Table Of ContentStatistics for Biomedical
Engineers and Scientists
Statistics for Biomedical
Engineers and Scientists
How to Visualize and Analyze Data
Andrew P. King
Robert J. Eckersley
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Dedication
A.P.K.–Formyparents,BernardandMaureen.
R.J.E.–InmemoryofProf.DavidCosgrove.
v
“Thequietstatisticianshavechangedtheworld,notbydiscoveringnewfacts
ortechnicaldevelopmentsbutbychangingthewayswereason,experiment,
andformouropinionsaboutit.”
IanHacking
About the Authors
Andrew King has over 15 years of experience of
teaching courses at university level. He is currently
a Reader in Medical Image Analysis in the School
of Biomedical Engineering and Imaging Sciences at
King’sCollegeLondon.
In 2001–2005, Andrew worked as an Assistant
Professor in the Computer Science department at
Mekelle University in Ethiopia and was responsible
forcurriculumdevelopment,design,anddeliveryof
modules.
Andrew’s research interests focus on the use of machine learning and medi-
calimagingtolearnclinicallyusefulinformation,withaspecialemphasison
movingorgans(http://kclmmag.org).
Robert Eckersley has been a Senior Lecturer in the
School of Biomedical Engineering and Imaging Sci-
ences at King’s College London since 2012. He has
been teaching at undergraduate and postgraduate
levelssince2006.Priorto2012,Robertwasalecturer
in the Department of Imaging Sciences at Imperial
CollegeLondon.
Robert’sresearchiscenteredaroundtheuseofultra-
sound in medical imaging. He has a long standing
interestintheuseofmicrobubblesascontrastagents
forultrasoundimaging.
Together Andrew and Robert run the Computational Statistics module for
BiomedicalEngineeringstudentsuponwhichthisbookwasbased.
xv
Preface
AIMS ANDMOTIVATION
Recentyearshaveseenarapidincreaseintheuseoftechnologyinhealthcare,
and the field of statistics provides essential tools for understanding and test-
ing the impact of new biomedical technologies and techniques. The authors
(cid:2)
have been teaching an undergraduate module on statistics using MATLAB
forBiomedicalEngineeringstudentsatKing’sCollegeLondonforanumberof
years,andthisbookhasgrownoutofthisexperience.Wehaveseenthewide
range of challenges, difficulties, and misconceptions faced by students when
trying to learn about statistical techniques and their practical application in
biomedicine,andwehavedevelopedavarietyofwaysofaddressingthem.We
have tried to incorporate these into this book, and we hope that the result is
a clear and logically structured introduction to the fundamental concepts of
statistics,featuringintuitiveexplanationsmotivatedbyrealisticexamples.
The module that we have been teaching is aimed at Biomedical Engineering
students, and so most of the examples and exercises reflect this fact. How-
ever,webelievethatthecontentofthebookanditspresentationwillbemore
widely applicable. Therefore the intended audience of this book is any un-
dergraduate or postgraduate student who wants to learn the fundamentals of
visualizingandanalyzingdatausingstatisticaltechniques.Wealsobelievethat
researchersworkinginthebiomedicalsciencesandrelatedareaswhoarelook-
ingtoincludestatisticalanalysisintheirworkmaybenefitfromthebook.
We believe that it is important not just to learn how to apply statistical meth-
ods,butalsotoappreciatesomeoftheirunderlyingconceptsandtheory.The
content of this book reflects this belief. However, we stop short of including
lengthy mathematical proofs and derivations of the techniques we present,
butratherwetrytogetacrossan“intuitive”feelfortheunderlyingtheory.To
makethingseasierforthereader,weoftenseparatetheseexplanationsofwhy
techniquesworkfromthedescriptionsofhowtheycanbeapplied.Thisallows
the readers to havemoreflexibilityinhowthey usethe book.Ifyou areonly
interestedinquicklygettingstartedonusingstatisticstoanalyzeandvisualize
yourdata,thenyoucanskipthesesections(whichareboxedoffwiththehead-
ingTheIntuition).If,however,youwanttocometoadeeperunderstandingof xvii
xviii Preface
the methods that you are using (which we hope you do), then you can read
andunderstandtheseextrasections.
Atthebeginningofeachchapter,clearlearningobjectivesareprovided.Inthe
chapterbodiesarangeofpracticalbiomedicalexamplesareusedtoillustrate
theconceptsbeingpresented.WealsoincludeActivitiesinthechapterbodies,
whichenablethereadertotesthowwelltheyhavemeteachofthelearningob-
jectives.Solutionstoallactivitiesareavailablefromthebook’swebsite.Weuse
MATLAB to illustrate the practical application of the statistical techniques we
describe.1However,theMATLABcontentisincludedattheendofeachchapter
inaseparatesection,whichcanthenbeusedbythereadertosolvethepracti-
calExercisesthatfollow(whicharealsolinkedtothelearningobjectivesatthe
beginningofthechapter).Thereforeitispossibletoreadthisbookpurelyasa
bookaboutstatisticsandnotengagewiththeMATLABcontentatall.Having
saidthis,usinganautomatedtoolsuchasMATLABmakesvisualizingandan-
alyzingdataaloteasier,sowestronglyrecommendusingone,evenifitisnot
MATLAB.Wehavedoneourbesttoensuretherealismofthedatathatweuse
inourexamples,activities,andexercises,andwhicharefreelyaccessibletothe
readeronthebook’swebsite.However,alldataarecompletelysynthetic,and
wetakefullresponsibilityforanylackofrealism.
At the end of each chapter, we include a brief pen portrait of a famous figure
fromthehistoryofthefieldofstatistics.Statisticsissometimesviewedasadry
andlifelesssubject.Wehopethatbybringingtolifesomeofthesesignificant
figuresandlinkingtheirworktotheconceptsthatwepresent,wecanhelpto
overcomethismyth.
LearningObjectives
Oncompletionofthebookthereadershouldbeableto:
■ Demonstrateanunderstandingofthefundamentalconceptsofdescrip-
tiveandinferentialstatistics.
■ Analyze data and choose an appropriate hypothesis test to answer a
givenquestion.
■ Compute numerical statistical measures and perform hypothesis tests
“byhand”.
■ VisualizedataandperformstatisticalanalysisusingMATLAB.
■ Analyzeaproblemanddesignanexperimenttogathertherequireddata
toanswerquestionsaboutit.
1AllMATLABcodesarecompatiblewithversion2018a.
