Statistical Design – Chemometrics

423 Pages·2005·4.052 MB·English

by  R.E. Bruns, I.S. Scarminio and B. de Barros Neto (Eds.)

DATA HANDLING INSCIENCE ANDTECHNOLOGY —VOLUME25
Statistical design — Chemometrics
i
DATAHANDLING IN SCIENCE ANDTECHNOLOGY
Advisory Editors: S.Rutan and B.Walczak
Other volumes in this series:
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Volume2 Chemometrics:ATextbook,byD.L.Massart,B.G.M.Vandeginste,S.N.Deming,
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Volume3 ExperimentalDesign:AChemometricApproach,byS.N.DemingandS.L.Morgan
Volume4 AdvancedScientificComputinginBASICwithApplicationsinChemistry,Biology
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Volume5 PCsforChemists,editedbyJ.Zupan
Volume6 ScientificComputingandAutomation(Europe)1990,PreceedingsoftheScientific
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TheNetherlands,editedbyE.J.Karjalainen
Volume7 ReceptorModelingforAirQualityManagement,editedbyP.K.Hopke
Volume8 DesignandOptimizationinOrganicSynthesis,byR.Carlson
Volume9 MultivariatePatternRecognitioninChemometrics,illustratedbycasestudies,
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Volume10 SamplingofHeterogeneousandDynamicMaterialSystems:Theoriesof
Heterogeneity,SamplingandHomogenizing,byP.M.Gy
Volume11 ExperimentalDesign:AChemometricApproach(Second,RevisedandExpanded
Edition)byS.N.DemingandS.L.Morgan
Volume12 MethodsforExperimentalDesign:PrinciplesandApplicationsforPhysicists
andChemists,byJ.L.Goupy
Volume13 IntelligentSoftwareforChemicalAnalysis,editedbyL.M.C.Buydensand
P.J.Schoenmakers
Volume14 TheDataAnalysisHandbook,byI.E.FrankandR.Todeschini
Volume15 AdaptionofSimulatedAnnealingtoChemicalOptimizationProblems,
editedbyJ.Kalivas
Volume16 MultivariateAnalysisofDatainSensoryScience,editedbyT.NæsandE.Risvik
Volume17 DataAnalysisforHyphenatedTechniques,byE.J.KarjalainenandU.P.Karjalainen
Volume18 SignalTreatmentandSignalAnalysisinNMR,editedbyD.N.Rutledge
Volume19 RobustnessofAnalyticalChemicalMethodsandPharmaceuticalTechnological
Products,editedbyM.W.B.Hendriks,J.H.deBoer,andA.K.Smilde
Volume20A HandbookofChemometricsandQualimetrics:PartA,byD.L.Massart,
B.G.M.Vandeginste,L.M.C.Buydens,S.deJong,P.J.Lewi,and
J.Smeyers-Verbeke
Volume20B HandbookofChemometricsandQualimetrics:PartB,byB.G.M.Vandeginste,
D.L.Massart,L.M.C.Buydens,S.deJong,P.J.Lewi,andJ.Smeyers-Verbeke
Volume21 DataAnalysisandSignalProcessinginChromatography,byA.Felinger
Volume22 WaveletsinChemistry,editedbyB.Walczak
Volume23 Nature-inspiredMethodsinChemometrics:GeneticAlgorithmsandArtificial
NeuralNetworks,editedbyR.Leardi
Volume24 HandbookofChemometricsandQualimetrics,byD.L.Massart,B.M.G.Vandeginste,
L.M.C.Buydens,S.deJong,P.J.Lewi,andJ.Smeyers-Verbeke
ii
DATAHANDLING IN SCIENCE ANDTECHNOLOGY—VOLUME 25
AdvisoryEditors: S. Rutan andB. Walczak
Statistical design —
Chemometrics
R.E. BRUNS
InstitutodeQuimica, UniversidadeEstadualde Campinas,Brazil
I.S. SCARMINIO
Departamento deQuimica, UniversidadeEstadualdeLondrina, Brazil
B. de BARROS NETO
Departamento deQuimica Fundamental,Universidade FederaldePernambuco,Brazil
Amsterdam – Boston – Heidelberg – London – New York – Oxford
Paris – San Diego – San Francisco – Singapore – Sydney – Tokyo
iii
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Preface
Utilityoughttobetheprincipalintentionofeverypublication.Wherever
this intention does not plainly appear, neither the books nor their authors
have the smallest claim to the approbation of mankind.
Thus wrote William Smellie in the preface to the first edition of
Encyclopaedia Britannica, published in 1768.
Our book has the modest intention of being useful to readers who wish
— or need — to do experiments. The edition you are reading is a
translation of a much revised, corrected and expanded version of our
original text, Como Fazer Experimentos, published in Portuguese. To
prepare this edition, every sentence was reconsidered, with the objective
of clarifying the text. All the errors that we were able to discover, or the
readers were kind enough to point out, have been corrected.
Duringthelast20yearsorsowehavespentconsiderabletimeteaching
chemometrics — the use of statistical, mathematical and graphical
techniques to solve chemical problems — to hundreds of students in our
ownuniversities,aswellasinover30differentindustries.Thesestudents
came principally from the exact sciences and engineering but other
professional categories were also represented, such as management,
medicine, biology, pharmacy and food technology. This diversity leads us
to believe that the methods described here can be learned and applied,
with varying degrees of effort, by any professional who has to do
experiments.
Statistics does not perform miracles and in no way can substitute
specialized technical knowledge. What we hope to demonstrate is that a
professional who combines knowledge of statistical experimental design
and data analysis with solid technical and scientific training in his own
area of interest will become more competent, and therefore even more
competitive.
We are chemists, not statisticians, and perhaps this differentiates our
bookfrommostotherswithsimilarcontent.Althoughwedonotbelieveit
is possible to learn the techniques of experimental design and data
analysiswithoutsomeknowledgeofbasicstatistics,inthisbookwetryto
keep its discussion at the minimum necessary — and soon go on to what
v
vi Preface
really interests the experimenter — research and development problems.
Ontheotherhand,recognizingthatstatisticsisnotverydeartotheheart
of many scientists and engineers, we assume that the reader has no
knowledgeofit.Inspiteofthis,wearriveearlierattreatingexperimental
problems with many variables than do more traditional texts.
Many people have contributed to making this book a reality. When the
first edition came out, the list was already too extensive to cite everyone
by name. We have been fortunate that this list has grown considerably
sincethattimeandourgratitudetoallhasincreasedproportionately.We
do,however,wishtothankespeciallythosewhoseworkhasallowedusto
include so many applications in this edition. These people are cited with
specific references when their results are discussed. We are also grateful
to Fapesp, CNPq and Faep-Unicamp research granting agencies for
partial financial support.
Ofcourse,weremainsolelyresponsibleforthedefectswehavenotbeen
able to correct. We count on the readers to help us solving this
optimization problem. Our electronic addresses are below. If you know
of places where we could have done better, we will be most interested in
hearing from you.
Campinas, July 2005.
B. de Barros Neto
Fundamental Chemistry Department
Federal University of Pernambuco
E-mail: [email protected]
I. S. Scarminio
Chemistry Department
State University of Londrina
E-mail: [email protected]
R. E. Bruns
Chemistry Institute
State University of Campinas
E-mail: [email protected]
Contents
Preface v
1 How statistics can help 1
1.1 Statistics can help 2
1.2 Empirical models 4
1.3 Experimental design and optimization 5
2 When the situation is normal 9
2.1 Errors 10
2.1.1 Types of error 11
2.2 Populations, samples and distributions 14
2.2.1 How to describe the characteristics
of the sample 17
2.3 The normal distribution 23
2.3.1 Calculating probabilities of occurrence 24
2.3.2 Using the tails of the standard normal
distribution 29
2.3.3 Why is the normal distribution so important 32
2.3.4 Calculating confidence intervals for the mean 34
2.3.5 Interpreting confidence intervals 35
2.4 Covariance and correlation 37
2.5 Linear combinations of random variables 41
2.6 Random sampling in normal populations 45
2.7 Applying the normal distribution 54
2.7.1 Making comparisons with a reference value 54
2.7.2 Determining sample size 58
2.7.3 Statistically controlling processes 60
2.7.4 Comparing two treatments 64
Comparing two averages 64
Making paired comparisons 66
Comparing two variances 69
2A Applications 70
2A.1 From home to work 70
2A.2 Bioequivalence of brand-name and generic
medicines 76
2A.3 Still more beans? 77
2A.4 Marine algae productivity 81
vii
viii Contents
3 Changing everything at the same time 83
3.1 A 22 factorial design 85
3.1.1 Calculating the effects 86
3.1.2 Geometrical interpretation of the effects 89
3.1.3 Estimating the error of an effect 89
3.1.4 Interpreting the results 93
3.1.5 An algorithm for calculating the effects 95
3.1.6 The statistical model 98
3.2 A 23 factorial design 103
3.2.1 Calculating the effects 104
3.2.2 Estimating the error of an effect 106
3.2.3 Interpreting the results 107
3.2.4 The statistical model 110
3.3 A 24 factorial design 110
3.3.1 Calculating the effects 111
3.3.2 Estimating the error of an effect 112
3.4 Normal probability plots 114
3.5 Evolutionary operation with two-level designs 119
3.6 Blocking factorial designs 123
3A Applications 125
3A.1 Resin hydrolysis 125
3A.2 Cyclic voltammetry of methylene blue 126
3A.3 Retention time in liquid chromatography 127
3A.4 Gas separation by adsorption 129
3A.5 Improving wave functions 131
3A.6 Performance of Ti/TiO electrodes 133
2
3A.7 Controlling detergent froth 138
3A.8 Development of a detergent 140
3A.9 A blocked design for producing earplugs 142
4 When there are many variables 147
4.1 Half-fractions of factorial designs 148
4.1.1 How to construct a half-fraction 152
4.1.2 Generators of fractional factorial designs 154
4.2 The concept of resolution 156
4.2.1 Resolution IV fractional factorial designs 156
4.2.2 Resolution V fractional factorial designs 157
4.2.3 Inert variables and factorials embedded
in fractions 158
4.2.4 Half-fractions of maximum resolution 161
4.3 Screening variables 163
4.3.1 Resolution III fractional factorial designs 163
4.3.2 Saturated designs 165
Contents ix
4.3.3 How to construct resolution III fractional
factorial designs 171
4.3.4 How to construct a 28(cid:1)4 fraction from a 27(cid:1)4fraction 171
IV III
4.3.5 Saturated Plackett–Burman designs 173
4.3.6 Taguchi techniques of quality engineering 175
4A Applications 179
4A.1 Adsorption on organofunctionalized silicas 179
4A.2 Calcium oxalate thermogravimetry 179
4A.3 Chromatographic analysis of gases 182
4A.4 Mn-porphyrin catalytic response 184
4A.5 Oxide drainage in the steel industry 185
4A.6 Violacein production by bacteria 187
4A.7 Polyester resin cure 189
4A.8 Screening design for earplug production 193
4A.9 Plackett–Burman designs for screening factors 194
5 Empirical model-building 199
5.1 A model for y¼fðXÞ 199
5.2 The analysis of variance 209
5.3 Confidence intervals 213
5.4 Statistical significance of the regression model 218
5.5 A new model for y¼fðXÞ 219
5.6 Lack of fit and pure error 223
5.7 Correlation and regression 231
5A Applications 233
5A.1 The spring of air 233
5A.2 Chromatographic calibration 235
5A.3 Multivariate calibration 239
5A.4 Forbidden energy gaps in semiconductors 240
5A.5 Heat of vaporization determination 241
5A.6 Another calibration 243
6 Exploring the response surface 245
6.1 Response surface methodology 245
6.1.1 Initial modeling 246
6.1.2 Determining the path of steepest ascent 250
6.1.3 Finding the optimum point 254
6.2 The importance of the initial design 259
6.3 An experiment with three factors and two responses 260
6.4 Treating problems with many variables 268
6.5 Central composite designs 273
6.6 Box–Behnken designs 277
6.7 Doehlert designs 281