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 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. Multi-Stage Cluster Sampling
Multistage sampling refers to sampling plans where the sampling is carried out in stages using 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
For example, suppose you wanted to sample 10th grade students in US. One method is:
stage 1: select sample of school districts
stage 2: select sample of schools within previously selected districts
stage 3: select sample of 10th grade class rooms
stage 4: select sample of students within class
Decreases data collection costs by clustering sample in a small number of early stage units
Much depends on data collection methodology (i.e. not applicable for telephone surveys); Note about Random Digit Dialing (RDD) studies – multistage sampling does not apply to these

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 simple random 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 simple random 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 from the demersal longline fleet. During the first stage 5 vessels out of 58 have been sampled. During the second stage a sample of 50 fish boxes was drawn from each selected vessel.
Estimate: The total and mean weight of fish landed.
Vessel
Total number of boxes
Number of boxes sampled
Total weight of the sample 1
200 50
990 2
100
1405 3
250
1440 4 90
1330 5
230
1105

20. Estimate total weight landing
Vessel (i)
Total number of boxes (Mi)
Number of boxes sampled (mi)
Total weight of the sample (yi) 1
200 50
990
200/50*990=3960 2
100
1405
2810 3
250
1440
7200 4 90
1330
2394 5
230
1105
5083
Total
870
6270
21447
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 with replacement, and unequal probabilities. During the second stage, a sample of 50 boxes was simple randomly drawn from each of the vessels selected in the first stage.
Estimate the total weight of shrimps landed
Vessel
Probability of the vessel being sampled
Total number of boxes
Number of boxes sampled
Total weight of the sample 1
0.02
250 50
24.8 2
0.03
300
26.48 3
0.01
100
26.7 4
0.04
150 26 5
0.1
200
25.4

22. Estimate total weight of shrimp landed
Vessel (i)
Probability of the vessel being sampled (Pi)
Total number of boxes (Mi)
Number of boxes sampled (mi)
Total weight of the sample
(yi) 1
0.02
250 50
24.8
250/50*24.8=124 2
0.03
300
26.48
158.88 3
0.01
100
26.7
53.4 4
0.04
150 26 78 5
0.1
200
25.4
101.6
Total
0.2
1000
129.38
515.88
Estimate total weight of shrimp landed