SamplingDesign

8/10/2019 SamplingDesign

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SAMPLINGSAMPLING

DESIGNSDESIGNS


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Two Ways of SelectingTwo Ways of Selecting

a Samplea Sample

ProbabilityNon-Probability


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ProbabilityProbability

SamplingSampling


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ProbabilityProbability

SamplingSamplingEvery individual in the population isgiven an equal chance to be selectedas a part of the sample.

Includes:

simple random sampling

systematic random sampling stratied random sampling

cluster sampling


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Simple RanomSimple Ranom

SamplingSamplingSimplest process

echnique of obtaining the sample

by giving each member of thepopulation an equal chance of beingincluded in the sample.

!an be inlottery met!o or by theuse of table of ranom n"mbers.


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Lottery met!oLottery met!o

E"ample:Professor !ell has #$$ students and he%ants only &$ to 'oin the free concert. In thiscase( he must have a list of his students %iththe corresponding number from ) to #$$ toeach student. Professor !ell should prepare#$$ strips of paper %ith numbers from )-#$$. hese strips %ere rolled or folded then

putting them in a bo". he bo" must besha*en %hile he pic* and dra% &$ pieces.

he numbers dra%n and the correspondingstudents name from the record are the onesto 'oin the concert.


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SystematicSystematic

SamplingSampling

Easier alternative to the simplerandom sampling in the sensethat there %ill be less pieces ofpaper to prepare and dra%n.


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Suppose %e have a sample of +$ students to bedra%n from the population of #$$ students. ,e%ill divide the population sie by the sample

and %e %ill get &. his means that %e %ill only& pieces of papers to prepare and dra% once.

Suppose that %e dra% a random start equal to (%hich is the rst member of the sample( then

for the remaining members %e %ill use thee"pression:

#$s%&S'kp

S- random start

k- ratio of the population and the samplesie

p-)(#(//.n-)


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he dra%n samples for thee"ample are as follo%s.01s234&pMembe

rp #$s% Sample

) 5andomstart

# ) 4&1)2 6

# 4&1#2 ))

& 4&12 )+

: : : :

&7 &6 4&1&62 )8)

&8 &7 4&1&72 )8+

+$ &8 4&1&82 )88


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Strati(e RanomStrati(e Ranom

SamplingSamplinghe population is divided intonon-overlapping groupsreferred to as strata.

9ave t%o methods


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he rst method is to dra% arandom sample %ithprescribed sample sie fromeach stratum independently.

0or e"ample( from apopulation sie of &$$

students classied asfreshman( sophomore( 'uniorand senior. nly 7$ students

%ill be chosen as presented:


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St"ent)lassi(cati

on

Strat"msi*e$N+%

Strat"msi*e$n+%

0reshman 7+ #$

Sophomore 8+ #$

;unior )$+ #$Senior ))+ #$


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he second method is todetermine the sample sie for the%hole sample and then allocatethe proportion of each stratum todetermine the sample sie.

0or e"ample( if the sample sie of7$ students %ill be chosen from

the rest of &$$ students classiedas freshman( sophomore( 'uniorand senior( then the studentschosen are presented:


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St"ent)lassi(c

ation

Strat"mSi*e$N+%

Proportion

Strat"m Si*e

$n+%

0reshman >$ $.)+ )#

Sophomore

7$ $.#$ )>

;unior )$$ $.#+ #$

Senior )>$ $.&$ #


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)l"ster Sampling)l"ster Sampling

?sed %hen the population is very largeand the usage of the simple randomsampling is very di@cult andcumbersome.

( A8( A))( A)>( A)7and A#$( so oursample sie n %ill be given by the equation:

n3N)4N&4N>4N84N))4N)>4N)74N#$


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Non,ProbabilityNon,Probability

SamplingSampling


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Duota SamplingDuota Sampling

he manner of selection is notrandom %hen dra%ing a sample%ith particular sample sie from

the population

< quota of sample units is

established.E"ample: +$ men and +$ %omen


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;udgment Sampling;udgment Sampling

he selection of respondents ispredetermined according to thecharacteristics of interest made

by the researchers.5andomiation is not present on

this process.


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Probability -s Non,Probability -s Non,

Probability SamplingProbability SamplingNon-probability sampling is less time

consuming and less e"pensive.he probability of selecting one

element over the other is not *no%n

and therefore the estimates cannot bepro'ected to the population %ith anyspecied level of condence.Duantitative generaliations aboutpopulation can only be done under

probability sampling.9o%ever( in practice( mar*eting

researchers also apply statistics tostudy non-probability samples.


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SamplingDesign

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