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

2. Materi Systematic sampling
Perbandingan systematic sampling dan simple random sampling
Prosedur systematic sampling
Kekurangan dan kelebihan

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. Can we use SRS all the time? - problems
Locating some sample units on the ground may be very time-consuming
Reference point to sample units
Access

5. Systematic Sampling
The initial sampling unit is randomly selected. All other sample units are spaced at uniform intervals throughout the area sampled

6. Systematic Sampling Cons: Pros:
Impossible to estimate the variance of one sample
Accuracy can be poor (i.e., bias) if a periodic or cyclic variation inherent in the population
Pros:
Sampling units are easy to locate
Sampling units appear to be “representative”
Generally acceptable estimates for the population mean

7. Systematic Random Sampling: Grid Example
Systematic random sampling sometimes gives a better spatial coverage than simple random sampling.
Often have to extend to two dimensions and do grid sampling. Imagine the practical complexity of doing a two dimensional simple random sample compared to sampling on a grid which is relatively simple.

8. Systematic Random Sampling: Applications
Physical file - Telephone directory, license file stubs. Pick the starting point at random and then sample every 50th entry say
Spatial Sampling - Air, soil, water, vegetation, mineral deposits
Aerial Surveys - In many wildlife surveys transects are flown that are regularly spaced to give good coverage. For example, marine mammals like dugong in Australia

9. Summary for Systematic Sampling
Use systematic sampling to obtain estimates about the mean of populations
Numerical statement of precision should be viewed as an approximation
Use SRS formulas

10. Sample Selection Procedure
List all the units in the population from 1,2,…,N – Sampling frame
Select a random number g in the interval
1 g K, using a random mechanism e.g. random number tables,
where K =
K is called the Sampling Interval
N is the population size; n is the sample size
The random number g is called the random start and constitutes the first unit of the sample

11. Sample Selection Procedure
Take every kth unit after the random start
The selected units will be
g, g+k, g+2k, g+3k, g+4k, …,g+(n-1)k
Until we have n units
Example N =10000, n=100
k = =100
Suppose g=87

12. Sample Selection Procedure
We select the following units
87, 187, 287, 387,…, 9987
NB: This procedure is however only valid if k is an integer (whole number)
If k is not an integer (whole number) there are a number of methods we can use. We will consider just two of them

13. Sample Selection Procedure
Method 1: Use Circular Sampling
Treat the list as circular so that the last unit is followed by the first
Select a random start g between 1 and N, using a random mechanism
Add the intervals k until n units are selected
Any convenient interval k will result into a random sample

14. Sample Selection Procedure
One suitable suggestion is to choose the integer k closest to the ratio
Method 2: Use Fractional Intervals
Suppose we want to select a sample of 100 units from a population of 21,156.
Calculate k = =211.56
Select a random start g between 1 and using a random mechanism

15. Sample Selection Procedure
Suppose g = 582
Add the interval successively obtaining exactly 100 numbers
The numbers will be 582, 21738, 42894, …
Divide each number by 100 and round to the nearest whole number to get the selected sample, i.e.
6, 217, 429, etc

16. Consider, n=175 and N=1000. So, k=1000/175 = 5.71
Selection of systematic sampling when sampling interval (k) is not an integer
Consider, n=175 and N=1000. So, k=1000/175 = 5.71
One of the solution is to make k rounded to an integer, i.e., k=5 or k=6.
Now, if k=5, then n=1000/5=200; or,
If k=6, then n=1000/6 = ~ 167.
Which n should be chosen?

17. if k=5 is considered, stop the selection of samples when n=175 achieved.
if k=6 is considered, treat the sampling frame as a circular list and continue the selection of samples from the beginning of the list after exhausting the list during the first cycle.
An alternative procedure is to keep k non-integer and continue the sample selection as follows:
Let us consider, k=5.71, and r=4.
So, the first sample is 4th in the list. The second = (4+5.71) =9.71 ~9th in the list, the third =(4+2*5.71) =15.42 ~ 15th in the list, and so on. (The last sample is: *(175-1) = ~ 997th in the list).
Note that, k is switching between 5 and 6.

18. Advantages and Disadvantages of Systematic sampling
The major advantage is that it is easy, almost foolproof and flexible to implement
It is especially easy to give instructions to fieldworkers
If we order our list prior to taking the sample, the sample will reflect the ordering and as such can easily give a proportionate sample
Maximum dispersion of sample units throughout the population
Requires minimum knowledge of the population

19. Advantages and Disadvantages of Systematic sampling
The main disadvantage is that if there is an ordering (monotonic trend or periodicity) in the list which is unknown to the researcher, this may bias the resulting estimates
There is a problem of estimating variance from systematic sampling- variance is biased
Less protection from possible biases
Can be imprecise and inefficient relative to other designs if the population being sampled is heterogeneous