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7/26/2019 Report Statistics

1/11

Jerne Kaz Niels B. Paber

1

Systematic

Sampling


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Session

Objectives

To introduce basic sampling concepts insystematic sampling

Demonstrate how to select a random sampleusing systematic sampling design


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Sam

pleSelec

tionProc

edure

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. randomnumber 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 andconstitutes the first unit of the sample

N

n


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Sam

pleSelec

tionProc

edure

Take every kthunit 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


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Sam

pleSelectionProcedure

We select the following units

87, 187, 287, 387,, 9987

NB: This procedure is however only valid if kis an integer (whole number)

If k is not an integer (whole number) there area number of methods we can use. We willconsider just two of them

5


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Sam


Method 1: Use Circular Sampling

Treat the list as circular so that the last unit is followed by thefirst

Select a random start g between 1 and N, using a randommechanism

Add the intervals k until n units are selected

Any convenient interval k will result into a random sample

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Sam


One suitable suggestion is to choose the integer kclosest 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


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Sam


Suppose g = 582

Add the interval 21156 successivelyobtaining exactly 100 numbers

The numbers will be 582, 21738, 42894,

Divide each number by 100 and round tothe nearest whole number to get theselected sample, i.e.

6, 217, 429, etc

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Adva

ntagesandDisadvantagesof

Systematicsampling

Advantages:

The major advantage is that it is easy, almostfoolproof and flexible to implement

It is especially easy to give instructions tofieldworkers

If we order our list prior to taking thesample, the sample will reflect the orderingand as such can easily give a proportionatesample

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Advantagesand

Disadvantag

esof

Systematicsampling

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 theresulting estimates

There is a problem of estimating variance

from systematic sampling- variance is

biased

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Thank You Very Much!

11

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