Methods of analysis of food components and additives

Methods of analysis of food components and additives

Methods of Analysis of Food

Components and Additives

1647_series 11/8/04 1:29 PM Page 1

Chemical and Functional Properties of Food Proteins

Edited by Zdzislaw E Sikorski

Chemical and Functional Properties of Food Components, Second Edition

Edited by Zdzislaw E Sikorski

Chemical and Functional Properties of Food Components SeriesSERIES EDITOR

Zdzislaw E Sikorski

Chemical and Functional Properties of Food Lipids

Edited by Zdzislaw E Sikorski and Anna Kolakowska

Toxins in Food

Edited by Waldemar M Dabrowski and Zdzislaw E Sikorski

Chemical and Functional Properties of Food Saccharides

Edited by Piotr Tomasik

Methods of Analysis of Food Components and Additives

Edited by Semih Ötles,

1647_title 1/21/05 12:21 PM Page 1

EDITED BYSemih Ötles

Ege University Department of Food Engineering

Izmir, Turkey

Methods of Analysis of Food

Components and Additives

,

Boca Raton London New York Singapore

A CRC title, part of the Taylor & Francis imprint, a member of the Taylor & Francis Group, the academic division of T&F Informa plc.

Published in 2005 by CRC Press Taylor & Francis Group

6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742

© 2005 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group

No claim to original U.S Government works Printed in the United States of America on acid-free paper

10 9 8 7 6 5 4 3 2 1 International Standard Book Number-10: 0-8493-1647-2 (Hardcover) International Standard Book Number-13: 978-0-8493-1647-0 (Hardcover) This book contains information obtained from authentic and highly regarded sources Reprinted material is quoted with permission, and sources are indicated A wide variety of references are listed Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use.

No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc (CCC) 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged.

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is the Academic Division of T&F Informa plc.

1647_C00.fm Page iv Wednesday, March 30, 2005 12:31 PM

The ability to accurately separate, identify, and analyze nutrients, additives, andtoxicological compounds found in food and food products has become criticallyimportant in recent decades, as knowledge of and interest in the relationshipsbetween diet and health have increased This requires training students and analysts

in the proper application of the best methods, as well as improving, developing, oradapting existing methods to meet specific analytic needs This book aids the analyst

by providing a valuable reference to both newly developed and established methods

of analysis of food components and additives

The book comprises 16 chapters, which take the reader through brief and sible descriptions of methods of analysis of food components and additives Rangingfrom chemical analysis of food components and additives to infrared (IR), nuclearmagnetic resonance (NMR), Fourier transform Raman (FTR), capillary electro-phoresis (CE), high-performance liquid chromatography (HPLC), gas chromatogra-phy (GC), mass spectrometry (MS), and more The book provides first-hand expla-nations of modern methods, contributed by 24 leading scientists, many of whomactually developed or refined the techniques, and presents new documented informa-tion on standard methods of analysis of food components and additives in a uniformformat and in a style that can be understood by a reader who is not familiar with theanalysis of each component Each chapter is structured to provide a description ofthe information about the component or additive that can be analyzed, a simplemethod explanation of how it works, examples of applications, and references formore detailed information This format also facilitates comparison of methods ofanalysis of each component The use of different authors to cover a broad spectrum

acces-of methods resulted in some differences acces-of style, but overall the book achieves its goalThe first chapter, “Selection of Techniques Used in Food Analysis,” covers topicsrelevant to all techniques, including sample preparation, quantitative measurements,and information management, and concentrates on what goals can be achieved byapplying different techniques for various purposes in food analysis The secondchapter, “Statistical Assessment of Results of Food Analysis,” provides an overview

of the need for statistical assessment of the results of food analysis and the evaluation

of most suitable methods for different situations at a level that is more completethan those found in most introductory analysis textbooks The remaining 14 chaptersaddress the major areas of analysis of food components and additives: analysis ofdrinking waters, proteins, peptides, amino acids, carbohydrates, food lipids, metalsand trace elements in foods, vitamins, carotenoids, chlorophylls, food polyphenols,aroma compounds, food volatiles, sensory analysis of foods and determination offood allergens, genetically modified components, pesticide residues, pollutants infoods, chemical preservatives in foods, radioactive contaminants in foods, and rapidanalysis techniques in food microbiology In most chapters, many examples of1647_C00.fm Page v Wednesday, March 30, 2005 12:31 PM

applications of methods to analytical problems are provided The references provided

in these chapters can be highly useful and valuable for those seeking additionalinformation

This comprehensive book should serve as a reference for scientists, analyticalchemists, engineers, researchers, food manufacturers, personnel from governmentagencies, standards writing bodies, students majoring in various science disciplines(biology, biochemistry, chemistry, environmental science, engineering, and foodchemistry, to name a few) interested in obtaining a stronger background in analysis,and all those involved in the analysis of both food components and food additives.1647_C00.fm Page vi Wednesday, March 30, 2005 12:31 PM

The Editor

A native of Izmir, Turkey, Semih Ötles¸ obtained a B.Sc degree from the Department

of Food Engineering (Ege University) in 1980 During his assistantship at EgeUniversity in 1985, he received an M.S in food chemistry, and in 1989, aftercompleting his thesis research on the instrumental analysis and chemistry of vitamins

in foods, he earned a Ph.D in food chemistry from Ege University In 1991–92, hecompleted postdoctoral training, including an OECD postdoctoral fellowship, at theResearch Center Melle at Ghent University, Belgium Afterward, Dr Ötles¸ joinedthe Department of Food Engineering at Ege University as a scientist of food chem-istry, being promoted to associate professor in 1993 and to professor in 2000 During1996–1998 he was deputy director at the Ege Vocational School of Higher Studies.Since 2003 he has been vice dean of the engineering faculty, Ege University.The research activities of Professor Ötles¸ have been focused on instrumentalanalysis of food compounds: he began a series of projects on the separation andanalysis techniques of high-performance liquid chromatography (HPLC), first foranalysis of vitamins in foods, then proteins and carbohydrates, and, most recently,carotenoids Other activities span the fields of GC, GC/MS analysis, soy chemistry,aromatics, medical and functional foods and nutraceutical chemistry; included aremultiresidue analysis of various foods, and n-3 fatty acids in fish oils

Professor Ötles¸ is the author or coauthor of more than 150 publications nical papers, book chapters, and books) and a presenter of seminars He is a member

(tech-of several scientific societies, associations, and organizations, including the AsianPacific Organization for Cancer Prevention (APOCP) and the International Society

of Food Physicists (ISFP) He is a member of the steering committee of APOCP’slocal scientific bureau and is the Turkish representative of ISFP, and has organizedinternational congresses on diet/cancer and food physics

He is a member of editorial advisory boards for Asian Pacific Journal of Cancer Prevention; Food Science & Technology Abstracts of IFIS (International Food Infor-mation Service); Current Topics in Nutraceutical Research; Electronic Journals of Environmental, Agricultural and Food Chemistry; Newsline; Journal of Oil, Soap, Cosmetics; Trends World Food; Trends Food Science & Technology; Pakistani Journal

of Nutrition; Journal of Food Technology; Academic Food; and Australian Journal of Science & Technology He is referee/reviewer for AOAC International, Journal of Experimental Marine Biology and Ecology, Journal of Medical Foods, die Nahrung, Journal of Alternative & Complementary Medicine, The Analyst, and Journal of Agricultural and Food Chemistry.

1647_C00.fm Page vii Wednesday, March 30, 2005 12:31 PM

Permission to reprint the following is gratefully acknowledged:

Table 4.1: Kolakowski, E., Protein determination and analysis in food systems, in

Chemical and Functional Properties of Food Proteins, Sikorski, Z.E., Ed., TechnomicPublishing, Lancaster/Basel, chap 4, pp 57–112, 2001

Figure 11.3: Orlandi, P.A et al., Analysis of flour and food samples for Cry9C frombioengineered corn, J Food Prot., 65, 426, 2002

Figure 11.4: Raybourne, R.B et al., Development and use of an ELISA test to detectIgE antibody to Cry9c following exposure to bioengineered corn, Int Arch Allergy Immunol., 132(4), 322, 2003

1647_C00.fm Page ix Wednesday, March 30, 2005 12:31 PM

U.S Food and Drug Administration

College Park, Maryland

Francisco Diez-Gonzalez

University of Minnesota

St Paul, Minnesota

Douglas G Hayward

U.S Food and Drug Administration

College Park, Maryland

Jae Hwan Lee

Department of Food Science and Technology

Seoul National University of Technology

Marian Naczk

St Francis Xavier University

Antigonish, Nova Scotia, Canada

Wageningen Agricultural University

Bilthoven, The Netherlands

Steven J Schwartz

Ohio State University

Columbus, Ohio

Fereidoon Shahidi

Memorial University of Newfoundland

St John’s, Newfoundland, Canada

Analysis of Drinking Water

Marek Biziuk and Malgorzata Michalska ⁄

Determination and Speciation of Trace Elements in Foods

Stephen G Capar and Piotr Szefer

Chapter 7

Analysis of Vitamins for the Health, Pharmaceutical, and Food Sciences

Semih Ötles¸ and Yildiz Karaibrahimoglu

Chapter 8

Analysis of Carotenoids and Chlorophylls in Foods

Jae Hwan Lee and Steven J Schwartz

1647_C00.fm Page xiii Wednesday, March 30, 2005 12:31 PM

Chapter 9

Analysis of Polyphenols in Foods

Fereidoon Shahidi and Marian Naczk

Chapter 10

Sensory Analysis of Foods

Kannapon Lopetcharat and Mina McDaniel

Chapter 11

Determination of Food Allergens and Genetically Modified

Components

Kristina M Williams, Mary W Trucksess, Richard B Raybourne,

Palmer A Orlandi, Dan Levy, Keith A Lampel, and Carmen D Westphal

Chapter 12

Determination of Pesticide Residues

Steven J Lehotay and Katerina Mastovska

Chapter 13

Determination of Pollutants in Foods

Douglas G Hayward

Chapter 14

Analysis of Chemical Preservatives in Foods

Adriaan Ruiter and Aldert A Bergwerff

Chapter 15

Measuring Radioactive Contaminants in Foods

Andras Szabo and Sandor Tarjan

Chapter 16

Rapid Analysis Techniques in Food Microbiology

Francisco Diez-Gonzalez and Yildiz Karaibrahimoglu

1647_C00.fm Page xiv Wednesday, March 30, 2005 12:31 PM

1 Selection of Techniques Used in Food Analysis

Michael H Tunick

CONTENTS

1.1 Introduction1.2 Sample Selection and Preservation1.3 Extraction

1.4 Technique Selection1.5 Application of Techniques1.5.1 Chromatographic Techniques1.5.1.1 Gas Chromatography (GC)1.5.1.2 High-Performance Liquid Chromatography (HPLC)1.5.1.3 Supercritical Fluid Chromatography (SFC)

1.5.2 Spectroscopic Techniques1.5.2.1 UV, Vis, and Fluorescence1.5.2.2 Infrared (IR)

1.5.2.3 Raman1.5.2.4 Atomic Absorption and Atomic Emission1.5.2.5 Mass Spectrometry (MS)

1.5.2.6 Nuclear Magnetic Resonance (NMR) andElectron Spin Resonance (ESR)

1.5.2.7 Other Spectroscopic Techniques1.5.3 Physical Techniques

1.5.3.1 Electrochemical1.5.3.2 Electrophoresis1.5.3.3 Flavor and Odor1.5.3.4 Particle Analysis1.5.3.5 Rheology and Texture1.5.3.6 Structure

1.5.3.7 Thermal Properties1.5.4 Biological Techniques1.5.4.1 Enzyme and Microbial Sensors1.5.4.2 Immunosensors

1.6 SummaryReferences1647_Book.book Page 1 Wednesday, March 30, 2005 11:42 AM

1.1 INTRODUCTION

Scientists analyze foods for their composition; structure; and chemical, physical,and biological properties The information obtained may be used for research or formonitoring product quality A host of different analyses can be conducted on anyfood For example, a cheese manufacturer or researcher could investigate the fol-lowing:

Composition

• Proximate analysis (protein, phosphorus)

• Specific components (beta-casein, fat in dry matter)Structure

• Macrostructure: Visible to naked eye (color, curd pieces)

• Microstructure: 0.1–100
m range (protein matrix, fat globules)

• Ultrastructure: Nanometer range (casein micelles and submicelles)Chemical and physical properties

• Flavor (bitter, salty)

• Odor (diacetyl, lactone)

• Rheology (hardness, elasticity)

• Stability (fat oxidation, whey leakage)

• Thermal properties (heat of combustion, melting profile)Biological properties

• Growth of microorganisms (starter bacteria, mold)

• Metabolic processes and products (enzymes, peptides)Sampling and method selection are of great importance in food analysis Food

is heterogeneous, and changes due to age, physical handling, temperature, and otherfactors will affect analytical results Food is eaten for enjoyment as well as nutrition,

so techniques dealing with aroma, flavor, and texture should not be ignored Thischapter will cover the most common methods used in food analysis, and will includesample preparation and choice of technique

1.2 SAMPLE SELECTION AND PRESERVATION

The first step in food analysis is sample selection Ideally, a sample will be identical

to the material from which it has been removed Samples can be chosen at random,

by judgment of the analyst, or according to a system based on timing or location(such as daily at noon, or within a specific portion of the product or its container).Samples must be representative, collected without contamination, and properly han-dled for the analytical results to be meaningful If the analysis is not to be performedimmediately, the sample will probably have to be preserved to prevent deterioration.Preservation involves the control of temperature, moisture, oxygen, and light, and1647_Book.book Page 2 Wednesday, March 30, 2005 11:42 AM

of the analyte before an analysis is attempted Common procedures include lation, filtration, and precipitation The sample may also have to be homogenized,ground, or treated in some other way Buldini et al.1 and Smith2 reviewed a number

distil-of modern extraction techniques, which include the following:

Digestion

• Microwave oven digestion, with acids such as nitric or sulfuric, forsolubilizing and oxidizing organic compounds to obtain free ions.Digestion by microwave is faster than the classical wet digestion

• UV photolysis digestion, with hydrogen peroxide, for degradingorganic compounds with hydroxyl radicals to obtain free ions Smallamounts of reagents are required, but digestion time is longer

• Solvent extraction, for dissolving compounds of interest

• Pressurized fluid extraction, at the near-supercritical region, whereextraction is faster and more efficient

• Supercritical fluid extraction, above the critical pressure and ture of carbon dioxide, which is nontoxic and nonpolluting Extraction

tempera-is completed in minutes instead of hours, and thermal degradation tempera-isreduced

• Microwave-assisted extraction, usually requiring 15 mL solvent,

10 min extraction time, and no elevated pressure

Sorbent

• Solid-phase extraction and microextraction, where analytes are held

by sorbents such as silica or polymers, and then solubilized and eluted.Headspace

• Purge and trap (or dynamic headspace), in which the analyte is flushedfrom a liquid or gaseous sample and concentrated in a cryogenic trap.1647_Book.book Page 3 Wednesday, March 30, 2005 11:42 AM

1.4 TECHNIQUE SELECTION

The analyst decides the problem to be solved and plans the analyses required,choosing techniques for their appropriateness using criteria in a number of catego-ries:

Ability to conduct analysis

• Sample size, reagents, instruments, cost, final state of sample(destroyed or intact)

to certain types of samples In these cases, in-house methods may be used if theyhave been validated A review of validation methods was published by Wood.7

1.5 APPLICATION OF TECHNIQUES

A multitude of analytical techniques are available for food Many gravimetric andtitrimetric methods are well established and will not be discussed here The number

of instrumental methods has been steadily growing, and can be broadly categorized

as chromatographic, spectroscopic, physical, and biological

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Chromatography is based on distribution or partition of a sample solute betweenstationary and mobile phases Chromatographic techniques in common use today infood analysis include gas chromatography (GC), high-performance liquid chroma-tography (HPLC), and supercritical fluid chromatography (SFC) These often serve

as a separation method when connected to another instrument such as a massspectrometer, which serves as the detector

1.5.1.1 Gas Chromatography (GC)

GC was introduced in the 1950s and has been applied to a wide range of foods It

is applicable to volatile substances that are thermally stabile; LC and SFC are moreappropriate chromatographic methods for analysis of amino acids, peptides, sugars,and vitamins GC is useful for analysis of nonpolar compounds, although polarcompounds may be analyzed if derivatized first Isolation of the analyte from thesample matrix is particularly important in GC to avoid false responses from matrixdegradation products Headspace methods (including direct sampling of the head-space), distillation, and solvent extraction are often employed Detectors includethermal conductivity (which is nonspecific), flame ionization (for most organiccompounds), electron capture (mainly for pesticide residues), and flame photometric(for pesticides and sulfur compounds) The most common food analysis applicationsfor GC involve carbohydrates, drugs, lipids, and pesticides.8

Improvements in chromatography are constantly occurring For instance, a newapproach is comprehensive chromatography, which allows a sample to be separatedalong two independent axes Comprehensive two-dimensional gas chromatography,

GC  GC, consists of a high-resolution column with a nonpolar stationary phase,

a modulator for separating the eluate into many small fractions, and a second columnwhich is short, narrow, and polar This technique has been applied to fatty acids,flavors, and pesticides, and was reviewed by Dallüge et al.9

1.5.1.2 High-Performance Liquid Chromatography (HPLC)

HPLC was developed in the 1960s as an improvement over column liquid tography and has been used to measure nonvolatile food components Spectroscopicdetectors are often employed Normal-phase HPLC, in which the stationary phase

chroma-is a polar adsorbent and the mobile phase chroma-is a nonpolar solvent, chroma-is often used forfat-soluble vitamins and carbohydrates Reversed-phase HPLC, with a nonpolarstationary phase and polar mobile phase, is more popular because of its widerapplication Ion-exchange HPLC, with a functionalized organic resin as packingmaterial, is used for detection of inorganic ions and analysis of carbohydrates andamino acids HPLC is currently the most popular food analysis technique (GC issecond) and is most used for amino acids, carbohydrates, drugs, lipids, and proteins.8

A new application of this technique is comprehensive two-dimensional liquidchromatography  gas chromatography, LC  GC Triglycerides can first be1647_Book.book Page 5 Wednesday, March 30, 2005 11:42 AM

separated according to double bond content and then by carbon number Janssen et

al.10 demonstrated fingerprinting of olive oil, which can be applied to place of originanalysis, by separation into mono-, di-, and triglycerides as well as sterols, esters,and other compound classes

1.5.1.3 Supercritical Fluid Chromatography (SFC)

Supercritical carbon dioxide serves as the mobile phase in SFC; an open tubularcolumn or a packed column is employed as the stationary phase, and any GC or LCdetector is used Instrumentation first became available in the 1980s Smith11reviewed the history and applications of supercritical fluids, citing its use in sepa-rating lipids from food matrices as a chief advantage over other methods However,SFC is prone to operational difficulties and is a normal-phase method; reversed-phase HPLC is often viewed as preferable

Spectroscopy is based on interactions of matter with electromagnetic radiation.Interactions can take the form of absorption and emission, and can be detected byusing emission, transmission, and reflection designs Food scientists most often dealwith the ultraviolet (UV), visible (Vis), infrared (IR), radio (nuclear magnetic res-onance, NMR), and microwave (electron spin resonance, ESR) regions of the spec-trum, and use spectroscopic techniques for quantitative and qualitative analyses

1.5.2.1 UV, Vis, and Fluorescence

UV and Vis spectroscopy measure absorbed radiation and have been used in foodlaboratories for many years A food component that absorbs in the ultraviolet orvisible range may be analyzed at its characteristic wavelength in a UV-Vis spectro-photometer, as long as there are no interfering compounds

Fluorescence spectroscopy deals with emitted radiation, and can be three orders

of magnitude more sensitive than UV or Vis spectroscopy Many organic moleculesfluoresce, including bacteria and some pesticide residues, making fluorescence spec-troscopy an option for detecting food contamination

fatty acids High-pressure and high-temperature ATR cells have been developed.This technique can be enhanced by using multiple internal reflection (MIR), in which1647_Book.book Page 6 Wednesday, March 30, 2005 11:42 AM

light is bounced off the surface several times Further developments in the opticalcomponents are needed before this method can be used more extensively on foods.The newest IR technique is diffuse reflectance infrared Fourier transform (DRIFT),which measures the sum of surface-reflected light and light that has been absorbedand reemitted DRIFT has been employed recently to monitor production and detectcompounds in coffee Recent developments in IR spectroscopy of foods have beenreviewed by Wilson and Tapp.12

1.5.2.3 Raman

Raman spectroscopy is a complementary technique to IR spectroscopy IR absorptiondepends on changes in dipole moment, meaning that polar groups have strong IRresponses Raman scattering deals with changes in polarizability of functionalgroups, so nonpolar groups produce intense responses Proteins and amino acidslend themselves to Raman spectroscopy, and carbohydrates, lipids, and minor foodcomponents are also examined by this technique In addition to basic research onmolecular structure, Raman spectroscopy is now being used for industrial processcontrol Li-Chan reviewed the application of Raman spectroscopy for food analysis.13

1.5.2.4 Atomic Absorption and Atomic Emission

Atomic absorption spectroscopy (AAS) is based on absorption of UV-Vis radiation

by atomized minerals, whereas atomic emission spectroscopy (AES) uses the sion of radiation by a sample Samples must usually be ashed, dissolved in water

emis-or dilute acid, and vapemis-orized In AAS, samples are atomized by nebulizer and burner(flame AAS), or by a graphite furnace (electrothermal AAS) Electrothermal AASuses smaller samples and has much lower detection limits than flame AAS, but it ismore costly and less precise In AES, atomization and excitation can be performed

by flame or by inductively coupled plasma (ICP), where samples are heated to over

6000 K in the presence of argon Both AAS and AES measure trace metal trations in complex matrices with excellent precision and accuracy AAS is the moreestablished technique, with a wider variety of instruments available, but ICP-AEScan be used to measure more than one element in a sample and can measurecompounds that are stable at high temperatures Both AAS and AES have supplantedclassical methods for detecting minerals in food

concen-1.5.2.5 Mass Spectrometry (MS)

A mass spectrometer ionizes molecules to produce charged fragments that areseparated by size and charge MS has been used for identification and analysis ofcomplex compounds since the early 1960s The coupling of separation techniqueswith MS, which began in the 1970s, has overcome the main analytical problem withchromatographic techniques — namely, ambiguity about the identity of the analyte

MS is frequently used in combination with GC, HPLC, ICP, and capillary phoresis, and there are tandem MS-MS instruments Three new ionization techniquesused in food analysis are electrospray ionization (ESI, where multiply charged ionsare produced by repeated formation and explosion of charged droplets), heated1647_Book.book Page 7 Wednesday, March 30, 2005 11:42 AM

nebulizer-atmospheric pressure chemical ionization (HN-APCI, where a gas-phaseion-molecule reaction process allows the analyte molecules to be ionized underatmospheric pressure), and matrix-assisted laser desorption/ionization (MALDI,where a sample is crystallized in a matrix of small aromatic compounds, and thecrystal is subjected to a pulsed ultraviolet laser that fragments the molecules) MStechniques have been used to analyze the gamut of food components, includingantioxidants, aroma compounds, carbohydrates, drug residues, lipids, peptides andproteins, toxins, and vitamins A summary of developments in the use of MS in foodanalysis was published by Careri et al.14

1.5.2.6 Nuclear Magnetic Resonance (NMR) and Electron Spin

Resonance (ESR)

NMR is a spectroscopic method in which atomic nuclei that are oriented by amagnetic field absorb characteristic frequencies in the radio range ESR deals withelectrons and microwave frequencies These techniques have several advantages:they are nondestructive, do not usually require sample separation or extraction, andcan analyze the interior of a sample Drawbacks include lower sensitivity andselectivity than some other techniques NMR experiments are performed usingcontinuous wave (magnetic field held constant and oscillating frequency varied, orvice versa) or pulse (short time, large amplitude) methods; ESR uses continuouswave Available NMR instruments include low-resolution (for moisture or oil con-tent), high-resolution liquid (analysis of liquid phase), high-resolution solid (analysis

of solid phase), and magnetic resonance imaging (three-dimensional views of crosssections of foods)

Virtually any food can be analyzed by NMR and ESR NMR is often used toexamine physical properties such as melting, crystallization, polymorphism, and oilcontent, and ESR is used for detecting free radicals produced in physical andchemical processes Mannina et al summarized the principles of NMR and appliedthe technique to analyzing free acidity, fatty acid profile, and sterol, squalene, andchlorophyll content as methods of authenticating olive oil.15

1.5.2.7 Other Spectroscopic Techniques

Consumers rely on color, flavor, odor, and texture to determine the quality of food.Colorimeters are used to qualitate and quantitate food color, with measurementsbased on hue, lightness, and saturation, and are often used in conjunction withsensory and shelf-life studies A digital camera and computer graphics software haverecently been applied to the analysis of surface color of food.16

Refractometry is based on the change in velocity of light by the analyte tive index measurements are useful in determining concentrations of beverages,sauces, and other liquid foods HPLC instruments sometimes have refractometerdetectors

Refrac-Polarimetry is the study of the rotation of polarized light by optically activesubstances Polarimetry is used to distinguish optical isomers, identify and charac-terize optically active substances, and measure their change in concentration during1647_Book.book Page 8 Wednesday, March 30, 2005 11:42 AM

1.5.3.1 Electrochemical

The most common electrochemical technique is the familiar pH electrode An native to AAS and AES is the ion-selective electrode, which is sensitive to a particularion This technique is simple, rapid, and relatively inexpensive However, theseelectrodes are not ion-specific, as there may be interference from ions other thanthose being examined

alter-1.5.3.2 Electrophoresis

The basis for gel electrophoresis, developed in the 1950s, is the separation of chargedmolecules when an electric field is applied The main types of electrophoresis arenondenaturing, where separation is according to charge, shape, and size; denaturing

or sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE), wherethe separation is primarily by molecular weight; isoelectric focusing, which separates

by charge; and two-dimensional, with separations in perpendicular directions byisoelectric focusing and SDS-PAGE The analysis is carried out on a porous gel and

is mainly used for studying nucleic acids and proteins

Capillary electrophoresis (CE), developed in the 1980s, uses a capillary tubeand photometric detection CE techniques include capillary zone electrophoresis,for charged analytes, and micellar electrokinetic chromatography, for neutral ana-lytes CE has been applied to analysis of amino acids, carbohydrates, proteins, andvitamins, as well as additives, natural toxins, and antibiotic and pesticide residues.Detection limits are relatively high, however, because of the low sample volume.Dong18 reviewed CE in the analysis of food

1.5.3.3 Flavor and Odor

No food will be eaten if its aroma and flavor are unacceptable, so characterizingthese attributes is important to the food industry Sensory panels are often used, butsince they rely on human judgment, instrumental techniques are being developed.Some 7000 aroma compounds have been identified by GC-MS The sensory char-acter of individual aroma compounds is often investigated by gas chromatography-olfactometry (GC-O), developed in the 1970s, where analysts sniff compounds as1647_Book.book Page 9 Wednesday, March 30, 2005 11:42 AM

they elute from a GC Atmospheric pressure ionization-mass spectroscopy MS) measures the concentration of volatiles as they are being inhaled, providinginformation on flavor release New advances in these areas were described by Rischand Ho,19 and Marsili20 covered sample preparation, instrumental techniques, andapplications One challenge to be overcome in characterizing flavors and odors isthat individual components are analyzed separate from the food matrix, and thereforeout of context

(API-1.5.3.4 Particle Analysis

Many processed foods contain particles produced by drying, grinding, milling, orother means Particle appearance and shape are examined by the optical microscope,and size uniformity is measured by particle sizing instruments based on principlessuch as laser diffraction and light scattering.21

1.5.3.5 Rheology and Texture

Rheology is the study of the flow and deformation of matter, and texture deals with

a consumer’s perception of rheology Rheology is a factor in food process ing, shelf-life testing, and quality control Food exhibits both elastic and viscousbehavior, which can be measured by viscometric, oscillatory shear, compression,extension, torsion, and other tests Bourne22 described rheological and textural mea-surement of food

engineer-1.5.3.6 Structure

Food structure is studied by light microscopy, scanning electron microscopy (SEM),transmission electron microscopy (TEM), and confocal laser scanning microscopy(CLSM) Light microscopy, with up to 2000 magnification, is used to surveystructural details Surface microstructure is examined through SEM, and internalstructures are visualized by TEM CLSM, which requires less sample preparation,

is used to obtain three-dimensional images Kalab23 maintains a Web site devoted

to food microscopy

1.5.3.7 Thermal Properties

Thermal transitions in food such as melting, decomposition, and glass transitionsare observed by using a differential scanning calorimeter, in which a sample is heatedand the amount of heat absorbed relative to a reference is measured The techniquehas been applied to components such as proteins, starches, and sugars, and isespecially useful for observing the melting of lipids, which have relatively high heats

of fusion Applications of thermal analysis in food have been reviewed by Harwalkarand Ma.24

Bomb calorimeters are used to determine the caloric value of a food by busting it in an oxygen atmosphere and measuring the temperature change in the1647_Book.book Page 10 Wednesday, March 30, 2005 11:42 AM

surrounding water However, many manufacturers obtain caloric values by simplecalculation, using percentages of each ingredient and caloric values for fat, carbo-hydrate, and protein

1.5.4.1 Enzyme and Microbial Sensors

Biosensors consist of a biological recognition element that produces a quantifiableresponse in a signal transduction element when in contact with the analyte Enzymebiosensors use enzymes to generate products that are detected by acoustic, electro-chemical, optical, and photothermal transduction elements Microbial biosensors usegenetically modified microorganisms that are immobilized on a membrane or trapped

in a matrix, with the transduction mechanism consisting of an oxygen or pH trode, or a luminometer if luciferin is added A popular type of optical elementdeveloped in the 1990s is surface plasmon resonance

elec-These types of biosensors are often applied to detection of contaminants such

as herbicides, pesticides, pathogens, and toxins, as well as food components such

as carbohydrates and amino acids Improvements in response time, sensitivity, andspecificity are needed for wider acceptance of this technique Recent reviews byPatel25 and Mello and Kabota26 describe biosensors and their suitability in foodanalysis

1.5.4.2 Immunosensors

Immunosensors are biosensors in which the biological recognition elements areantibodies that are attached to a solid support and bind to a particular antigen orantibody in the sample The most common immunoassay is enzyme-linked immu-nosorbent assay (ELISA), in which an enzyme-linked antibody is applied after theantigen or antibody is bound A substrate is then added to produce a secondaryreaction that has a colored product that is measured spectroscopically The anti-body/antigen interaction is specific enough to allow detection of species of origin,and it is also used to detect allergens, enzymatic inactivation, genetically modifiedorganisms, microbial contamination, and toxins

1.6 SUMMARY

The analytical techniques now available to food researchers provide faster results atlower cost with lower solvent and reagent use and higher precision and accuracythan classical methods Choosing the appropriate method requires the scientist to

be aware of its strengths and limitations When the technique is successfully applied,

a wealth of information on composition, properties, and structure of food and foodcomponents can be uncovered

1647_Book.book Page 11 Wednesday, March 30, 2005 11:42 AM

REFERENCES

1 Buldini, P L., Ricci, R., and Sharma, J L 2002 Recent applications of sample

preparation techniques in food analysis J Chromatogr A 975:47–70.

2 Smith, R M 2003 Before the injection — modern methods of sample preparation

for separation techniques J Chromatogr A 1000:3–27.

3. Official Methods of Analysis of AOAC International 17th ed 2003 AOAC

Interna-tional: Gaithersburg, MD.

4. Approved Methods of the AACC 10th ed 2001 American Association of Cereal

Chemists: St Paul, MN.

5. Official Methods and Recommended Practices of the AOCS. 5th ed 1997 American

Oil Chemists’ Society: Champaign, IL.

6. Food Chemical Codex. 5th ed 2004 National Academy Press: Washington, D.C.

7 Wood, R 1999 How to validate analytical methods Trends Anal Chem 18:624–632.

8 Lehotay, S.J., Hajülov, J 2002 Application of gas chromatography in food analysis.

Trends Anal Chem 21:686–697.

9 Dallüge, J., Beens, J., and Brinkman, U.A.T 2003 Comprehensive two-dimensional

gas chromatography: A powerful and versatile analytical tool J Chromatogr A

1000:69–108.

10 Janssen, H G., Boers, W., Steenbergen, H., Horsten, R., Flöter, E 2003

Compre-hensive two-dimensional liquid chromatography  gas chromatography: Evaluation

of the applicability for the analysis of edible oils and fats J Chromatogr A

1000:385–400.

11 Smith, R M 1999 Supercritical fluids in separation science — the dreams, the reality,

and the future J Chromatogr A 856:83–115.

12 Wilson, R H., Tapp, H S 1999 Mid-infrared spectroscopy for food analysis: Recent

new applications and relevant developments in sample presentation methods Trends

Anal Chem 18:85–93.

13 Li-Chan, E C Y 1996 The applications of Raman spectroscopy in food science.

Trends Food Sci Technol. 17:361–370.

14 Careri, M., Bianchi, F Corradini, C 2002 Recent advances in the application of

mass spectrometry in food-related analysis J Chromatogr A 970:3–64.

15 Mannina, L., Sobalev, A P., Segre, A 2003 Olive oil as seen by NMR and

chemo-metrics Spectrosc Europe 15(2):6–14.

16 Yam, K L., Papadakis, S E 2003 A simple digital imaging method for measuring

and analyzing color of food surfaces J Food Eng. 61:137–142.

17 Coupland, J N., Saggin, R 2003 Ultrasonic sensors for the food industry Adv Food

Nutr Res. 45:101–166.

18 Dong, Y 1999 Capillary electrophoresis in food analysis Trends Food Sci Technol.

10:87–93.

19 Risch, S J., Ho, C.-T 2000 Flavor Chemistry: Industrial and Academic Research.

American Chemical Society: Washington, D.C.

20 Marsili, M 2001 Flavor, Fragrance and Odor Analysis. Marcel Dekker: New York.

21 Duke, S D 2003 Setting up a particle analysis laboratory: An overview Am Lab.

35(16):12–14.

22 Bourne, M C 2002 Food Texture and Viscosity: Concept and Measurement

Aca-demic Press: New York.

23 Kalab, M 2002 Foods Under the Microscope web site http://anka.livstek.lth.se:2080/

microscopy/foodmicr.htm

24 Harwalkar, V R., Ma, Y C 1990 Thermal Analysis of Foods. Elsevier: London.

1647_Book.book Page 12 Wednesday, March 30, 2005 11:42 AM

25 Patel, P D 2002 (Bio)sensors for measurement of analytes implicated in food safety:

A review Trends Anal Chem 21:96–115.

26 Mello, L D., Kabota, L T 2002 Review of the use of biosensors as analytical tools

in the food and drink industries Food Chem 77:237–256.

1647_Book.book Page 13 Wednesday, March 30, 2005 11:42 AM

2 Statistical Assessment of Results of Food Analysis

2.2.6 Reporting Uncertainty2.3 Accuracy and Bias

2.3.1 Definitions2.3.2 Determination of Accuracy2.3.3 Significance of Difference in Means2.4 Calibration

2.4.1 Classical Calibration2.4.2 Inverse Calibration2.4.3 Error Analysis2.4.4 Confidence IntervalsAcknowledgments

References

2.1 INTRODUCTION

Most analytical techniques aim to obtain a measurement — such as from tography or spectroscopy — and relate this measurement to the concentration of acompound in a material such as food There are two principal needs for statisticalmethods The first is determining how well the concentration of a single sample can

chroma-be estimated in a laboratory This may, for example, chroma-be a reference sample using astandard method of analysis, and it may be important to compare this againstpublished data or with other laboratories A second need arises during calibrationwhen establishing a new method, using a series of standards of different concentra-tions to develop an analytical technique that will be employed to estimate the1647_Book.book Page 15 Wednesday, March 30, 2005 11:42 AM

Uncertainty is influenced by three main factors The first is measurement error Mostmeasurements consist of several steps For example, extraction, weighing, dilution,and then recording an instrumental response Each step involves errors If a 100 mLvolumetric flask is used, the amount of solvent is not always exactly 100 mL; there

is a range of flasks dependent on the manufacturing process and one flask may have

a volume of 99.93 mL, the next 100.21 mL, and so on In addition, the volumeswill depend on temperature as well as on the skill and consistency of the analyst.Thus, the amount of liquid measured will form a distribution: the wider the distri-bution, the greater the uncertainty

The second class of factors relates to sampling error; for example, if we want

to determine the amount of additive in a food, each sample may be slightly different,because it is not evenly distributed In addition, the production process will notalways result in products that are identical in composition This is especially impor-tant if the source of material varies — for example, according to time of year,cultivation, geography, genetic makeup — and for plant material, even what time

of day the plant was harvested

The third class relates to calibration error This may arise, for example, frombias in the calibration model Although the replicate measurements on a sample may

be very similar, and the sampling may be performed well, there may be problemswith the original calibration, adding an extra source of error

Measurement error will always be present The importance of sampling errordepends on how broad a question we want to answer In some cases the mainobjective is to determine the level of a component in a specific batch or sample from

a discrete origin; in other cases, we might pose a broader question — for example,the amount of tannin in a commercial brand of tea The more generic the question,the greater the uncertainty

The experimentally estimated value of a concentration, c, relates to the intrinsicvalue in absence of measurement error, , by%c

1647_Book.book Page 16 Wednesday, March 30, 2005 11:42 AM

(2.1)

where the e terms are called error terms

Each of the measurement and sampling error terms in themselves form a bution, and they originate from several different sources In practice, the error termsare sums of several distinct distributions, but an important theorem states that thesums of different symmetric distributions normally approximate to what is described

distri-as a normal distribution,5 characterized by a mean and standard deviation The largerthe standard deviation, the larger the uncertainty

Sufficient replicates should be performed to provide a good estimate of thestandard deviation of the measurements If, for example, we measure 100 replicates,and the true standard deviation is 0.136 mg/kg, it is quite likely we will obtain agood estimate of this value If only five replicates are measured, the value of thestandard deviation may be seriously in error There are methods for overcoming thisproblem, but they are a bit complex, and it is easiest to use a large number ofreplicates

where c i is the ith value of the measured concentration, and the mean This isalso sometimes called the precision This step may be at any stage of the procedure;for example, it may involve weighing, dilution, recording spectra, or sampling Thisvalue is the experimental estimate of the precision, u j, of each step

The overall precision can be calculated by

(2.3)

For some steps, such as calibration, it is not always possible to measure thevalue of u j by replication, but alternatives such as mean square calibration errorscan be used instead

Normally, the individual uncertainties are expressed in percentage terms; forexample, a volumetric flask may have an uncertainty of 2%, and balance of 1%, anextraction procedure of 5% and so on Hence, if there are five factors, with uncer-tainties of 8, 1, 3, 11, and 4%,

= 0.145 or 14.5% (2.4)

If the intrinsic or true concentration of a compound in a food is 32.61 mg/kg,then a 14.5% uncertainty corresponds to a precision of 4.74 mg/kg Note that if weneglect the two smallest sources of uncertainty, the overall uncertainty changes only

by 0.3 to 14.2%, despite the fact that their levels are 1 and 3%, respectively Thismeans that it is fairly safe to neglect these sources and so we will get satisfactoryanswers by replicating just three of the five factors

Sometimes it is not necessary to determine all the uncertainties experimentally,

as these are often provided either as a standard reference or by the manufacturer.For example, it may be specified that 95% of 100 mL volumetric flasks from a givenmanufacturer are certified within 0.6 mL This means that the volume of 95% ofthe flasks is between 99.4 and 100.6 mL To convert from this to an uncertainty, it

is usual to use the normal distribution, in which it is expected that 95% of allmeasurements are within 1.96 standard deviations of the mean, so that 0.4 mL isequivalent to 1.96 times the uncertainty, meaning that u
0.6/1.96
0.306 mL.Sometimes manufacturers quote a range instead; for example, a 5 mL pipettemay have a minimum volume of 4.92 mL and a maximum of 5.08 mL It is usual

to divide this range by 3 to provide an estimate of the standard deviation, whichthen allows uncertainties to be calculated in the normal manner

Note that in order for these calculations to have meaning, the method of analysismust be similar in all cases — for example, using a balance, volumetric, measuringcylinder, and instrumental conditions that are identical If the levels of concentrations

in a sample vary substantially, this is not always possible, so it may be necessary toconcentrate or dilute samples prior to analysis to obtain comparable results Alter-natively, one could calculate different uncertainties according to the concentration

The concept of confidence is closely related to that of uncertainty (see The NISTReference on Constants, Units, and Uncertainty8 and Chapter 2 of Miller andMiller9) Assuming a normal distribution, we can compute this from the secondcolumn of Table 2.1 If the number of samples used to calculate the uncertainty islarge, then this implies that 50% of samples are within 0.674 standard deviations ofthe mean, or one in two samples are expected to fall within this region and 95% or

19 out of 20 within 1.960 standard deviations of the mean Because the uncertaintyequals the standard deviation, if, for example, the uncertainty of an analysis is 3.2%,then, if the experimental measurement of a concentration is 56.3 mg/kg, the uncer-tainty is 1.80 mg/kg and so we are 95% confident that the true value is between52.77 and 59.83 mg/kg

Sometimes the error standard deviation is measured on a small number ofsamples The t-distribution corrects for this For the normal distribution, it is assumedthat there are a large number of degrees of freedom for determination of the standarddeviation If there are fewer samples, then the number of degrees of freedom equalsone less than the number of samples, so if we use 11 samples for determination ofthe uncertainty, there will be 10 degrees of freedom The resultant measurements

TABLE 2.1 Number of Standard Deviations Away from the Mean Required to Obtain a Given Confidence Level

do not exactly form a normal distribution, and it is usual to use a t-distribution Theright-hand columns of Table 2.1 represent the equivalent number of standard devi-ations away from the mean when sample sizes are restricted So, if only 11 samplesare used to determine uncertainty, 95% of samples will lie within 2.228 rather than1.960 standard deviations of the experimentally determined mean In many practicalsituations it is acceptable to use a smaller sample size, such as, if the main objective

is to see whether a compound is likely to exceed a given limit, rather than to provide

an exact measurement of concentration

Uncertainty can be reported in various ways The simplest is to state, for example,that the uncertainty of a batch of 5 mL volumetric flasks is 0.32 mL; this impliesthat the standard deviation of their volumes is 0.32 mL

More usually, uncertainty is reported by using a range; for example, the estimate

of the concentration of compound is reported as 86.69 ± 3.27 mg/kg The number3.27 is recommended to be twice the uncertainty It is said that the “coverage factor”

is 2, and so we report the concentration as being c ± 2 u. This corresponds toapproximately 95% confidence in the analysis

2.3 ACCURACY AND BIAS

Accuracy relates to how close a result is to the true result (see Chapter 1 of TheNIST Reference on Constants, Units, and Uncertainty9 and Chapter 2 of Caulcuttand Boddy11) For example, if a true concentration is 103.24 mg/kg and the measuredconcentration 105.61 mg/kg, there is a 2.37 mg/kg inaccuracy in the measurementprocess The closer the measured concentration (which is usually the average ofseveral individual measurements) is to the true concentration, the more accurate it

is Accuracy is different from precision or uncertainty in that the latter measures thespread of results, whereas the former how well the result agrees with the true value.Sometimes a measurement process can be precise but not accurate; for example,

a balance might be poorly calibrated, so although the results of replicate analysesmight appear quite similar, in fact they are all in error by a given amount This type

of error is often called bias

1647_Book.book Page 20 Wednesday, March 30, 2005 11:42 AM

In all cases it is recommended that several replicated measurements be performed

on the material, so in each case a mean and standard deviation of the measuredquantity, such as a concentration, is obtained

The main statistical technique consists of asking whether a mean measurement fromone source (e.g., laboratory A) is significantly different from that from another source(e.g., laboratory B) In order to determine this value, we compare the differencebetween the means from both sources to their standard deviations If the meanmeasurements are many standard deviations apart, then the difference between means

is significant, and we can state that there is bias in one of the procedures relative tothe other

To do this, the first step is to calculate the pooled standard of the two procedures,defined by

(2.6)

where s A is the standard deviation obtained from procedure A, and I A the ing number of samples This is an average standard deviation for the two procedures.The next step is to compare the means and calculate what is called a t-statistic,defined by

correspond-(2.7)

which is normally presented as a positive number, so procedure A is the one thatresults in a higher average concentration estimate The larger this number, the morelikely it is that the two procedures differ

Consider an example as follows For Reference Procedure A, we record 50measurements, with a mean of 12.1 and a standard deviation of 1.8 For Laboratory Procedure B, we record 10 measurements, with a mean of 10.4 and a standarddeviation of 2.1 The t-statistic is 2.65

The final step is to convert this into a significance value In order to do this it

is necessary to know the number of degrees of freedom, which in this case equals

49  9 or 58, and look at the probability value of the what is called t-statistic (seeChapter 3 of The NIST Reference on Constants, Units, and Uncertainty,9 AppendixA.3 of Brereton,10 and Chapter 4 of Caulcutt and Boddy11) The higher the t-statistic,the lower the chance that the difference of means could occur by chance, and so themore likely it is that there is a real difference between means Many traditionalstatistical texts present critical values of this statistic in tabular form, so we candetermine whether, for example, the likelihood this occurs by chance is less than

10, 5, or 1% When using these tables, be sure to use the two-tailed distribution if

the question being asked is whether Procedure B differs significantly from Procedure

A, because a mean that is either higher or lower than the reference is equally

significant However, it is not always necessary to use these tables, and values can

be obtained using common packages such as Excel In order to do this for the

example above, type the function TDIST(2.65,58,2), where the first number

repre-sents the t-value, the second the total number of degrees of freedom, and the third

that the test is two tailed We find, in this case, the probability is 0.010, so we can

be 99% sure that there is a significant difference between the means, and so the two

procedures are really quite different

2.4 CALIBRATION

Calibration is an important procedure in analytical chemistry.12,13 It involves forming

a mathematical relationship, or model, between concentration and a measured

vari-able such as a chromatographic peak area or a spectroscopic absorbance This model

is first developed using a series of standards of known concentration, and then, in

a separate step, used to predict the concentration of unknowns

There are several ways in which a calibration model can be formed between

con-centration (c) and an analytical response (x) The traditional approach is to employ

so-called classical calibration (see Chapter 5 of Brereton10 and Chapter 3 of Martens

and Maes14), where we obtain a model of the form

(2.8)or

(2.9)

where the latter includes the intercept, and may be useful, for example, when there

are baseline problems The “^” over the x means that this is the predicted rather

than the experimentally observed value The equation for determining the value of

a1 without the intercept is quite simple and given by

i i i I

i i

where the “–” over the numbers refers to the mean.

For the data set of Table 2.2, the best fit equations are or

Some analytical chemists favor inverse calibration In classical calibration, it is

assumed that all the errors are in x or the response, and none in the c or concentration

values If the calibration is from a well-established reference standard, this may be

true, but if the calibration standards are prepared in a laboratory, there are often

sample preparation errors that in some cases can be more significant than the

instrumental measurement errors This is especially true for modern instrumentation,

which is quite reproducible compared to several years ago In such cases, an inverse

regression equation of the form

(2.12)or

TABLE 2.2 Sample Data for Univariate Calibration

i i I

(2.13)

is fitted to the data For the data set of Table 2.2, the best fit equations are

or Note that the values of the coefficients forthe classical and inverse models are only approximately related; for example, the

inverse of the coefficient for the single-parameter classical model is 0.3882 as

compared to 0.3847 for the inverse model This is because each model rests on

different assumptions about errors

A good rule of thumb is to determine both models and see whether they give

comparable predictions If they do not, there are probably samples that are outliers,

perhaps samples prepared in error, which have undue influence on the calibration

and should be eliminated

Below we will illustrate calculations using classical calibration models

It is important to have an idea of how precise the instrumental calibration is, and so

how well we can predict concentrations from the analytical method

A second issue is to determine how well a calibration model is obeyed This

tells whether there is really a linear relationship between analyte concentration and

response Sometimes, the relationship is nonlinear The most common problems are

if the concentration is too high, so the detector is overloaded, or too low, so the

signal is dominated by noise Normally there are concentration ranges within which

the relationship is expected to be linear In order to achieve these, it is sometimes

necessary to dilute or concentrate samples, or to change instrumental conditions

such as injection volumes

There are a large number of approaches for studying the goodness of fit to

calibration models, ranging from the graphical to the statistical In most cases, the

first step is to predict the value of x from c using the best-fit model The residuals

are calculated by

(2.14)One of the simplest approaches is to represent these graphically For the data of

Table 2.2, and a two-parameter classical model, the residuals are represented in

Figure 2.1 Such graphs can be used to spot if there are obvious difficulties — for

example, an outlier, which may have a very large residual, or heteroscedasticity, in

which case the residuals may change in magnitude as the concentration increases

If it appears that there is no significant trend in the residuals, the next step is

normally to calculate a root mean square error, given by

where there are P parameters in the model, and I samples, so that in our case I 

P
10  2 or 8 and the error
1.0229 for the two-parameter classical model.

This error can be reported as a percentage of the mean (11.19%) of the data, andcan be used as an indication of the average uncertainty of the measurements, and

so whether the technique is acceptable or not

A second aim is to determine how well the underlying model is obeyed (seeChapter 2 of Brereton10) In order to do this, it is usual to compare the replicate orexperimental error to the lack of fit to the linear model Provided there are sufficientreplicates in the calibration, it is possible to obtain this information quite easily Inour example, we performed four replicates, at concentrations 1, 3, 4, and 6 mmol/L.Note that having only four replicates will give us a rough idea of the experimentaluncertainty and should be used for guidance only; if it is important to achieve amore accurate estimate (e.g., for regulatory purposes), many more replicates arerequired

In order to perform this calculation, we need to calculate the average response

at each concentration level,

At 1 mmol/L, this is 3.540, the average of the two values 3.803 and 3.276 At

2 mmol/L, there is only one measured response, so the average is simply the value

at that concentration The total sum of square replicate error is defined by

(2.16)

equaling 5.665 in this example

FIGURE 2.1 Residual plot of the data of Table 2.2, after fitting to a two-parameter classical model.

However, the total sum of square residual error is given by

square error For the replicate error, the number of degrees of freedom, R, equals

the number of replicates, or 4 in this case For the lack of fit, the number of degrees

of freedom equals the number of experiments minus the number of parameters inthe model minus the number of replicates, or

equaling 10  2  4
4 in the case of the two-parameter classical model We then

calculate a statistic called the F-ratio

or 0.478 Since the average lack-of-fit is less than the replicate error, it is notsignificant; this means that there is no evidence to say that the model is incorrectand so we can assume that the method is good enough to provide a linear relationship

If the average lack-of-fit is larger than the replicate error, it can be assessed using

an F-test (see Appendix A.3 of Brereton10), and the confidence that there is a linearrelationship expressed as a probability

calibration limits; if the procedure we employ results in a predicted concentration

of 18 mmol/L, what is the uncertainty of this prediction? There may be a 95%confidence limit that the true concentration is between 14 and 22 mmol/L; thisprovides us with some information about the sample

There are several different equations, but a common one is to calculate

= (2.21)

as the limits Some of the terms in this equation require explanation The term s is the total root mean square error, in our example 1.0229 The value of t depends on

the number of degrees of freedom for the overall model, which equals the number

of experiments minus the number of parameters or 10  2 or 8 in our case, and theconfidence limits It is most usual to determine 95% confidence for the predictions;this means that we would expect 19 of 20 measurements to be within the computed

limits To obtain this value, we use a two-tailed t-distribution at 5% confidence

because we want both positive and negative bounds; in Excel we can use the functionTINV(0.05,8) for this purpose, the first parameter providing the percentage confi-dence, and the second the number of degrees of freedom, giving a value of 2.306

The value of I is the number of samples in the calibration, and r relates to the number

of replicates for a specific measurement If we are determining the concentrationfrom a single replicate, this is equal to 1; however, sometimes we determine the

concentration by averaging several (r) replicates.

The calculation is illustrated in Table 2.3 for both 95 and 50% confidence limitsusing individual rather than average replicate values at each concentration As thepercentage decreases, the limits get narrower It can be seen that in our example, allsamples are predicted within the 95% limit, but 4 of the 10 are outside the 50%

limit; for example, the observed value of x for the fourth sample is 6.948, but the

50% confidence limits for a concentration of 3 mmol/L are 7.160 and 8.681, so it

is below the lowest 50% limit We would expect roughly half the samples to beoutside the 50% confidence limit, although on a small data set this prediction willnot be obeyed exactly; however, the results are promising in this example The fullcalibration line together with confidence limits can be presented graphically, as inFigure 2.2 The graphical representation is useful because it is possible to spotwhether there are any obvious outliers or trends A similar calculation then can beused to determine uncertainties of estimates in concentrations for unknown samples

ˆx l±

1 Natrella M G., Experimental Statistics, NBS Handbook 91, Revised Edition, U.S.

Dept of Commerce, Washington, D.C 1966.

TABLE 2.3

95 and 50% Confidence Limits for the Prediction of x from c Using a

Two-Parameter Classical Model

2 Tobias P., Croarkin C., eds., NIST/SEMATECH Engineering Statistics Internet book, National Institute of Standards and Technology, U.S Dept of Commerce, Washington, D.C., found at http://www.itl.nist.gov/div898/handbook/.

Hand-3 Ellison S., Wegscheider W., Williams A., Measurement Uncertainty, Anal Chem., 69,

607A, 1997.

4 Guide to the Expression of Uncertainty in Measurement, International Organisation

for Standardisation, Geneva, 1993.

5 Miller J C., Miller J N., Basic Statistical Methods for Analytical Chemistry, Part 1.

Statistics of Repeat Measurements, Analyst, 113, 1351, 1988.

6 Ellison S L R., Rosslein M., Williams A., Quantifying Uncertainty in Analytical Measurement, Eurachem/CITAC Guide, 2000, found at http://www.eurachem.ul.pt/ guides/QUAM2000-1.pdf.

7 Eurachem, Quantifying Uncertainty in Analytical Measurement, found at http:// www.measurementuncertainty.org/mu/guide/index.html.

8 The NIST Reference on Constants, Units, and Uncertainty, found at ics.nist.gov/cuu/Uncertainty/.

http://phys-9 Miller J C., Miller J N., Statistics for Analytical Chemistry, Third Edition, Prentice

Hall, New York, 1993.

10 Brereton R G., Chemometrics: Data Analysis for the Laboratory and Chemical Plant,

Wiley, Chichester, 2003.

11 Caulcutt R., Boddy R., Statistics for Analytical Chemists, Chapman and Hall, 1995.

12 Coleman D., Vanatta L., American Laboratory, 35, 18, 2003.

13 Miller J N., Basic Statistical Methods for Analytical Chemistry, Part 2 Calibration

and Regression Methods, Analyst, 116, 3, 1991.

14 Martens H., Naes T., Multivariate Calibration, Wiley, Chichester, 1989.

15 Coleman D., Vanatta L., American Laboratory, 35, 60, 2003.