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

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

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

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

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

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

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.

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

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

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

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

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

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

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 21156 using a random mechanism

Sample Selection Procedure Suppose g = 582 Add the interval 21156 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

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 = 166.67 ~ 167. Which n should be chosen?

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: 4+5.71*(175-1) = 997.54 ~ 997th in the list). Note that, k is switching between 5 and 6.

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

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