • A two-stage sampling has been undertaken with the aim of estimating the total weight of shrimp landed. During the first stage, 5 out of 58 trawlers were randomly sampled withreplacement, and unequal probabilities. During the second stage, a sample of 50 boxeswas simple randomly drawn from each of the vessels selected in the first stage. Estimate the total weight of shrimps landed

22. Estimate total weight of shrimp landed