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1 Module 3 Session 7 Systematic Sampling

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2 Session Objectives To introduce basic sampling concepts in systematic sampling Demonstrate how to select a random sample using systematic sampling design

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3 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

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4 Sample Selection Procedure Take every k th 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

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5 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

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6 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

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7 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 = = Select a random start g between 1 and using a random mechanism

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8 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

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9 Advantages and Disadvantages of Systematic sampling Advantages: 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

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10 Advantages and Disadvantages of Systematic sampling Disadvantages: 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

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