4 random samples and random sampling design

8/7/2019 4 Random samples and Random sampling design

1/17

RANDOM SAMPLING

NILESH KOLAMBE

y Under this everyitem of population has anequalchance of being included in the sample


2/17

RANDOM SAMPLING DESIGN

NILESH KOLAMBE

y Systematic Sampling

y Stratified sampling

y Cluster Sampling

y Area Sampling

y Multi Stage Sampling

y Sequential Sampling


3/17

Systematic sampling

NILESH KOLAMBE

Selectingeveryith item in the list.

First unit is Randomlyselected and others are at equalintervals.

If we want 4 out of 100 as a sample then we take anynumber from 1 to 25 and thenevery25th item would beselected.

It spreadmoreevenlyover theentire population.

Easier and less costliermethod. It is used in case of large population and when the list of

population is available and is of considerable length.


4/17

Stratified sampling

NILESH KOLAMBE

y It is used when the population is not homogeneous.

y Population is divided into several sub- populationsthat are individuallymore homogeneous than the

total population. Thedifferent sub populations arecalled strata.

y We select items fromeach stratum to constitute asample

y Results aremorereliable anddetailed information.


5/17

NILESH KOLAMBE

y Threequestions are highlyrelevant, theyare

- How to form strata.

- How should item be selected fromeach stratum.

- Howmanyitems be selected fromeach stratum orhow to allocate the sample size ofeach stratum.

y Strata should be formed on the basis of commoncharacteristics of the items.

y Items from strata are selected on simplerandomsampling or systematic sampling can also be used


6/17

NILESH KOLAMBE

Items are selected in the same proportion as that of thesub population ie proportional allocation.

Eg: 100o is divided into three sub populations say500

300 and 200. and the sample sizerequired is 100. thenno. of items would be 50 30 and 20.

If in case strata differ innot onlyin size but also invariability then it is required to take larger samples fromthemorevariable strata.

We are taking both difference in size anddifference invariabilityfor the strata. Byusingdisproportionatesamplingdesign which is known as optimum allocation.


7/17

NILESH KOLAMBE

The allocation in such a situationresults in the followingformula fordetermining the sample sizes of strata.Standarddeviation is coefficient ofvariation. Less thevalue, more the homogeneiuity.

ni= n* Ni * i

N1 1 + N2 2+..+Nk k for i= 1,2 and k

Eg: population is divided into 7000 , 2000, and 1000

and standarddeviations are 12 , 7 and 2 respect. Howshould a sample of 100 be allocated to the three strata ,if we want optimum allocation usingdisproportionatesamplingdesign. (Ans = 84,14 and 2)


8/17

Cluster sampling

NILESH KOLAMBE

y Cluster analysis consists ofmethods of classifyingvariables into clusters.

y Cluster consists ofvariables that correlate highly

with one another and have comparativelylowcorrelations with variables in other clusters.

y There should be high internal homogeneityand highexternal heterogeneity.

y This is used increasinglyin classifying consumersand products


9/17

NILESH KOLAMBE

y Example: companyproducing ornaments ordecorative items.

Purchasing capacityandexpenditure on ornaments

Purchasingcapacity

Expenditure on

ornaments


10/17

Area sampling

NILESH KOLAMBE

y It is a type of cluster sampling in which sample itemsare clustered on a geographical area basis. Saya state, town , district, village , locality

y It saves time since the sampleelements are fromgeographical area.


11/17

Multi stage sampling

NILESH KOLAMBE

This method is applied in case of largegeographicalarea.

This involves selection of units inmore than one

stage. In this the population consists ofno. of first stage

units ie primarysampling units(PSU) . Each of thisPSU consists of a no. of second stage units. First asample is taken from PSU and then the sample is

taken from Second stage units. The process continues until the selection of the final

sampling units.


12/17

NILESH KOLAMBE

y Number of stages varies anddepends uponconvenience and the availabilityof suitable samplingframes.

y Cost factor is also considered.


13/17

NILESH KOLAMBE

y Forexample suppose 10,000 households are to beselected from all over India.

y First stage- states consider 10 states

y Second stage- districts- 200 (total)- consider 25 only

y Third stage- cities- 4 fromeach district- 100 cities

y Fourth stage- localities 10 fromeach citythen1000.localities total.

y Then finally10 households fromeach locality. ie asample of 10,000 households from country.


14/17

Sampling with probabilityproportional to size

NILESH KOLAMBE

In case cluster sampling units do not have the samenumber or approximatelythe same number ofelements, It is considered appropriate to use arandom selection .

In this we have to list no. ofelements ineach clusterand then wemust sample systematicallytheappropriatenumber ofelements from the cumulativetotal.

Forexample there are 10 cities havingdifferent no.of shops ( 100) and I have to select a sample of 6shops.


15/17

NILESH KOLAMBE

CityNumber

No ofshops

Cumulative total

Sample(5)

1 20 20

2 15 35 40

3 25 604 30 90 80

5 35 125 120

6 10 135

7 10 145

8 20 165 160

9 15 180

10 20 200 200


16/17

Sequential sampling

NILESH KOLAMBE

In this, size of sample is not fixed in advance, but isdetermined on the basis of informationyielded as surveyprogresses.

In this no. of samples n1,n2,n3 arerandomlydrawn from

the population. It is not necessarythat each sampleshould be ofequal size.

Samples are selected aftergetting some additionalinformation from the original sample.

Generallyfirst sample is largest , second is smaller thanthe first, third is smaller than the second and so on.

Sequential sampling is to bringdown the cost and hencesmallest possible sample is used.


17/17

NILESH KOLAMBE

y Forexample, effect of internet on pune cityis to befound out. Then I collect the sample and found outthe some kind ofexposure to the internet.

y High frequencyuser are then selected.y Sites for which theyare surfing arereferred then.

Again samplereduces.

4 random samples and random sampling design

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