Sample size estimation: Basics & selected examples Dr. S. A. Rizwan, M.D.

Public Health SpecialistSBCM, Joint Program – Riyadh

Ministry of Health, Kingdom of Saudi Arabia

Learningobjectives

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• Importanceofsamplesizeestimation• Basicconceptsinsamplesizecalculation• Howdoessamplesizerelatetostudyresults• Samplesizecalculationinspecificsituations

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Booksandsoftware

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• Books• Samplesizedeterminationinhealthstudies- apracticalmanual(Lwanga &Lemeshow)

• SampleSizeCalculationsinClinicalResearch(Shein-ChungChow,HanshengWang,JunShao)

• Software• Epitools,onlinecalculators,Statcal inEpi Info,Gpower• PASS,nmaster,Statsdirect,Stata• Manyothers

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Obligatoryopeningjoke!

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RethinkingAesop’sfables…

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Let’splayagame!

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Samplesize:Basicconcepts

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Prerequisitesforthisclass

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• Understandingofthefollowingbasicconcepts• Typesofstudydesigns• Measuresofassociation• Mean/SD• Proportion• Standarderror• Hypothesistestingandtypes• Confidenceintervals

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Somerelatedterms

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• Significancelevel• Power• Effectsize• Variability• Precision

Con.level Zα95% 1.96(2sided)95% 1.64(1sided)99% 2.57(2sided)99% 2.32(1sided)Power Zβ90% 1.28285% 1.03780% 0.84275% 0.67570% 0.524

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Samplesize&statisticalinference

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• Twomethodsofstatisticalinference• Hypothesistesting• Confidenceintervalestimation

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Twoaspectsofagoodsample

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• Thesamplesize• Ifadequate,thengoodinternalvalidity

• Thesamplingmethod• Ifrepresentative,thengoodexternalvalidity

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Whycalculatesamplesize?

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• Statingtheassumptionsandparametersbeforestartofthestudyincreasesthevalidityofstatisticalconclusionsmadeafterthestudy

• Post-hocanalysisandresultsareconsideredmerelyexploratory

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Thoughtexercise

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• IamapplyingforajobandintheresumeIhavestatedthatmytypingspeedisveryfast.

• Myfriendisapplyingforthesamejobandinhisresumehestatedthathistypingspeedwas60words/min.

Whichcandidateareyoumorelikelytoassessinavalidmanner?

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Whycalculatesamplesize?(contd.)

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• Fundsandtimeconstraints

• Reallynotnecessarytostudytheentirepopulation(ethicalproblem!)

• Smallsamplesunabletodetectclinicallyrelevantdifferences

• Ifastudywithsmallsamplefindsnon-significantresults– whatdoesitmean?

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Thoughtexercise

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• Study 1: A study was conducted for an anti-hypertensive drug on 10,000 people whichshowed a statistically significant fall in BP of1mm Hg over 3 months

• Study 2: It was found that there was 30%reduction in mortality due to propranolol amongMI patients. But that was not significant. 66cases and 64 controls were studied

Stateyourcommentoneachoftheabovescenario.

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Thoughtexercise

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Then,howlargeshouldSSbe?

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• Neither too small nor too large

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Samplesizeestimatedforprimaryobjective

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• Samplesizeiscalculatedfor‘primaryoutcomevariable’

• Ifthereare>1primaryoutcomessamplesizecalculatedforeachoutcomeandlargestchosen

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Commonscenariosforsamplesize

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• 100sofscenariosforcalculationsamplesize

• Descriptive:• Proportion,mean/SD

• Analytical:• Twoproportions,2means/SD• Also,riskdiff,OR&RR,incidencedensity

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Uncommonscenariosforsamplesize

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• Survival• Regression• Correlation• Qualityassurance• Diagnosticteststudies• Andmanymore

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Furtherconsiderationsforsamplesize

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• Studydesign• Clusterdesign• Crossover• Matched/paired• Typeofhypothesis(inequality,equivalence,non-inferiority&superiority)

• Fixedfollowupduration• Ratioofcontrolstocases

• HypothesistestingorCIestimation?

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HowtoapproachaSSproblem?

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1. Converttheresearchquestionintoastatisticalproblemstatement2. Determineformulaorsoftwarecommand&determineinputsneeded3. Selectthesourcesfortheinputs4. Substitutethevaluesintheformulaorenterinthesoftware5. Factorinnon-response/drop-outrate

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HowtoapproachaSSproblem?

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• First:Converttheresearchquestionintoastatisticalproblemstatement

• Foreg.,• ToestimatethemeanbirthweightofneonatesborntomotherswithanaemiaintheeasternsectorofRiyadh

• Estimationofasinglemeanwithstatedprecision

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HowtoapproachaSSproblem?

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• Second:Findouttheformulaorthesoftwarecommandappropriateforthisproblem

• Foreg.,• Estimationofasinglemeanwithstatedprecision

N=(Zα2 *S2)/L2

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HowtoapproachaSSproblem?

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• Second:anddeterminetheingredientsyourequiretoinputintheformula• Exp.proportion,incidence• Exp.SD• Exp.RRorOR• Power,precision• Confidencelevel• Others(DE,ICC,COV,clustersize)

• Foreg.,• EstimateofSD,alfa &precision

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HowtoapproachaSSproblem?

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• Third:Selectingthesourcesfortheinputs

• Matchthelocationascloseaspossible• Matchthestudypopulationascloseaspossible• Matchthestudysettingascloseaspossible• Matchthestatisticascloseaspossible• Orconductapilotstudy

• Foreg.,• OthersectorinRiyadh->someothercityinKSA->Middleeast->anydevelopingcountry->anywhere

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HowtoapproachaSSproblem?

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• Third(contd.):Whatsourcestouse?

• Fromwhere• PublishedLiterature• Pilotstudy• Expertsinthefield• Educatedguess(gutfeeling)

Itbegsthequestionthatifwealreadyknowtheseinputsthenwhyconductthestudyinthefirstplace!

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HowtoapproachaSSproblem?

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• Third(Contd.):eg., anappropriatesource

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HowtoapproachaSSproblem?

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• Fourth:Substitutethevaluesintheformulaorenterinthesoftware

N=(Zα2 *S2)/L2

N=(1.96*1.96*600*600)/100*100N=138.2N=Roundedto140

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HowtoapproachaSSproblem?

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• Fifth:Factorinnon-response/drop-outrate

• Finalsamplesize= !"#$%&()*&+,$&-.&/0&($12(&0".&

• Foreg.,• Foranon-responserateof20%• Finalsamplesize=140/0.80=175

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Samplesize:Someselectedscenarios

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Samplesizeinspecificsituations

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Authors Originalresearchquestion Simplifiedproblemstatement

1.Dr. Nariman Whatistheproportion ofpatientswhoquitsmoking inatobaccocessationprogram?

Estimationofasingleproportionforaspecialgroup

2.Dr. GhadeerWhatistheincidenceofDMinobesehypertensivesandwhatistheincidenceofDMinnon-obesehypertensiveduringafiveyearfollow-upperiod?

Comparisonofincidenceratesintwogroupsinacohortstudy

3.Dr. Rahma

Whatistheproportion ofLBWneonatesborn tosicklecellmothersandwhatistheproportion ofLBWneonatesborn tonormalmothers inacohortofmothers?

Comparisonoftwoproportionsinacohortstudy

4.Dr. Abrar

Whatistheproportion of ILIabsentstudentsinthehandwashingschoolsandwhatistheproportion ofILIabsentstudents inthecontrolschools?Hereschoolsaretheunitsofrandomisation

Comparisonoftwoproportionsina2groupclusterRCT

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Scenario1:Estimatingasingleproportion

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Scenario1– Step1

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• Whatistheproportionofpatientswhoquitsmokinginatobaccocessationprogram?

• Specifically,whatistheproportionofpatientswithDMandHTNwhoquitsmokinginatobaccocessationprogram?

• Itisacross-sectionalstudybasedonsecondarydataanalysis

• Estimatingasingleproportion

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Scenario1– Step2

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• SSformulaforestimationadifferencebetweentwoproportionsincohortstudy• Inputsrequiredareexpectedproportionofquitting,precision&confidencelevel

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Scenario1– Step3

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• Athoroughliteraturereviewandpreliminarydataanalysisshowedawidevariationintheexpectedproportion– from10%to50%

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Scenario1– Step4

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• Substitutingthevaluesforanumberofscenariosinthesoftware

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Scenario1– Step5

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• Theconceptofdropoutsorlosstofollow-upinnotapplicable inthiscasebecauseitissecondarydataanalysis

• Sothesamplesizeshouldbe>400andbutneednotbe>3500

• Finaldecisionwilldependonfeasibility

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Scenario2:Comparisonofincidenceratesinatwogroupcohortstudy

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Scenario2– Step1

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• Hypothesis:theriskofdeveloping(incidence)DMwillbehigherinobesehypertensivepatientsascomparedtonon-obesehypertensivepatientsduringa5yearfollow-upperiod

• Itisacohortstudywithtwogroups• Exposedisobesehypertensive• Non-exposedisnon-obesehypertensive• OutcomeisincidenceofDM

• Estimatingadifferencebetweentwoincidenceratesinacohortstudy

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Scenario2– Step1

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• Thisproblemcanbevisualisedinanumberofways:

1. Comparingtwoincidenceratesinacohortstudy(RelativeRisk– hypothesistest)

2. Comparingtwoincidence ratesinacohortstudy(RelativeRisk– statedprecision)

3. Comparingtwoincidence ratesinacohortstudywithsmallproportionandfixedstudyduration(Riskdifference– hypothesistest)

4. Comparingtwoproportions(Riskdifference–hypothesistest)

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Scenario2– Step2

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• Method1:SSformulaforestimatingRRwithstatedprecision• Inputsrequiredareexpected proportionofdiseaseamongexposed&unexposed,RR,Precision,

confidence level

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Scenario2– Step2

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• Method2:SSformulaforhypothesistestingofRR• Inputsrequiredareexpected proportionofdiseaseamongexposed&unexposed,RR,power,

confidence level

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Scenario2 – Step2

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• SSformulafordifferenceintwoproportions(akariskdifference)canalsobeusedforthisscenario

Riskdifferencebetween2proportions Riskdifferencebetween2incidence rateswith fixedstudyduration

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Scenario2 – Step2

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Scenario2– Step3

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• AcasualliteraturereviewshowedthattheriskofDMwas5timesamongobeseHTNascomparedtonon-obeseHTN,theincidenceamongnon-obesewas5.4andamongobesewas24.2per1000personyears

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Scenario2– Step4

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• Method1&2:Substitutingthevaluesforanumberofscenariosinthesoftware

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Scenario2– Step5

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• Consideringalosstofollow-upof10%

• Finalsamplesize=716/0.90=795pergroup

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Scenario3:Comparisonofproportionsinatwogroupcohortstudy

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Scenario3– Step1

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• Hypothesis:theproportionofLBWneonateswillbehigherinthesicklecellmothersascomparedtothenon-sicklecellmother

• Itisacohortwithtwogroups• Exposedismotherswithsicklecelldisease• Non-exposedisnormalmothers• OutcomeisproportionofLBW

• Estimatingadifferencebetweentwoproportionsinacohortstudy

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Scenario3– Step1

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• Thisproblemcanbevisualisedinanumberofways:

1. Comparingtwoincidence ratesinacohortstudy(RelativeRisk– hypothesistest)

2. Comparingtwoincidence ratesinacohortstudy(RelativeRisk– statedprecision)

3. Comparingtwoincidence ratesinacohortstudywithsmallproportionandfixedstudyduration(Riskdifference– hypothesistest)

4. Comparingtwoproportions(Riskdifference–hypothesistest)

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Scenario3– Step2

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• Method1:SSformulaforestimatingriskdifference(hypothesistest)• Inputsrequiredareexpectedproportionofdiseaseamongexposed&unexposed,power,confidence level

Differencebetween2proportions

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Scenario3– Step3

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• AliteraturereviewshowedthatproportionofLBWamongSCDmotherswas16.5%andinthenormalmothersitwas8.3%,withanRRof~2

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Scenario3– Step4

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• Substitutingthevaluesforanumberofscenariosinthesoftware

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Scenario3– Step5

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• Consideringalosstofollow-upof10%

• Finalsamplesize=331/0.90=368pergroup

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Scenario4:ComparisonofproportionsintwogroupclusterRCT

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Scenario4– Step1

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• Hypothesis:theproportionofstudentsbeingabsentduetoILIwillbehigherinthecontrolschools ascomparedtotheschoolsimplementingthehandwashing programduringafollowupperiodof6weeks

• ItisaclusterRCTwithtwogroups• Exposedishandwashingprogram• Non-exposedisnohandwashingprogram• OutcomeisproportionofILIabsenteeism• Schoolistheunitofrandomisation

• EstimatingadifferencebetweentwoproportionsinaclusterRCT

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Scenario4– Step1

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• Thisproblemcanbevisualisedinanumberofways:

1. Comparingtwoproportions(Riskdifference–hypothesistestusingICC)

2. Comparingtwoproportions(Riskdifference–hypothesistestusingDesignEffect)

3. Comparingtwoproportions(Riskdifference–hypothesistestusingCoefficientofvariation)

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Scenario4– Step2

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• Method1:SSformulaforcomparisonofproportionsusingdesigneffect• Inputsrequiredareproportionofoutcomeintheexp.group&controlgroup,sizeofcluster,DE,power,

confidence level

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Scenario4– Step2

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• Method2:SSformulaforcomparisonofproportionsusingintraclustercorrelationcoefficient• Inputsrequiredareproportionofoutcomeintheexp.group&controlgroup,sizeofcluster,ICC,

power,confidencelevel

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Scenario4– Step3

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• AliteraturereviewshowedthatincidenceofILIabsenteeismwas0.043intheexp.groupand0.070inthecontrolgroup

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Scenario4– Step4

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• Substitutingthevaluesforanumberofscenariosinthesoftware

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Scenario4

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• Method3:SSformulaforcomparisonofincidencerates(persontime)• Inputsrequiredareincidence rates(PT)intheexp.group&controlgroup,coeff.ofvariation,power,

confidence level

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Scenario4 – Step5

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• Consideringalosstofollow-upof10%

• Finalsamplesize=1625/0.90=1805pergroup

• No.ofclustersrequired=1805/40=45pergroup

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Review

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• Whyissamplesizecalculationimportant?

• WhatarethefivestepstocalculatetheSS?

• Whatarethesomeofthecommoninputs requiredforsamplesizeformulae?

• HowwillyouselectanappropriatesourcefortheinputsofSSformula?

• HowwillyourelatetheSSofyourstudyaftertheresults?

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Takehomemessages

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• Apriorisamplesizecalculationisverycrucialformakingvalidconclusions

• Followthestepwiseapproach

• Samplesizeestimationdoesnotneedtobeveryaccurate,onlyadequate

• Incaseofnon-significantfindingsinastudy,calculatepowerfordeeperunderstanding

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Thankyou!Emailyourqueriestosarizwan1986@outlook.com

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