Research Methods for Science

237 Pages·2011·8.151 MB·English

by  Marder M.P.

A unique introduction to the design, analysis, and presentation of M
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• Gives an overview of the main methods used in scientific research,
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tionships, and observational research.
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• Describes important features of experimental design, such as the e
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control of errors, instrument calibration, data analysis, laboratory
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safety, and the treatment of human subjects. a
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• Discusses important concepts in statistics, focusing on standard
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error, the meaning of p-values, and use of elementary statistical

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• Introduces some of the main ideas in mathematical modeling,
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research Methods
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Michael P. Marder is Professor of Physics at The
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University of Texas at Austin. He is co-director
and co-founder of UTeach, a program preparing
www.cambridge.org/Marder secondary teachers of science and mathematics. for
s c i e n c e
He has been teaching a course on how to do
Extensive instructor’s manual containing scientific research, which led to the writing of
sample lessons and student papers. this textbook. He is author of the graduate text
Condensed Matter Physics.
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MARDER: RESEARCH METHODS FOR SCIENCE CVR CMYBLK
RESEARCH METHODS FOR SCIENCE
A unique introduction to the design, analysis, and presentation of scientific
projects,thisisanessentialtextbookforundergraduatemajorsinscienceandmath-
ematics.
Thetextbookgivesanoverviewofthemainmethodsusedinscientificresearch,
including hypothesis testing, the measurement of functional relationships, and
observationalresearch.Itdescribesimportantfeaturesofexperimentaldesign,such
asthecontroloferrors,instrumentcalibration,dataanalysis,laboratorysafety,and
the treatment of human subjects. Important concepts in statistics are discussed,
focusing on standard error, the meaning of p-values, and the use of elementary
statistical tests. The textbook introduces some of the main ideas in mathematical
modeling, including order-of-magnitude analysis, function fitting, Fourier trans-
forms,recursionrelations,anddifferenceapproximationstodifferentialequations.
It also provides guidelines on accessing scientific literature, and preparing scien-
tificpapersandpresentations.Anextensiveinstructor’smanualcontainingsample
lessonsandstudentpapersisavailableatwww.cambridge.org/Marder.
MICHAEL P. MARDER is Professor of Physics at The University of Texas at
Austin. He is co-director and co-founder of UTeach, a program preparing sec-
ondary teachers of science and mathematics. He has been teaching a course on
howtodoscientificresearchwhichledtothewritingofthistextbook.Heisauthor
ofthegraduatetextCondensedMatterPhysics.

Research Methods for Science
MICHAEL P. MARDER
TheUniversityofTexasatAustin
CAMBRIDGE UNIVERSITY PRESS
Cambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,
SãoPaulo,Delhi,Dubai,Tokyo,MexicoCity
CambridgeUniversityPress
TheEdinburghBuilding,CambridgeCB28RU,UK
PublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYork
www.cambridge.org
Informationonthistitle:www.cambridge.org/9780521145848
(cid:2)c M.Marder2011
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2011
PrintedintheUnitedKingdomattheUniversityPress,Cambridge
AcatalogrecordforthispublicationisavailablefromtheBritishLibrary
ISBN978-0-521-14584-8Paperback
Additionalresourcesforthispublicationatwww.cambridge.org/Marder
CambridgeUniversityPresshasnoresponsibilityforthepersistenceor
accuracyofURLsforexternalorthird-partyInternetwebsitesreferredto
inthispublication,anddoesnotguaranteethatanycontentonsuch
websitesis,orwillremain,accurateorappropriate.
Contents
Preface pagevii
1 Curiosityandresearch 1
1.1 Coursegoals 1
1.2 Kindsofquestions 1
1.3 Researchmethodsforscience 3
1.4 Puttingmethodstogether 15
Assignments 15
2 Overviewofexperimentalanalysisanddesign 18
2.1 Hypothesis-drivenexperiments 18
2.2 Measuringvalues 30
2.3 Improvingexperiments 39
2.4 Safetyandethics 43
Assignments 48
3 Statistics 51
3.1 Motivationsforstatistics 51
3.2 Reducingmanynumberstofew 55
3.3 Probabilitydistributions 61
3.4 Connectingdataandprobabilitydistributions 70
3.5 WhathappenstoaveragesasN increases 75
3.6 CentralLimitTheorem 81
3.7 Comparingmanyexperimentalmeasurements 92
3.8 Datawithmanyvaluesofindependentvariable 97
3.9 Otherstatisticaltests 105
Assignments 105
4 Mathematicalmodels 112
4.1 Ingredientsofmathematicalmodeling 112
4.2 Estimation 121
4.3 Linearregression 125
v
vi Contents
4.4 Matchingarbitraryfunctionstodata 128
4.5 Fouriertransforms 133
4.6 Deterministicmodeling 136
Assignments 146
5 Scientificinformation 151
5.1 Introduction 151
5.2 Writingaproposal 151
5.3 Writingscientificpapers 152
5.4 Scientificfigures 161
5.5 Givingscientificpresentations 166
5.6 Searchingforscientificinformation 168
5.7 Obtainingscientificarticles 172
5.8 Readingscientificpapers 173
5.9 Finalwords 177
Assignments 178
AppendixA Spreadsheetsforbasicscientificcomputation 182
A.1 Spreadsheetprograms 182
A.2 Basicprogramfeatures 183
A.3 Built-infunctions 189
A.4 Charts 194
Assignments 199
AppendixB ExtractfromGalileo’sTwoNewSciences 201
AppendixC Safetyinthelaboratory 204
C.1 Safetycontract 204
C.2 Chemicalsafetyforms 207
AppendixD Gradingrubrics 210
D.1 Writtenpresentation 211
D.2 Oralpresentation 222
Index 224
Preface
This book accompanies a one-semester undergraduate introduction to scientific
research. The course was first developed at The University of Texas at Austin
forstudentspreparingtobecomescienceandmathematicsteachers,andhassince
grown to include a broad range of undergraduates who want an introduction to
research. The heart of the course is a set of scientific inquiries that each stu-
dent develops independently. In years of teaching the course, the instructors have
heard many questions that students naturally ask as they gather data, develop
models, and interpret them. This book contains answers to those most common
questions.
Because the focus is on supporting student inquiries, the text is relatively brief,
andfocusesonconceptssuchasthemeaningofstandarderror, p-values,anddeter-
ministic modeling. If a single statistical test, such as χ2, is adequate to deal with
moststudentexperiments,thetextdoesnotintroducealternatives,suchasANOVA,
eveniftheyarestandardforprofessionalresearcherstoknow.
Themathematicallevelofthebookisintermediate,andinsomeplacespresumes
knowledge of calculus. It could probably be used with students who don’t know
calculus,skippingthesesectionswithoutgreatloss.
Thereisaninstructor’smanualthatdescribesdailyactivitiesfora14-weekclass
thatmeetstwohoursperweekinaclassroomandtwohoursperweekinalab.Itis
available at www.cambridge.org/Marder. The classroom sessions are not lectures
coveringthematerialinthesechapters,butinsteadconsistinactivitiesfocusingon
basic concepts. The text in many cases contains more complete explanation than
thereistimetodeliverinclass.
The basic idea for the class and hence of this book is due to David Laude,
Professor of Chemistry and Associate Dean for Undergraduate Education at UT
Austin. He had two essential insights: First, the way to learn about scientific
research is actually to do some. Second, it doesn’t matter if research results are
notnewsolongastheyarenewtothepersonwhodoesthem.Theingeniousorder
vii
viii Preface
“BECURIOUS!!” in the first inquiry assignment (page 15) comes from his first
assignmentinthefirstsemesterhetaughtit.
Manyothercourseinstructorshavecontributed.MaryWalkerandDeniseEkberg
both brought in course elements because of their backgrounds that span scientific
research and secondary teaching. They emphasized the importance of procedures
to ensure student safety, and also insisted on rubrics and checklists so that stu-
dents received clear messages during an otherwise free-wheeling class of what
wasacceptable,whatwasforbidden,whatwasdesired,andwhatwasdiscouraged.
ThomasHillsemphasizedtheimportanceofopenquestions.Manyteachingassis-
tantshavealsocontributedtothecoursecontent,particularlySedKeller,whowrote
thefirstdraftoftheappendixonuseofspreadsheets.
For many years, I have co-taught the class with Pawan Kumar, Professor of
Astronomy, and Dan Bolnick, Associate Professor of Integrative Biology. Pawan
Kumar helped create all the homeworks, and insistedwe find ways to tie research
on closed questions back into research on areas of social concern. Dan Bolnick
gentlyproddedmetothrowoutallpreviousapproachestostatistics,andmakeuse
ofexamplesfrombiologythatworkedmuchbetter.
Finally, I would like to thank Mary Ann Rankin, Dean of the College of Nat-
ural Sciences, who insisted passionately from the start that future teachers in our
UTeach program learn about scientific research, and has provided every form of
supportneededtohelptheclassgrow.
PreparationofthistextwaspartiallysupportedbytheNationalScienceFounda-
tionunderDMR–0701373.
1
Curiosity and research
1.1 Coursegoals
Sciencestartswithcuriosityabouttheworld.Itstartswithquestionsaboutwhythe
sky is blue, why dogs wag their tails, whether electric power lines cause cancer,
and whether God plays dice with the universe. But while curiosity is necessary
forscience,itisnotenough.Sciencealsodependsuponlogicalthought,carefully
plannedexperiments,mathematicalandcomputermodels,specializedinstruments,
andmanyotherelements.Inthiscourse,youwilllearnsomeoftheresearchmeth-
odsthatturncuriosityintoscience.Inparticular,youwilllearnto
• Createyourownexperimentstoanswerscientificquestions.
• Designexperimentstoreducesystematicandrandomerrorsandusestatisticstointerpret
theresults.
• Useprobesandcomputerstogatherandanalyzedata.
• Treathumansubjectsinanethicalfashion.
• Applysafelaboratoryprocedures.
• Findandreadarticlesinthescientificliterature.
• Createmathematicalmodelsofscientificphenomena.
• Applyscientificargumentsinmattersofsocialimportance.
• Writescientificpapers.
• Reviewscientificpapers.
• Giveoralpresentationsofscientificwork.
Youwillnotjustbelearningabouttheseskills.Youwillbeacquiringandapplying
thembycarryingoutscientificinquiries.
1.2 Kindsofquestions
Testablequestions Everyscientificinquiryanswersquestions,andmostscientific
inquiries begin with specific questions. People often wonder about questions that
arehardtoaddress,suchas
1