1

Module 3

Session 7

Systematic Sampling

2

Session Objectives

To introduce basic sampling concepts in systematic sampling

Demonstrate how to select a random sample using systematic sampling design

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

N

n

4

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

10000

100

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

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

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 = =211.56

Select a random start g between 1 and 21156 using a random mechanism

N

n

21156

100

8

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

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

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