Statistical Methods in Medical Research

165 Pages·2018·3.668 MB·English

by  Charan Singh Rayat

Charan Singh Rayat
Statistical
Methods in
Medical Research
Statistical Methods in Medical Research
Charan Singh Rayat
Statistical Methods in
Medical Research
CharanSinghRayat
DepartmentofHistopathology
PostgraduateInstituteofMedicalEducation&Research
Chandigarh,India
ISBN978-981-13-0826-0 ISBN978-981-13-0827-7 (eBook)
https://doi.org/10.1007/978-981-13-0827-7
LibraryofCongressControlNumber:2018954730
#SpringerNatureSingaporePteLtd.2018
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartofthe
materialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,
broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation
storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology
nowknownorhereafterdeveloped.
Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication
doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant
protectivelawsandregulationsandthereforefreeforgeneraluse.
The publisher, the authors, and the editorsare safeto assume that the adviceand informationin this
bookarebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor
theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany
errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional
claimsinpublishedmapsandinstitutionalaffiliations.
ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSingaporePteLtd.
The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721,
Singapore
Foreword
ItgivesmegreatpleasureinwritingtheforewordtoStatisticalMethodsinMedical
ResearchbyDr.CSRayat,whohasmorethan32years’experienceinapplications
of statistical methods in Biomedical Research. Dr. Rayat has more than 13 years
postdoctoral research and teaching experience with great instinct for quantitative
diagnostic pathology and has been on the editorial boards of reputed international
medicaljournals.
The main aim of his book is to create interest of medical researchers and
postgraduate students in the wonderful applications of statistical methods for
analyzing the research findings as well as routine determinations of biochemical
investigationsforfindingsignificanceofoutcomeofresearchand“statisticalquality
control”ofroutine“medicallaboratories”foraccreditationandcompetence.
The book would be of great use for medical professionals, researchers, and
students of biomedical sciences and other disciplines too. I wish Dr. Rayat great
success in his endeavor and feel really happy for the release of the first edition of
thebook.
DepartmentofCytology, PranabDeyMD.FRCPath.
PGIMER
Chandigarh,India
March2018
v
Preface
Null hypothesis (H ) is the cardinal principle of equality in groups of objects or
o
subjects under study. It is the foundation of Statistical Science. The extent of
rejection of null hypothesis through statistical analysis validates our research or
inferenceaboutgroupofsubjects,objects,orstandardoperatingprocedures(SOPs)
understudy.
Statisticalanalysisplaysavitalroleinmaterialscience,businessanalysis,sports,
management,andbiomedicalresearch.Avarietyofbooksareavailableonstatistical
analysisforstudentsofmathematics,commerce,andmanagement,butnotasingle
bookisavailablefor biomedicalresearchers andbasicmedicalscientistswho have
notstudiedmathematicsatundergraduatelevel.IexpressmygratitudetoDr.Pranab
Dey, Professor, Department of Cytology, PGIMER, Chandigarh, for encouraging
metowritethisbookforbiomedicalresearchersandbasicmedicalscientists.
This book has been written with a focus on the requirements of students of
variousspecialtiesofmedicalscience,basicmedicalscientists,andhealthworkers.
Problems with solutions have been illustrated under various chapters for compre-
hensive understanding of the statistical methods and their applications. I am of the
definiteviewthatthisbookwouldmeettherequirementsofstudentsofmedicineand
basic medical sciences. I adore the pioneers in the subject whose theories and
methodshavebeencitedinthisbookanddedicatethebooktothegalaxyofpioneers.
IwouldliketoconveymythankstomysonEr.HarpreetSinghRayat,asoftware
engineer,anddaughterMs.AmandeepKaur,M.Com.,ICWA,fortheirsupportand
critical comments on the manuscript.Microsoft Office 365ProPlus, Version 1708,
licensed to my son, has been used as source of Microsoft Excel for generating
probability tables and data handling. I am very thankful to Ms. Jagjeet Kaur Saini
and Dr. Naren Aggarwal of Springer India Pvt. Ltd, for taking interest in my
manuscriptandputtinginsincereeffortsforpublishingthisbook.
vii
viii Preface
I hope that this book would be liked by teachers and researchers in the field of
MedicineandBasicMedicalSciences,andwouldlessentheirdependencyonothers
for statistical analysis. Any suggestions for improving this book would be highly
acknowledgedandappreciated.
Chandigarh C.S.Rayat
India
March2018
Contents
1 IntroductiontoStatistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 DefinitionsofStatistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 OriginandDevelopmentofStatistics. . . . . . . . . . . . . . . . . . . 1
1.3 ConceptofProbability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.4 DefinitionofProbability. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.5 TypesofEvents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.6 DifferentTheoriesofProbability. . . . . . . . . . . . . . . . . . . . . . 4
1.6.1 ClassicalorPrioriProbability. . . . . . . . . . . . . . . . . 4
1.6.2 RelativeTheoryofProbability. . . . . . . . . . . . . . . . . 5
1.6.3 SubjectiveApproach. . . . . . . . . . . . . . . . . . . . . . . . 5
1.6.4 AxiomaticTheoryofProbability. . . . . . . . . . . . . . . 5
1.7 UsesofProbability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.8 TheoremsofProbability. . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 CollectingStatisticalData. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1 MethodsofCollectionofData. . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 ProcedureforCollectionofData. . . . . . . . . . . . . . . 13
2.1.2 PlanningtheStudy. . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.3 DevisingtheQuestionsandMakingtheSchedule. . . 14
2.1.4 PopulationandSamples. . . . . . . . . . . . . . . . . . . . . 14
2.1.5 UsingSchedulestoObtaintheInformation. . . . . . . . 15
2.1.6 EditingtheSchedules. . . . . . . . . . . . . . . . . . . . . . . 16
2.1.7 OrganizingtheData. . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.8 PresentationandAnalysis. . . . . . . . . . . . . . . . . . . . 16
3 TabulatedPresentationofData. . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1 ExamplesDepictingTabulatedPresentationofData. . . . . . . . 17
4 DiagrammaticPresentationofData. . . . .. . . . . .. . . . . .. . . . . . .. 21
4.1 Usefulness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.2 Limitations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.3 CharacteristicsofDiagramsandRulesforDrawingThese. . . . 21
4.4 DifferentTypesofDiagrams. . . . . . . . . . . . . . . . . . . . . . . . . 22
ix
x Contents
5 GraphicPresentationofData. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.1 ConstructionofGraph. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.2 ChoiceofScale. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.3 PlottingofData. .. . . . . . .. . . . . .. . . . . .. . . . . .. . . . . . .. 28
5.4 GraphsofTimeSeriesorHistorigrams. . . . . . . . . . . . . . . . . . 28
5.5 ComparisonofTimeSeries. . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.6 SemilogarithmicScale. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.7 InterpretationsofSemilogCurves. .. . . . . . . . .. . . . . . . . . .. 29
5.8 PropertiesofaLogarithmicScale. . . . . . . . . . . . . . . . . . . . . . 30
5.9 NormalFrequencyCurve:PropertiesofNormal
FrequencyCurveAreGivenBelow. . . . . . . . . . . . . . . . . . . . 30
5.10 ModeratelyAsymmetricalCurve. . . . . . . . . . . . . . . . . . . . . . 31
5.11 ExtremelyAsymmetricalCurve. . . . . . . . . . . . . . . . . . . . . . . 31
6 MeasuresofCentralTendency. . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
6.1 PropertiesofAverage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
6.2 Characteristicsof“RepresentativeAverage”. . . . . . . . . . . . . . 33
6.3 TypesofAverages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
6.4 ArithmeticMean(x(cid:1)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
6.5 ArithmeticMean(x(cid:1))ofUngroupedData. . . . . . . . . . . . . . . . . 34
6.6 ArithmeticMean(x(cid:1))ofGroupedData. .. . . . . . . .. . . . . . . .. 34
6.7 ShortcutMethodforCalculating“Mean”(x(cid:1)). . . . . . . . . . . . . . 35
6.8 MeritsandDrawbacksofMean(x(cid:1)):AsListedinTable6.4. . . 37
6.9 GeometricMean(G(cid:1)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
6.10 UsefulnessofGeometricMean(G(cid:1)). .. . . . . . . . .. . . . . . . . .. 37
6.11 MeritsandDrawbacksofGeometricMean(G(cid:1)):AsListedin
Table6.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6.12 WeightedMean. . .. . . . .. . . .. . . .. . . . .. . . .. . . .. . . . .. 39
6.13 CrudeDeathRate(CDR). . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
6.14 StandardizedDeathRate(SDR). . . . . . . . . . . . . . . . . . . . . . . 40
6.15 Median(~x). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
6.16 UsefulnessofMedian(~x). . . . . . . . . . . . . . . . . . . . . . . . . . . 41
6.17 TheComputationofMedian(~x)ofUnclassifiedData. . . . . . . 41
6.18 TheComputationofMedian(~x)ofClassifiedData. . . . . . . . . 42
6.19 MeritsandDrawbacksofMedian(~x). . . . . . . . . . . . . . . . . . . 42
6.20 Mode(bx). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
6.21 CalculatingMode(bx)inUngroupedData. . . . . . . . . . . . . . . . 43
6.22 CalculatingMode(bx)inGroupedData. . . . . . . . . . . . . . . . . . 43
6.23 PropertiesofMode(bx). .. . . . . . . . . . . . .. . . . . . . . . . . .. . . 44
6.24 ComparisonofMean(x(cid:1)),Median(~x),andMode(bx). . . . . . . . 44
6.25 WhentoUseMean(x(cid:1)),Median(~x),andMode(bx)?. . . . . . . . . 44
6.25.1 UseofMean(x(cid:1)). . . . . . . . . . . . . . . . . . . . . . . . . . . 44
6.25.2 UseofMedian(~x). . . . . . . . . . . . . . . . . . . . . . . . . 44
6.25.3 UseofMode(bx). . . . . . . . . . . . . . . . . . . . . . . . . . . 45
6.26 Quartiles,Deciles,andPercentiles. . . . . . . . . . . . . . . . . . . . . 45
Contents xi
7 MeasuresofDispersion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
7.1 Definition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
7.2 VariousMeasuresofDispersion. . . . . . . . . . . . . . . . . . . . . . . 47
7.2.1 Range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
7.2.2 QuartileDeviation. . . . . . . . . . . . . . . . . . . . . . . . . 48
7.2.3 MeanDeviation. . . . . . . . . . . . . . . . . . . . . . . . . . . 49
7.2.4 StandardDeviation. . . . . . . . . . . . . . . . . . . . . . . . . 52
7.3 SymbolsRepresentingtheStandardDeviation. . . . . . . . . . . . . 53
7.4 SymbolsUsedinStatisticalAnalysis. . . . . . . . . . . . . . . . . . . 53
7.5 FormulaeforCalculatingStandardDeviation
fromUngroupedData. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
7.6 ComputationofMeasuresofDispersion. . . . . . . . . . . . . . . . . 54
7.6.1 FromUngroupedData. . . . . . . . . . . . . . . . . . . . . . 54
7.7 FormulaeforCalculatingStandardDeviation
fromGroupedData. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
7.8 ComputingStandardDeviationfromClassifiedData. . . . . . . . 56
7.9 ShortcutMethodforComputing“StandardDeviation”
fromClassifiedData. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
7.10 MeritsandDemeritsofVariousMeasuresofDispersion. . . . . 59
7.11 WhentoUseVariousMeasuresofDispersion?. . . . . . . . . . . . 60
8 Correlation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
8.1 CausationandCorrelation. . . . . . . . . . . . . . . . . . . . . . . . . . . 61
8.2 OneVariableBeingaCauseofAnother. . . . . . . . . . . . . . . . . 61
8.2.1 BothVariablesBeingtheResult
ofaCommonCause. . . . . . . . . . . . . . . . . . . . . . . . 61
8.2.2 Chance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
8.3 MethodsofStudyingCorrelation. . . . . . . . . . . . . . . . . . . . . . 62
8.3.1 TheScatterDiagram. . . . . . . . . . . . . . . . . . . . . . . . 62
8.3.2 PearsonCoefficientofCorrelation
forUngroupedData. . . . . . . . . . . . . . . . . . . . . . . . 62
8.3.3 RegressionLine. . . . . . . . . . . . . . . . . . . . . . . . . . . 67
8.4 Proportionsof“r”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
9 Chi-SquareTest(χ2–Test). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
9.1 DegreesofFreedom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
9.2 LevelsofSignificance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
9.3 Applicationsofχ2–Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
9.3.1 DoubleVariableData. . . . . . . . . . . . . . . . . . . . . . . 70
9.3.2 GoodnessofFitTest. . . . . . . . . . . . . . . . . . . . . . . . 71
9.4 CoefficientofContingency. . . . . . . . . . . . . . . . . . . . . . . . . . 74
9.5 Yates’Correction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
9.6 ApplicationofYates’CorrectiontoMultivariableData. . . . . . 78
9.7 Inference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79