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Sampling Theory and
MethodsLesson 1
Basics of Sampling Theory
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Sampling
• Very important part of the research process.
• Concerned with selecting a relatively small
number of elements sample! from a largergroup of elements population!.
• "ften used in a survey research when it is
di#cult or impossible to conduct a censuswhere data are gathered from everyelement of the population.
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Population
•$ set of elements usually grouped e.g.
people+ organi,ations! from which datapertinent to a problem may be collected.
•-ened target population / consists ofelements identied as 0ey informantsessential for investigation based on thelimitations of the research proect.
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Sample
•
Synonymous to an element of thepopulation
•$ person or obect from which data
are collected and information isderived.
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Sampling units
•)lements of the target population available
for selection during the sampling process
Sampling Distribution
• Theoretical concept referring to thefre2uency distribution of a specic samplestatistics.
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Sampling Error
•
$ny type of bias that results frommista0es either in the determination ofthe sample si,e or in the utili,ation ofthe sampling techni2ue or method.
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Confdence Interval (Margin o Error)
•Statistical range of values within which
the true value of the target populationparameter is e3pected to lie.
•
&t determines how much higher or lowerthan the population mean you are willingto let your sample fall.
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Confdence Level
•4ow condent do you want to be that theactual mean falls within your condenceinterval5
•Most common condence intervals 678condent+ 698 condent+ and 668condent.
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Central Limit Teorem
•:or almost all target populations+ the samplingdistributions of the means or the percentage valuederived from a simple random sample will beappro3imately be normally distributed providedthat the sample si,e is su#ciently large. 4air+;77
• The probability is high when the mean of anysample ta0en from the target population closelyapproach as one increases the si,e of the sample.
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Standard Deviation
•
Variance e3pected in responses
•=se 7.9+ a safe decision and ensures
that the sample will be large enough
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• :actors that determine sample si,e are? – 'ature of data and data analysis – @ind and number of comparisons –
'umber of variables to be investigated – -esired degree of accuracy – 4omogeneity of samples
• -etermining Sample si,e for? – =n0nown population – @nown population
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• Condence level corresponds to a >Ascore+ aconstant value needed for the e2uation.
• >Ascores for the most common condence levels? – 78 A >Ascore !"#$! – 678 A >Ascore !"%&' – 698 A >Ascore !"% – 6D8 A >Ascore #"!
• :or other valueshttp?EEwww.utdallas.eduEdeptEabpE,scoretable.pdf!
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S&>)-)T)*M&'$T&"'
• Sample si,es as small as F7 aregenerally ade2uate to ensure that thesampling distribution of the mean will
appro3imate the normal curve Shott+1667 as cited in Cristobal+ ;71F!
• Ghen the total population is e2ual to orless than 177+ this same number mayserve as the sample si,e universalsampling!.
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:"*M=L$=n0nown %opulation Si,e
• =sed in determining sample si,esfrom un0nown population
'ecessary Sample Si,e
(*+score)# , StdDev , (! - StdDev) .(margin o error)#
Sample si,e 7.;9 desired certainty Eacceptable error! ;
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)3ample 1
• $ssuming you chose 698 condence level+ 7.9standard deviation+ and a margin of errorcondence interval! of HEA 98. 4ow manyrespondents are needed5
recall? 'ecessary Sample Si,e (*+score)# , StdDev , (! - StdDev) . (margin oerror)#
1.6
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)3ample ;
• &f a survey of a group of teachers re2uiresa condence level of 698 and 9 8acceptable error+ then the researcherneeds a sample si,e of FJ teachers that
will have to be surveyed.
:or 698 certainty+ use 1.6<
7.;9 1.6< E 7.79!; 5
7.;9 1+9F
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)3ample F
• &f a researcher wants to e3amine agroup of students with 6D8 certainty+then.
:or 6D8 certainty+ use ;.1D
7.;9 ;.1D E 7.7F!; 57.;9 9+;F;.111! 5
1+F7 students 5
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)3ercise
• $ssume you wish to randomly sampleteachers across the southeast =S$.Gith a 678 condence level+ what
sample si,e would be needed5
7.;9 1.
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)3ercise
• Kou wish to estimate the proportion ofall buyers that are young buyers with698 condence. 4ow many
observations are needed to estimate thepopulation proportion within 7.7< error5
– $ssuming that nothing is 0nown about thepopulation proportion.
– $ssuming that the population proportion hasrecently been estimated to be 7.FJ.
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)3ercise
– $ssuming that nothing is 0nown aboutthe population proportion.
1.6
F.J1< I 7.;9! E7.77F<
7.6
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)3ercise
– $ssuming that the population proportion hasrecently been estimated to be 7.FJ.
Since a prior estimate of the population
proportion is known (0.34), use it as thestandard deviation.
1.6
F.J1
7.
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:"*M=L$@nown %opulation Si,e
• =se of Slovins :ormula used to calculate anappropriate sample si,e from a population!.
n = N / (1 + Ne2 )
Ghere?n sample si,e' populatione estimate of error acceptable error!
I The error tolerance+ e+ can be given in a2uestion! or if you want to gure it out onyour own+ ust subtract the condence levelfrom 1.
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)3ample 1
• )stimate the sample si,e from apopulation of 9777 freshmen studentsusing 98 acceptable error.
n ' E 1H 'e;!
9777 E 1 H 9777!7.79!;!
9777 E 1 H 1;.9! 9777 E 1F.9
FD7 students
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)3ample 1
• )stimate the sample si,e from apopulation of 9777 freshmen studentsusing 98 acceptable error.
n ' E 1H 'e;!
9777 E 1 H 9777!7.79!;!
9777 E 1 H 1;.9! 9777 E 1F.9
FD7 students
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)3ercise
• $ researcher plans to conduct a survey. &fthe population on Smith City is 1+777+777nd the sample si,e if the margin of error is198
n ' E 1H 'e;!
1+777+777 E 1 H 1+777+777!7.19!;! 1+777+777 E 1 H 1+777+777!7.7;;9!! 1+777+777 E 1 H ;;+977!
1+777+777 E ;;+971 J9 people rounded up!
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S/MPLI01 T2E345 /0DMET23DS
Lesson ;
Sampling Methods
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The %roblem
• Suppose a school would li0e todetermine the wee0ly foode3penditure of its students+ if there
are 1+777 students and the guidancecounselor decided to use only 177students as a sample+ who will be
included in the sample5
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Sampling Method
• Sampling Method or Sampling Techni2ueis the process of determining or selectingthose sample units which would providethe re2uired estimates with associatedmargins of error+ arising from e3aminingonly a part and not the whole.
•
Two methods are used? probabilitysampling and nonAprobability sampling.
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Sampling MethodSampling Tecni6ue
%robabilitySampling
Simple *andom Sampling
Systematic *andom
SamplingStratied *andomSamplingCluster Sampling
MultiAstage Sampling
'onA%robabilitySampling
Convenience Sampling
uota Sampling
%urposive Sampling
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%robability Sampling
• )ach eligible member of the populationhas a specic and 0nown chance ofbeing included in the sample.
• $lso termed as scientic sampling.
•
Ghen using this techni2ue+ it isimportant to have a complete list ofthe members of the population.
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%robability SamplingSimple *andom Sampling
• Lottery method
– Grite names or codes on a piece ofpaper
– %ut in a container
– *andomly select the desired number ofsamples
• :ishbowl techni2ue
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%robability SamplingSystematic *andom Sampling
• Choose a starting point then select everyk th element of the population using k = N /n.
• )3. The town of :airfa3 is divided up into9D< bloc0s which are numberedconsecutively. $ 17 percent sample bloc0s
is to be ta0en for the study. &f the randomnumber chosen between 1 to 0 is F+ whatare the bloc0s considered for the sample5
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%robability SamplingSystematic *andom Sampling
• Solution? – -etermine 0N k = !" # $0 percent of !"
= !" # !." = $0
this means %ou have to include ever% $0th mem&er of the population after choosing arandom start.
– *andom number F can be determined
via the lottery method! – Bloc0s considered for the ample are? 7F+
1F+ ;F+ FF+ JF+ O+ 9DF
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%robability SamplingStratied *andom Sampling
• %opulation is subdivided into at leasttwo diPerent subpopulations orstrata! that share the same
characteristics such as gender+ age!.Samples are derived from these
strata using the other sampling
techni2ues.
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%robability SamplingStratied *andom Sampling
• )3. $ssuming a barangay of 17+777families belonging to diPerentincome brac0ets+ a survey to nd out
how many are in favor of the *4 billis to be conducted. To ensure that allincome groups are represented+
respondents will be divided into 4ighA&ncome+ $verageA&ncome+ and LowA&ncome.
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%robability SamplingStratied *andom Sampling
Strata 0umber o amilies
4igh / &ncome ;+777
$verage / &ncome 9+777
Low / &ncome F+777
' 17+777
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%robability SamplingStratied *andom Sampling
• =sing a 98 margin of error+ howmany families should be included inthe sample5
•
=sing either proportional or e2ualallocation+ how many from eachgroup should be ta0en as samples5
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%robability SamplingStratied *andom Sampling
• =sing a 98 margin of error+ how manyfamilies should be included in the sample5
n 17+777 E 1 H 17+777!7.79!; !
n 17+777 E 1 H 17+777!7.77;9!
n 17+777 E 1 H ;9!
n 17+777 E ;<
n F9 families rounded up!
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%robability SamplingStratied *andom Sampling
• =sing either proportional or e2ualallocation+ how many from eachgroup should be ta0en as samples5
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%robability SamplingStratied *andom Sampling
Strata0umber o
amiliesPercent
Proportional
E6ual
4igh /&ncome ;+777
;+777 E17+777 7.;7 or
;78
7.;F9! DD
F9EF 1;
$verage /&ncome 9+777
9+777 E17+777
7.97 or978
7.9F9!
16F1;6
Low /&ncome F+777
F+777 E17+777 7.F7 or
F78
7.FF9! 119
1;
' 17+777
1778 F9 F9
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%robability SamplingCluster Sampling
• 'ormally used in largeAscale studies inwhich the population is geographicallyspread out where sampling procedures may
be di#cult and time consuming.
• %rocess?
– -ivide the population area into sections or
clusters! – Then randomly select a few of those sections
– *andomly select a sample from those sections
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%robability SamplingCluster Sampling
• )3. Suppose we want to determinethe average daily e3penses offamilies in the City of Santa *osa.
Ge can draw a random sample of 9barangays from the total 19 usingrandom sampling and then get a
certain number of families from eachof the 9 barangays.
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%robability SamplingMultiAStage Sampling
• Combination of several samplingtechni2ues discussed
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'onA%robability Sampling
• Members of the sample si,e are drawnbased on the udgment of the researcher.
•&t is a process of selection in which not allmembers of the entire population aregiven a chance of being selected assamples.
• Sometimes referred to as su&'ectivesampling or nonscientic sampling.
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'onA%robability SamplingConvenience Sampling
• Simply use results that are readilyavailable.
• $lso called accidental or incidental sampling.
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'onA%robability Samplinguota Sampling
• Similar to stratied sampling in whichthe researcher rst identies thestrata and their proportions as they
are represented in the population.
• Convenience or udgment sampling is
used to select the re2uired numberof subects from each stratum.
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'onA%robability Sampling%urposive Sampling
• 4andpic0ing of subectsN also called 'udgmental sampling
•
Selects members or elements based on theparticular purpose of the e3periment orstudy.
•
=seful for situations where you need to reacha targeted sample 2uic0ly and wheresampling for proportionality is not theprimary concern.
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The %roblem
• Suppose a school would li0e to determine thewee0ly food e3penditure of its students+ ifthere are 1+777 students and the guidancecounselor decided to use only 177 studentsas a sample+ who will be included in thesample5
•
7ind a partner and elp te scool decide on8ic sampling tecni6ue sould te9 use inselecting students or te sample" Presenttree (:) coices"
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)3ercise
• &dentify which sampling techni2ue wasused in the following scenarios?
1. Ghen she wrote omen and *moticons+
author @C %ascual based conclusions on J+977responses from 177+777 2uestionnairesdistributed to women.
;. The (uidance Counselor of a high schoolsurveys all students from each of the ;7randomly selected classes.
F. $ sociologist at selects 19 men and 19 womenfrom each of J Math classes.
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)3ercise
• &dentify which sampling techni2ue wasused in the following scenarios contd!?
J. &BM selects ;77th compact dis0 from theassembly line and conducts a thorough test of2uality
9. The court secretary writes the name of eachMunicipal Qudge on a separate card+ shuResthe cards+ and then draws F names.
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)3ercise
• &dentify which sampling techni2ue wasused in the following scenarios contd!?D. The mar0eting manager of ebay.ph tests a
new sales strategy by randomly selecting197 consumers with less than %177+777 ingross income and 197 consumers withgross income of at least %177+777.
. $ mar0et researcher for Champion-etergent interviews all passengers oneach of 17 randomly selected %=Vs.
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)3ercise
• &dentify which sampling techni2ue wasused in the following scenarioscontd!?
6. $ medical researcher from =nilever %hils.interviews all leu0emia patients in eachof ;7 randomly selected hospitals.
17.&n conducting research for the eveningnews+ a reporter for $BSACB' interviews19 people as they leave a shopping mall.
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)3ercise
• Solve the following?
– $ researcher would li0e to investigatethe perception of students on
mathematics. 4e divided the populationinto subApopulations as shown in thetable. =se stratied random sampling ifthe sample to be drawn consists of 977
students.
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)3ercise
Strata 0umber o Students
:irst year 1