P1:SFK/UKS P2:SFK/UKS QC:SFK/UKS T1:SFK BLBK106-Bower January28,2009 7:44 Statistical Methods for Food Science Statistical Methods for Food Science: Introductory procedures for the food practitioner John A. Bower © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-16764-2 i P1:SFK/UKS P2:SFK/UKS QC:SFK/UKS T1:SFK BLBK106-Bower January28,2009 7:44 To Jonathan and Cassandra and to Pushka-Latitia with love ‘‘Everything is on a scale ...’’ ii P1:SFK/UKS P2:SFK/UKS QC:SFK/UKS T1:SFK BLBK106-Bower January28,2009 7:44 Statistical Methods for Food Science Introductory procedures for the food practitioner By JohnA.Bower LecturerandCourseLeader(BScFoodStudies) QueenMargaretUniversity,Edinburgh,UK A John Wiley & Sons, Ltd., Publication iii P1:SFK/UKS P2:SFK/UKS QC:SFK/UKS T1:SFK BLBK106-Bower January28,2009 7:44 Thiseditionfirstpublished2009 (cid:2)C 2009BlackwellPublishingLtd BlackwellPublishingwasacquiredbyJohnWiley&SonsinFebruary2007.Blackwell’s publishingprogrammehasbeenmergedwithWiley’sglobalScientific,Technical,andMedical businesstoformWiley-Blackwell. Registeredoffice JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussex,PO198SQ, UnitedKingdom Editorialoffices 9600GarsingtonRoad,Oxford,OX42DQ,UnitedKingdom 2121StateAvenue,Ames,Iowa50014-8300,USA Fordetailsofourglobaleditorialoffices,forcustomerservicesandforinformationabouthow toapplyforpermissiontoreusethecopyrightmaterialinthisbookpleaseseeourwebsiteat www.wiley.com/wiley-blackwell. Therightoftheauthortobeidentifiedastheauthorofthisworkhasbeenassertedin accordancewiththeCopyright,DesignsandPatentsAct1988. Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem, ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recordingor otherwise,exceptaspermittedbytheUKCopyright,DesignsandPatentsAct1988,withoutthe priorpermissionofthepublisher. Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsin printmaynotbeavailableinelectronicbooks. Designationsusedbycompaniestodistinguishtheirproductsareoftenclaimedastrademarks. Allbrandnamesandproductnamesusedinthisbookaretradenames,servicemarks, trademarksorregisteredtrademarksoftheirrespectiveowners.Thepublisherisnotassociated withanyproductorvendormentionedinthisbook.Thispublicationisdesignedtoprovide accurateandauthoritativeinformationinregardtothesubjectmattercovered.Itissoldonthe understandingthatthepublisherisnotengagedinrenderingprofessionalservices.If professionaladviceorotherexpertassistanceisrequired,theservicesofacompetent professionalshouldbesought. LibraryofCongressCataloging-in-PublicationData Bower,JohnA.,MSc. Statisticalmethodsforfoodscience:introductoryproceduresforthefoodpractitioner/by JohnA.Bower.–1sted. p. cm. Includesbibliographicalreferencesandindex. ISBN978-1-4051-6764-2(hardback:alk.paper) 1.Food–Research–Statisticalmethods. I.Title. TX367.B6882009 664(cid:3).0072–dc22 2008034869 AcataloguerecordforthisbookisavailablefromtheBritishLibrary. Setin10/13ptTimesNewRomanbyAptara(cid:2)R Inc.,NewDelhi,India PrintedandboundinSingaporebyMarkonoPrintMediaPteLtd 1 2009 iv P1:SFK/UKS P2:SFK/UKS QC:SFK/UKS T1:SFK BLBK106-Bower January28,2009 7:44 Contents Preface ix Acknowledgements xi PartI Introductionandbasics Chapter1 Basicsandterminology 3 1.1 Introduction 3 1.2 Whatthebookwillcover 4 1.3 Theimportanceofstatistics 6 1.4 Applicationsofstatisticalproceduresinfoodscience 6 1.5 Focusandterminology 9 References 12 Softwaresourcesandlinks 12 Chapter2 Thenatureofdataandtheircollection 14 2.1 Introduction 14 2.2 Thenatureofdataandtheircollection 14 2.3 Collectionofdataandsampling 25 2.4 Populations 35 References 41 Chapter3 Descriptivestatistics 43 3.1 Introduction 43 3.2 Tabularandgraphicaldisplays 44 3.3 Descriptivestatisticmeasures 57 3.4 Measurementuncertainty 67 3.5 Determinationofpopulationnatureandvariancehomogeneity 83 References 86 Chapter4 Analysisofdifferences–significancetesting 88 4.1 Introduction 88 4.2 Significance(hypothesis)testing 89 4.3 Assumptionsofsignificancetests 99 4.4 Stagesinasignificancetest 100 4.5 Selectionofsignificancetests 105 4.6 Parametricornon-parametrictests 109 References 109 v P1:SFK/UKS P2:SFK/UKS QC:SFK/UKS T1:SFK BLBK106-Bower January28,2009 7:44 vi Contents Chapter5 Typesofsignificancetest 111 5.1 Introduction 111 5.2 Generalpoints 111 5.3 Significancetestsfornominaldata(non-parametric) 112 5.4 Significancetestsforordinaldata(non-parametric) 118 5.5 Significancetestsforintervalandratiodata(parametric) 126 References 135 Chapter6 Association,correlationandregression 137 6.1 Introduction 137 6.2 Association 138 6.3 Correlation 140 6.4 Regression 144 References 149 Chapter7 Experimentaldesign 150 7.1 Introduction 150 7.2 Terminologyandgeneralprocedure 150 7.3 Sourcesofexperimentalerroranditsreduction 154 7.4 Typesofdesign 159 7.5 Analysismethodsandissues 168 7.6 Applicabilityofdesigns 170 References 171 PartII Applications Chapter8 Sensoryandconsumerdata 174 8.1 Introduction 174 8.2 Thequalityandnatureofsensoryandconsumerdata 174 8.3 Experimentaldesignissues 176 8.4 Consumerdata(sensoryandsurvey) 176 8.5 Trainedpanelsensorydata 192 8.6 Analysisofrelationships 208 References 209 Chapter9 Instrumentaldata 211 9.1 Introduction 211 9.2 Qualityandnatureofinstrumentaldata 211 9.3 Samplingandreplication 214 9.4 Experimentaldesignissues 216 9.5 Statisticalanalysisofinstrumentaldata 218 9.6 Chemicalanalysisapplications 220 9.7 Analysisofrelationships 235 References 235 P1:SFK/UKS P2:SFK/UKS QC:SFK/UKS T1:SFK BLBK106-Bower January28,2009 7:44 Contents vii Chapter10 Foodproductformulation 238 10.1 Introduction 238 10.2 Designapplicationinfoodproductdevelopment 238 10.3 Singleingredienteffects 240 10.4 Twoormoreingredients 244 10.5 Screeningofmanyingredients 249 10.6 Formulationbyconstraints 255 References 260 Chapter11 Statisticalqualitycontrol 262 11.1 Introduction 262 11.2 Typesofstatisticalqualitycontrol 263 11.3 Samplingprocedures 264 11.4 Controlcharts 265 11.5 Acceptancesampling 279 References 283 Chapter12 Multivariateapplications 284 12.1 Introduction 284 12.2 Multivariatemethodsandtheircharacteristics 284 12.3 Multivariatemodes 285 12.4 Relationshipofconsumerpreferencewithsensorymeasures 301 References 302 Index 305 P1:SFK/UKS P2:SFK/UKS QC:SFK/UKS T1:SFK BLBK106-Bower January28,2009 7:44 Preface Therecordingandanalysisoffooddataarebecomingincreasinglysophisticated. Consequently, the practicing food scientist in industry or at study faces the task of using and understanding statistical methods. Unfortunately, statistics is often viewedasadifficultsubjectandtendstobeavoidedbecauseofcomplexityandlack ofspecificapplicationtothefoodfield.Whilethissituationischangingandthere ismuchmaterialonmultivariateapplicationsforthemoreadvancedreader,acase existsforaunivariateapproachforthenon-statistician.Thatistheintentofthis book.Itprovidesfoodscientists,technologistsandotherfoodpractitionerswitha sourcetextonaccessiblestatisticalprocedures.Materialforstudentsandworkers inthefoodlaboratoryisincluded,coveringthefoodanalyst,thesensoryscientist andtheproductdeveloper.Otherswhoworkinfood-relateddisciplinesinvolving consumersurveyinvestigationswillalsofindmanysectionsofuse.Emphasisis on a ‘hands-on’ approach with worked examples using computer software with theminimumofmathematicalformulae. ix P1:SFK/UKS P2:SFK/UKS QC:SFK/UKS T1:SFK BLBK106-Bower January28,2009 7:44 Acknowledgements I thank all students of food at Queen Margaret University, Edinburgh (1985– 2007), for their enthusiasm and contribution to experimentation in the study of foodscienceandconsumerstudies.Also,thanksareduetomycolleaguesinthe Department of Consumer Studies, in particular Dr Monika Schro¨der for many stimulatingconversationsandforherhelpwithreadingandeditingofearlydrafts. Thepublishersandauthorthankthefollowingforpermissiontoincludeoutput material: SPSSgraphsandtablesbySPSS,Inc. ExcelspreadsheettablesandgraphsbyMicrosoft(cid:2)R Corp. Design-Expert(R)softwareoutputbyStat-Ease,Inc. Examples of Minitab output by Minitab Inc.: Portions of the input and output containedinthispublication/bookareprintedwithpermissionofMinitabInc.All materialremainstheexclusivepropertyandcopyrightofMinitabInc.Allrights reserved. Trademarknotice Thefollowingaretrademarksorregisteredtrademarksoftheirrespectivecompa- nies: ExcelisatrademarkofMicrosoft(cid:2)R Corporation Minitab(Minitab(cid:2)R StatisticalSoftwareTM)isatrademarkofMinitabInc. Design-Expert(R)softwareisatrademarkofStat-EaseInc.,Minneapolis,MN SPSSisatrademarkofSPSSInc.,Chicago,IL MegastatisatrademarkofMcGraw-Hill/Irwin,McGraw-HillCompaniesInc. MINITAB(cid:2)R andallothertrademarksandlogosforthecompany’sproductsandser- vicesaretheexclusivepropertyofMinitabInc.Allothermarksreferencedremain thepropertyoftheirrespectiveowners.Seeminitab.comformoreinformation. xi P1:SFK/UKS P2:SFK/UKS QC:SFK/UKS T1:SFK BLBK106-Bower January24,2009 20:17 Part I Introduction and basics Statistical Methods for Food Science: Introductory procedures for the food practitioner John A. Bower © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-16764-2 1