Methods of Analysis of Food Components and Additives - Chemical and Functional Properties of Food Components Series

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(2) Methods of Analysis of Food Components and Additives.

(3) Chemical and Functional Properties of Food Components Series SERIES EDITOR. Zdzislaw E. Sikorski 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 Lipids Edited by Zdzislaw E. Sikorski and Anna Kolakowska. Chemical and Functional Properties of Food Saccharides Edited by Piotr Tomasik. Toxins in Food. Edited by Waldemar M. Dabrowski and Zdzislaw E. Sikorski. Methods of Analysis of Food Components and Additives Edited by Semih Ötles,.

(4) Methods of Analysis of Food Components and Additives EDITED BY. Semih Ötles, Ege University Department of Food Engineering Izmir, Turkey. 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..

(5) 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. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe.. Library of Congress Cataloging-in-Publication Data Catalog record is available from the Library of Congress. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com Taylor & Francis Group is the Academic Division of T&F Informa plc.. and the CRC Press Web site at http://www.crcpress.com.

(6) Preface The ability to accurately separate, identify, and analyze nutrients, additives, and toxicological compounds found in food and food products has become critically important in recent decades, as knowledge of and interest in the relationships between diet and health have increased. This requires training students and analysts in the proper application of the best methods, as well as improving, developing, or adapting 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 accessible descriptions of methods of analysis of food components and additives. Ranging from chemical analysis of food components and additives to infrared (IR), nuclear magnetic resonance (NMR), Fourier transform Raman (FTR), capillary electrophoresis (CE), high-performance liquid chromatography (HPLC), gas chromatography (GC), mass spectrometry (MS), and more. The book provides first-hand explanations of modern methods, contributed by 24 leading scientists, many of whom actually developed or refined the techniques, and presents new documented information on standard methods of analysis of food components and additives in a uniform format and in a style that can be understood by a reader who is not familiar with the analysis of each component. Each chapter is structured to provide a description of the information about the component or additive that can be analyzed, a simple method explanation of how it works, examples of applications, and references for more detailed information. This format also facilitates comparison of methods of analysis of each component. The use of different authors to cover a broad spectrum of methods resulted in some differences of style, but overall the book achieves its goal The first chapter, “Selection of Techniques Used in Food Analysis,” covers topics relevant to all techniques, including sample preparation, quantitative measurements, and information management, and concentrates on what goals can be achieved by applying different techniques for various purposes in food analysis. The second chapter, “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 complete than those found in most introductory analysis textbooks. The remaining 14 chapters address the major areas of analysis of food components and additives: analysis of drinking waters, proteins, peptides, amino acids, carbohydrates, food lipids, metals and trace elements in foods, vitamins, carotenoids, chlorophylls, food polyphenols, aroma compounds, food volatiles, sensory analysis of foods and determination of food allergens, genetically modified components, pesticide residues, pollutants in foods, chemical preservatives in foods, radioactive contaminants in foods, and rapid analysis techniques in food microbiology. In most chapters, many examples of.

(7) applications of methods to analytical problems are provided. The references provided in these chapters can be highly useful and valuable for those seeking additional information. This comprehensive book should serve as a reference for scientists, analytical chemists, engineers, researchers, food manufacturers, personnel from government agencies, standards writing bodies, students majoring in various science disciplines (biology, biochemistry, chemistry, environmental science, engineering, and food chemistry, 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..

(8) 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 Ege University in 1985, he received an M.S. in food chemistry, and in 1989, after completing 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, he completed postdoctoral training, including an OECD postdoctoral fellowship, at the Research Center Melle at Ghent University, Belgium. Afterward, Dr. Ötles¸ joined the Department of Food Engineering at Ege University as a scientist of food chemistry, being promoted to associate professor in 1993 and to professor in 2000. During 1996–1998 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 instrumental analysis of food compounds: he began a series of projects on the separation and analysis techniques of high-performance liquid chromatography (HPLC), first for analysis 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 are multiresidue analysis of various foods, and n-3 fatty acids in fish oils. Professor Ötles¸ is the author or coauthor of more than 150 publications (technical papers, book chapters, and books) and a presenter of seminars. He is a member of several scientific societies, associations, and organizations, including the Asian Pacific Organization for Cancer Prevention (APOCP) and the International Society of Food Physicists (ISFP). He is a member of the steering committee of APOCP’s local scientific bureau and is the Turkish representative of ISFP, and has organized international 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 Information 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..

(9) Acknowledgments 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., Technomic Publishing, Lancaster/Basel, chap. 4, pp. 57–112, 2001. Figure 11.3: Orlandi, P.A. et al., Analysis of flour and food samples for Cry9C from bioengineered corn, J. Food Prot., 65, 426, 2002. Figure 11.4: Raybourne, R.B. et al., Development and use of an ELISA test to detect IgE antibody to Cry9c following exposure to bioengineered corn, Int. Arch. Allergy Immunol., 132(4), 322, 2003..

(10) Contributors Aldert A. Bergwerff Utrecht University Utrecht, The Netherlands Marek Biziuk Gdansk University of Technology Gdansk, Poland Richard Brereton University of Bristol Bristol, United Kingdom Stephen G. Capar 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 Yildiz Karaibrahimoglu U.S. Department of Agriculture Wyndmoor, Pennsylvania. Jae Hwan Lee Department of Food Science and Technology Seoul National University of Technology Seoul, Korea Steven J. Lehotay U.S. Department of Agriculture Wyndmoor, Pennsylvania Dan Levy U.S. Food and Drug Administration Laurel, Maryland Kannapon Lopetcharat Unilever Corporation Edgewater, New Jersey Katerina Mastovska U.S. Department of Agriculture Wyndmoor, Pennsylvania Mina McDaniel Oregon State University Corvallis, Oregon. Edward Kolakowski Agricultural University of Szczecin Szczecin, Poland. Malgorzata Michalska Institute of Maritime and Tropical Medicine Gdynia, Poland. Keith A. Lampel U.S. Food and Drug Administration Laurel, Maryland. Robert A. Moreau U.S. Department of Agriculture Wyndmoor, Pennsylvania.

(11) Marian Naczk St. Francis Xavier University Antigonish, Nova Scotia, Canada. Andras Szabo Szent Istvan University Budapest, Hungary. Palmer A. Orlandi U.S. Food and Drug Administration Laurel, Maryland. Piotr Szefer Medical University of Gdansk Gdansk, Poland. Semih Ötles¸ Ege University Izmir, Turkey. Sandor Tarjan National Food Control Institute Budapest, Hungary. Richard B. Raybourne U.S. Food and Drug Administration Laurel, Maryland. Mary W. Trucksess U.S. Food and Drug Administration Laurel, Maryland. Adriaan Ruiter Wageningen Agricultural University Bilthoven, The Netherlands. Michael H. Tunick U.S. Department of Agriculture Wyndmoor, Pennsylvania. Steven J. Schwartz Ohio State University Columbus, Ohio. Carmen D. Westphal U.S. Food and Drug Administration Laurel, Maryland. Fereidoon Shahidi Memorial University of Newfoundland St. John’s, Newfoundland, Canada. Kristina M. Williams U.S. Food and Drug Administration Laurel, Maryland.

(12) Contents Chapter 1 Selection of Techniques Used in Food Analysis ......................................................1 Michael H. Tunick Chapter 2 Statistical Assessment of Results of Food Analysis ...............................................15 Richard Brereton Chapter 3 Analysis of Drinking Water.....................................................................................31 ⁄ Marek Biziuk and Malgorzata Michalska Chapter 4 Analysis of Proteins, Peptides, and Amino Acids in Foods ...................................59 Edward Kolakowski Chapter 5 Extraction and Analysis of Food Lipids .................................................................97 Robert A. Moreau Chapter 6 Determination and Speciation of Trace Elements in Foods .................................111 Stephen G. Capar and Piotr Szefer Chapter 7 Analysis of Vitamins for the Health, Pharmaceutical, and Food Sciences ..........159 Semih Ötles¸ and Yildiz Karaibrahimoglu Chapter 8 Analysis of Carotenoids and Chlorophylls in Foods............................................179 Jae Hwan Lee and Steven J. Schwartz.

(13) Chapter 9 Analysis of Polyphenols in Foods.........................................................................199 Fereidoon Shahidi and Marian Naczk Chapter 10 Sensory Analysis of Foods ....................................................................................261 Kannapon Lopetcharat and Mina McDaniel Chapter 11 Determination of Food Allergens and Genetically Modified Components ...........................................................................................................303 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 ....................................................................329 Steven J. Lehotay and Katerina Mastovska Chapter 13 Determination of Pollutants in Foods ...................................................................361 Douglas G. Hayward Chapter 14 Analysis of Chemical Preservatives in Foods.......................................................379 Adriaan Ruiter and Aldert A. Bergwerff Chapter 15 Measuring Radioactive Contaminants in Foods ...................................................403 Andras Szabo and Sandor Tarjan Chapter 16 Rapid Analysis Techniques in Food Microbiology...............................................415 Francisco Diez-Gonzalez and Yildiz Karaibrahimoglu Index......................................................................................................................433.

(14) 1. Selection of Techniques Used in Food Analysis Michael H. Tunick. CONTENTS 1.1 1.2 1.3 1.4 1.5. Introduction ......................................................................................................2 Sample Selection and Preservation..................................................................2 Extraction .........................................................................................................3 Technique Selection .........................................................................................4 Application of Techniques ...............................................................................4 1.5.1 Chromatographic Techniques................................................................5 1.5.1.1 Gas Chromatography (GC)......................................................5 1.5.1.2 High-Performance Liquid Chromatography (HPLC)..............5 1.5.1.3 Supercritical Fluid Chromatography (SFC) ............................6 1.5.2 Spectroscopic Techniques .....................................................................6 1.5.2.1 UV, Vis, and Fluorescence .......................................................6 1.5.2.2 Infrared (IR) .............................................................................6 1.5.2.3 Raman.......................................................................................7 1.5.2.4 Atomic Absorption and Atomic Emission...............................7 1.5.2.5 Mass Spectrometry (MS) .........................................................7 1.5.2.6 Nuclear Magnetic Resonance (NMR) and Electron Spin Resonance (ESR) ..............................................8 1.5.2.7 Other Spectroscopic Techniques..............................................8 1.5.3 Physical Techniques ..............................................................................9 1.5.3.1 Electrochemical ........................................................................9 1.5.3.2 Electrophoresis .........................................................................9 1.5.3.3 Flavor and Odor .......................................................................9 1.5.3.4 Particle Analysis.....................................................................10 1.5.3.5 Rheology and Texture ............................................................10 1.5.3.6 Structure .................................................................................10 1.5.3.7 Thermal Properties.................................................................10 1.5.4 Biological Techniques .........................................................................11 1.5.4.1 Enzyme and Microbial Sensors .............................................11 1.5.4.2 Immunosensors.......................................................................11 1.6 Summary ........................................................................................................11 References................................................................................................................12. 1.

(15) 2. 1.1. Methods of Analysis of Food Components and Additives. INTRODUCTION. Scientists analyze foods for their composition; structure; and chemical, physical, and biological properties. The information obtained may be used for research or for monitoring product quality. A host of different analyses can be conducted on any food. For example, a cheese manufacturer or researcher could investigate the following: 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 other factors 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. This chapter will cover the most common methods used in food analysis, and will include sample 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 handled for the analytical results to be meaningful. If the analysis is not to be performed immediately, the sample will probably have to be preserved to prevent deterioration. Preservation involves the control of temperature, moisture, oxygen, and light, and.

(16) Selection of Techniques Used in Food Analysis. 3. may be as simple as sealing the sample in a container and placing it in a refrigerator. Containers must be dry, sterile, and unbreakable.. 1.3. EXTRACTION. Food samples frequently have to undergo extraction, separation, or concentration procedures prior to analysis. Foods contain a myriad of compounds and are not homogeneous, often forcing the removal of interfering components and the isolation of the analyte before an analysis is attempted. Common procedures include distillation, 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 of modern extraction techniques, which include the following: Digestion • Microwave oven digestion, with acids such as nitric or sulfuric, for solubilizing 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 degrading organic compounds with hydroxyl radicals to obtain free ions. Small amounts of reagents are required, but digestion time is longer. Membrane • Microfiltration or ultrafiltration, based on size exclusion. Polymer membranes are often used for separation. • Dialysis, based on ionic charge and size exclusion. Cellulose membranes are typically used. Solvent • Solvent extraction, for dissolving compounds of interest. • Pressurized fluid extraction, at the near-supercritical region, where extraction is faster and more efficient. • Supercritical fluid extraction, above the critical pressure and temperature of carbon dioxide, which is nontoxic and nonpolluting. Extraction is completed in minutes instead of hours, and thermal degradation is reduced. • 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 flushed from a liquid or gaseous sample and concentrated in a cryogenic trap..

(17) 4. Methods of Analysis of Food Components and Additives. • Adsorbent trap, where a synthetic porous polymer adsorbs a gas which is then desorbed. The digestion methods are employed for extracting ions, and the other methods are used to extract compounds. Dialysis is used for both. Some of the extraction methods, such as supercritical fluid and sorbent, are used in conjunction with analytical techniques.. 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 categories: Ability to conduct analysis • Sample size, reagents, instruments, cost, final state of sample (destroyed or intact) Fundamental characteristics • Precision, accuracy, sensitivity, specificity, detection limit, reproducibility Personnel concerns • Safety, simplicity, speed Technique status • Official method, in-house method Official methods are developed by being comprehensively studied and compared between laboratories. Standardized official methods include those published by AOAC International,3 American Association of Cereal Chemists,4 and American Oil Chemists’ Society.5 More specialized method collections, such as Food Chemical Codex6 for determination of additives, have also been compiled. Many techniques are not listed as official because they are relatively new or have not yet been applied to certain types of samples. In these cases, in-house methods may be used if they have 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 and titrimetric 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..

(18) Selection of Techniques Used in Food Analysis. 1.5.1. 5. CHROMATOGRAPHIC TECHNIQUES. Chromatography is based on distribution or partition of a sample solute between stationary and mobile phases. Chromatographic techniques in common use today in food analysis include gas chromatography (GC), high-performance liquid chromatography (HPLC), and supercritical fluid chromatography (SFC). These often serve as a separation method when connected to another instrument such as a mass spectrometer, 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 more appropriate chromatographic methods for analysis of amino acids, peptides, sugars, and vitamins. GC is useful for analysis of nonpolar compounds, although polar compounds may be analyzed if derivatized first. Isolation of the analyte from the sample matrix is particularly important in GC to avoid false responses from matrix degradation products. Headspace methods (including direct sampling of the headspace), distillation, and solvent extraction are often employed. Detectors include thermal conductivity (which is nonspecific), flame ionization (for most organic compounds), electron capture (mainly for pesticide residues), and flame photometric (for pesticides and sulfur compounds). The most common food analysis applications for GC involve carbohydrates, drugs, lipids, and pesticides.8 Improvements in chromatography are constantly occurring. For instance, a new approach is comprehensive chromatography, which allows a sample to be separated along 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 column which 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 chromatography and has been used to measure nonvolatile food components. Spectroscopic detectors are often employed. Normal-phase HPLC, in which the stationary phase is a polar adsorbent and the mobile phase is a nonpolar solvent, is often used for fat-soluble vitamins and carbohydrates. Reversed-phase HPLC, with a nonpolar stationary phase and polar mobile phase, is more popular because of its wider application. Ion-exchange HPLC, with a functionalized organic resin as packing material, is used for detection of inorganic ions and analysis of carbohydrates and amino acids. HPLC is currently the most popular food analysis technique (GC is second) and is most used for amino acids, carbohydrates, drugs, lipids, and proteins.8 A new application of this technique is comprehensive two-dimensional liquid chromatography gas chromatography, LC GC. Triglycerides can first be.

(19) 6. Methods of Analysis of Food Components and Additives. 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 origin analysis, 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 tubular column or a packed column is employed as the stationary phase, and any GC or LC detector is used. Instrumentation first became available in the 1980s. Smith11 reviewed the history and applications of supercritical fluids, citing its use in separating lipids from food matrices as a chief advantage over other methods. However, SFC is prone to operational difficulties and is a normal-phase method; reversedphase HPLC is often viewed as preferable.. 1.5.2. SPECTROSCOPIC TECHNIQUES. Spectroscopy is based on interactions of matter with electromagnetic radiation. Interactions can take the form of absorption and emission, and can be detected by using emission, transmission, and reflection designs. Food scientists most often deal with the ultraviolet (UV), visible (Vis), infrared (IR), radio (nuclear magnetic resonance, NMR), and microwave (electron spin resonance, ESR) regions of the spectrum, 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 food laboratories for many years. A food component that absorbs in the ultraviolet or visible range may be analyzed at its characteristic wavelength in a UV-Vis spectrophotometer, 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 molecules fluoresce, including bacteria and some pesticide residues, making fluorescence spectroscopy an option for detecting food contamination. 1.5.2.2. Infrared (IR). Many molecular groups absorb IR light at specific wavelengths in an infrared spectrum, with the fingerprint region of the spectrum leading to positive identification of compounds. This long-standing technique has been expanded upon in recent years. Fourier transform infrared (FTIR) spectrometers are now used on production lines for determining concentrations of fat, protein, and moisture. This on-line method of analysis has a large advantage over other techniques because the sample does not have to be extracted or treated in any way. Attenuated total reflectance (ATR) deals with internal reflection of IR light, and it has been used to examine sugars and trans fatty acids. High-pressure and high-temperature ATR cells have been developed. This technique can be enhanced by using multiple internal reflection (MIR), in which.

(20) Selection of Techniques Used in Food Analysis. 7. light is bounced off the surface several times. Further developments in the optical components 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 absorbed and reemitted. DRIFT has been employed recently to monitor production and detect compounds in coffee. Recent developments in IR spectroscopy of foods have been reviewed by Wilson and Tapp.12 1.5.2.3. Raman. Raman spectroscopy is a complementary technique to IR spectroscopy. IR absorption depends on changes in dipole moment, meaning that polar groups have strong IR responses. Raman scattering deals with changes in polarizability of functional groups, so nonpolar groups produce intense responses. Proteins and amino acids lend themselves to Raman spectroscopy, and carbohydrates, lipids, and minor food components are also examined by this technique. In addition to basic research on molecular structure, Raman spectroscopy is now being used for industrial process control. 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 emission of radiation by a sample. Samples must usually be ashed, dissolved in water or dilute acid, and vaporized. In AAS, samples are atomized by nebulizer and burner (flame AAS), or by a graphite furnace (electrothermal AAS). Electrothermal AAS uses smaller samples and has much lower detection limits than flame AAS, but it is more 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 concentrations in complex matrices with excellent precision and accuracy. AAS is the more established technique, with a wider variety of instruments available, but ICP-AES can be used to measure more than one element in a sample and can measure compounds that are stable at high temperatures. Both AAS and AES have supplanted classical methods for detecting minerals in food. 1.5.2.5. Mass Spectrometry (MS). A mass spectrometer ionizes molecules to produce charged fragments that are separated by size and charge. MS has been used for identification and analysis of complex compounds since the early 1960s. The coupling of separation techniques with MS, which began in the 1970s, has overcome the main analytical problem with chromatographic techniques — namely, ambiguity about the identity of the analyte. MS is frequently used in combination with GC, HPLC, ICP, and capillary electrophoresis, and there are tandem MS-MS instruments. Three new ionization techniques used in food analysis are electrospray ionization (ESI, where multiply charged ions are produced by repeated formation and explosion of charged droplets), heated.

(21) 8. Methods of Analysis of Food Components and Additives. nebulizer-atmospheric pressure chemical ionization (HN-APCI, where a gas-phase ion-molecule reaction process allows the analyte molecules to be ionized under atmospheric pressure), and matrix-assisted laser desorption/ionization (MALDI, where a sample is crystallized in a matrix of small aromatic compounds, and the crystal is subjected to a pulsed ultraviolet laser that fragments the molecules). MS techniques have been used to analyze the gamut of food components, including antioxidants, aroma compounds, carbohydrates, drug residues, lipids, peptides and proteins, toxins, and vitamins. A summary of developments in the use of MS in food analysis 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 a magnetic field absorb characteristic frequencies in the radio range. ESR deals with electrons and microwave frequencies. These techniques have several advantages: they are nondestructive, do not usually require sample separation or extraction, and can analyze the interior of a sample. Drawbacks include lower sensitivity and selectivity than some other techniques. NMR experiments are performed using continuous wave (magnetic field held constant and oscillating frequency varied, or vice versa) or pulse (short time, large amplitude) methods; ESR uses continuous wave. Available NMR instruments include low-resolution (for moisture or oil content), high-resolution liquid (analysis of liquid phase), high-resolution solid (analysis of solid phase), and magnetic resonance imaging (three-dimensional views of cross sections of foods). Virtually any food can be analyzed by NMR and ESR. NMR is often used to examine physical properties such as melting, crystallization, polymorphism, and oil content, and ESR is used for detecting free radicals produced in physical and chemical processes. Mannina et al. summarized the principles of NMR and applied the technique to analyzing free acidity, fatty acid profile, and sterol, squalene, and chlorophyll 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 measurements based on hue, lightness, and saturation, and are often used in conjunction with sensory and shelf-life studies. A digital camera and computer graphics software have recently been applied to the analysis of surface color of food.16 Refractometry is based on the change in velocity of light by the analyte. Refractive index measurements are useful in determining concentrations of beverages, sauces, and other liquid foods. HPLC instruments sometimes have refractometer detectors. Polarimetry is the study of the rotation of polarized light by optically active substances. Polarimetry is used to distinguish optical isomers, identify and characterize optically active substances, and measure their change in concentration during.

(22) Selection of Techniques Used in Food Analysis. 9. reactions. It is commonly applied to the measurement of oils in the flavor industry, sugars, and starches. Circular dichroism and optical rotatory dispersion are based on the interaction of circularly polarized light with optically active species; the former depends on wavelength and the latter on molar absorptivity. These techniques are often applied to amino acids, peptides, proteins, and complex natural products. Ultrasonic sensors have been applied to the determination of compositional and textural properties by measurement of velocity of ultrasound waves through a sample. Ultrasonic imaging is used to examine structure in foods, but is too timeconsuming for routine inspections. Coupland and Saggin17 summarized the use of ultrasonic sensors in food analysis.. 1.5.3 1.5.3.1. PHYSICAL TECHNIQUES Electrochemical. The most common electrochemical technique is the familiar pH electrode. An alternative to AAS and AES is the ion-selective electrode, which is sensitive to a particular ion. This technique is simple, rapid, and relatively inexpensive. However, these electrodes are not ion-specific, as there may be interference from ions other than those being examined. 1.5.3.2. Electrophoresis. The basis for gel electrophoresis, developed in the 1950s, is the separation of charged molecules when an electric field is applied. The main types of electrophoresis are nondenaturing, where separation is according to charge, shape, and size; denaturing or sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE), where the separation is primarily by molecular weight; isoelectric focusing, which separates by charge; and two-dimensional, with separations in perpendicular directions by isoelectric 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 tube and photometric detection. CE techniques include capillary zone electrophoresis, for charged analytes, and micellar electrokinetic chromatography, for neutral analytes. CE has been applied to analysis of amino acids, carbohydrates, proteins, and vitamins, 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 characterizing these attributes is important to the food industry. Sensory panels are often used, but since they rely on human judgment, instrumental techniques are being developed. Some 7000 aroma compounds have been identified by GC-MS. The sensory character of individual aroma compounds is often investigated by gas chromatographyolfactometry (GC-O), developed in the 1970s, where analysts sniff compounds as.

(23) 10. Methods of Analysis of Food Components and Additives. they elute from a GC. Atmospheric pressure ionization-mass spectroscopy (APIMS) measures the concentration of volatiles as they are being inhaled, providing information on flavor release. New advances in these areas were described by Risch and Ho,19 and Marsili20 covered sample preparation, instrumental techniques, and applications. One challenge to be overcome in characterizing flavors and odors is that individual components are analyzed separate from the food matrix, and therefore out of context. 1.5.3.4. Particle Analysis. Many processed foods contain particles produced by drying, grinding, milling, or other means. Particle appearance and shape are examined by the optical microscope, and size uniformity is measured by particle sizing instruments based on principles such 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 engineering, shelf-life testing, and quality control. Food exhibits both elastic and viscous behavior, which can be measured by viscometric, oscillatory shear, compression, extension, torsion, and other tests. Bourne22 described rheological and textural measurement of food. 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 survey structural details. Surface microstructure is examined through SEM, and internal structures 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 transitions are observed by using a differential scanning calorimeter, in which a sample is heated and the amount of heat absorbed relative to a reference is measured. The technique has been applied to components such as proteins, starches, and sugars, and is especially useful for observing the melting of lipids, which have relatively high heats of fusion. Applications of thermal analysis in food have been reviewed by Harwalkar and Ma.24 Bomb calorimeters are used to determine the caloric value of a food by combusting it in an oxygen atmosphere and measuring the temperature change in the.

(24) Selection of Techniques Used in Food Analysis. 11. surrounding water. However, many manufacturers obtain caloric values by simple calculation, using percentages of each ingredient and caloric values for fat, carbohydrate, and protein.. 1.5.4. BIOLOGICAL TECHNIQUES. 1.5.4.1. Enzyme and Microbial Sensors. Biosensors consist of a biological recognition element that produces a quantifiable response in a signal transduction element when in contact with the analyte. Enzyme biosensors use enzymes to generate products that are detected by acoustic, electrochemical, optical, and photothermal transduction elements. Microbial biosensors use genetically modified microorganisms that are immobilized on a membrane or trapped in a matrix, with the transduction mechanism consisting of an oxygen or pH electrode, or a luminometer if luciferin is added. A popular type of optical element developed in the 1990s is surface plasmon resonance. 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, and specificity are needed for wider acceptance of this technique. Recent reviews by Patel25 and Mello and Kabota26 describe biosensors and their suitability in food analysis. 1.5.4.2. Immunosensors. Immunosensors are biosensors in which the biological recognition elements are antibodies that are attached to a solid support and bind to a particular antigen or antibody in the sample. The most common immunoassay is enzyme-linked immunosorbent assay (ELISA), in which an enzyme-linked antibody is applied after the antigen or antibody is bound. A substrate is then added to produce a secondary reaction that has a colored product that is measured spectroscopically. The antibody/antigen interaction is specific enough to allow detection of species of origin, and it is also used to detect allergens, enzymatic inactivation, genetically modified organisms, microbial contamination, and toxins.. 1.6. SUMMARY. The analytical techniques now available to food researchers provide faster results at lower cost with lower solvent and reagent use and higher precision and accuracy than 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 food components can be uncovered..

(25) 12. Methods of Analysis of Food Components and Additives. 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 International: 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. Comprehensive 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 chemometrics. 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. Academic 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..

(26) Selection of Techniques Used in Food Analysis. 13. 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..

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(28) 2. Statistical Assessment of Results of Food Analysis Richard Brereton. CONTENTS 2.1 2.2. Introduction ....................................................................................................15 Uncertainty and Precision..............................................................................16 2.2.1 Concept................................................................................................16 2.2.2 Origin of Uncertainty ..........................................................................16 2.2.3 Determination of Uncertainty .............................................................17 2.2.4 Calculation of Uncertainty ..................................................................17 2.2.5 Confidence...........................................................................................19 2.2.6 Reporting Uncertainty .........................................................................20 2.3 Accuracy and Bias .........................................................................................20 2.3.1 Definitions ...........................................................................................20 2.3.2 Determination of Accuracy .................................................................20 2.3.3 Significance of Difference in Means ..................................................21 2.4 Calibration ......................................................................................................22 2.4.1 Classical Calibration ...........................................................................22 2.4.2 Inverse Calibration ..............................................................................23 2.4.3 Error Analysis......................................................................................24 2.4.4 Confidence Intervals............................................................................26 Acknowledgments....................................................................................................27 References................................................................................................................28. 2.1. INTRODUCTION. Most analytical techniques aim to obtain a measurement — such as from chromatography or spectroscopy — and relate this measurement to the concentration of a compound in a material such as food. There are two principal needs for statistical methods. The first is determining how well the concentration of a single sample can be estimated in a laboratory. This may, for example, be a reference sample using a standard method of analysis, and it may be important to compare this against published data or with other laboratories. A second need arises during calibration when establishing a new method, using a series of standards of different concentrations to develop an analytical technique that will be employed to estimate the 15.

(29) 16. Methods of Analysis of Food Components and Additives. concentration of an unknown. There are more comprehensive guides to the statistical methods described in this chapter1,2 to which the reader who wishes to delve further is referred.. 2.2 2.2.1. UNCERTAINTY AND PRECISION CONCEPT. A key concept is that of uncertainty of measurements.3,4 It is often desirable to be able to cite a range within which we are confident that the true value of a concentration lies. For example, after performing a measurement, we may be 99% confident that the true concentration of a compound in a food is between 21.52 and 23.65 mg/kg. The broader this range, the larger the uncertainty.. 2.2.2. ORIGIN. OF. UNCERTAINTY. Uncertainty is influenced by three main factors. The first is measurement error. Most measurements consist of several steps. For example, extraction, weighing, dilution, and then recording an instrumental response. Each step involves errors. If a 100 mL volumetric 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 volumes will 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 distribution, 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 not always result in products that are identical in composition. This is especially important 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, from bias 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 problems with the original calibration, adding an extra source of error. Measurement error will always be present. The importance of sampling error depends on how broad a question we want to answer. In some cases the main objective 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 intrinsic value in absence of measurement error, c , by.

(30) Statistical Assessment of Results of Food Analysis. c = c + emeasurement + esampling + ecalibration. 17. (2.1). where the e terms are called error terms. Each of the measurement and sampling error terms in themselves form a distribution, and they originate from several different sources. In practice, the error terms are sums of several distinct distributions, but an important theorem states that the sums of different symmetric distributions normally approximate to what is described as a normal distribution,5 characterized by a mean and standard deviation. The larger the standard deviation, the larger the uncertainty.. 2.2.3. DETERMINATION. OF. UNCERTAINTY. To determine uncertainty, it is normal to first decide which factors are to be studied. For example, do we wish to include variability between samples, or are we studying a single sample? Are the measurements restricted to using a single analyst or set of apparatus? For an official method of analysis, it is essential to define these factors in advance, and organizations such as IUPAC, Eurachem, and NIST provide suitable guidelines.6–8 Once the limits to the range of factors have been determined, it is usual then to perform replicate analyses, and measure the spread of the results over these replicate analyses. Normally some form of experimental design is required to ensure that there is no bias in the replication. For example, if four analysts and two instruments are to be used in the replication study, and we make 24 measurements, then, ideally each analyst should perform six measurements, three on each of the two instruments. The more the factors to be studied, the more complex the design. Sufficient replicates should be performed to provide a good estimate of the standard 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 a good estimate of this value. If only five replicates are measured, the value of the standard deviation may be seriously in error. There are methods for overcoming this problem, but they are a bit complex, and it is easiest to use a large number of replicates.. 2.2.4. CALCULATION. OF. UNCERTAINTY. Often the procedure is broken down into a series of steps, j. It is usual to calculate the standard deviation of measurements obtained by replicating step j, defined by. (2.2) 1.

(31) 18. Methods of Analysis of Food Components and Additives. where ci is the ith value of the measured concentration, and c the mean. This is also 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. This value is the experimental estimate of the precision, uj, of each step. The overall precision can be calculated by J. u=. ∑u. 2 j. (2.3). j =1. For some steps, such as calibration, it is not always possible to measure the value of uj by replication, but alternatives such as mean square calibration errors can be used instead. Normally, the individual uncertainties are expressed in percentage terms; for example, a volumetric flask may have an uncertainty of 2%, and balance of 1%, an extraction procedure of 5% and so on. Hence, if there are five factors, with uncertainties of 8, 1, 3, 11, and 4%, u = (0.082 + 0.012 + 0.032 + 0.112 + 0.042 ) = 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 we neglect 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. This means that it is fairly safe to neglect these sources and so we will get satisfactory answers 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 given manufacturer are certified within 0.6 mL. This means that the volume of 95% of the 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 all measurements are within 1.96 standard deviations of the mean, so that 0.4 mL is equivalent 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 pipette may 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, which then allows uncertainties to be calculated in the normal manner. Note that in order for these calculations to have meaning, the method of analysis must be similar in all cases — for example, using a balance, volumetric, measuring cylinder, 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 to concentrate or dilute samples prior to analysis to obtain comparable results. Alternatively, one could calculate different uncertainties according to the concentration.

(32) Statistical Assessment of Results of Food Analysis. 19. level of a compound, because a different analytical procedure may be employed to measure concentrations centering on 1, 10, or 100 mg/kg. If it is known that measurement error is heteroscedastic — for example, it depends on the concentration of analyte or intensity of spectroscopic peaks — there are methods for adjusting the basic equations for uncertainty. In some cases, certain apparatus in the analytical procedure remain the same; therefore, uncertainty is independent of analyte, and only one step is influenced by concentration. The equation for uncertainty can be modified under such circumstances with each of the individual uncertainties given a weight cj as follows: J. u=. ∑c u j. 2 j. (2.5). j =1. 2.2.5. CONFIDENCE. The concept of confidence is closely related to that of uncertainty (see The NIST Reference on Constants, Units, and Uncertainty8 and Chapter 2 of Miller and Miller9). Assuming a normal distribution, we can compute this from the second column of Table 2.1. If the number of samples used to calculate the uncertainty is large, then this implies that 50% of samples are within 0.674 standard deviations of the 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 uncertainty equals 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 uncertainty is 1.80 mg/kg and so we are 95% confident that the true value is between 52.77 and 59.83 mg/kg. Sometimes the error standard deviation is measured on a small number of samples. The t-distribution corrects for this. For the normal distribution, it is assumed that there are a large number of degrees of freedom for determination of the standard deviation. If there are fewer samples, then the number of degrees of freedom equals one less than the number of samples, so if we use 11 samples for determination of the 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 Degrees of Freedom Probability (%). Large. 100. 50. 10. 5. 50 90 95 99. 0.674 1.645 1.960 2.576. 0.677 1.660 1.984 2.626. 0.679 1.676 2.009 2.678. 0.700 1.812 2.228 3.169. 0.727 2.015 2.571 4.032.

(33) 20. Methods of Analysis of Food Components and Additives. do not exactly form a normal distribution, and it is usual to use a t-distribution. The right-hand columns of Table 2.1 represent the equivalent number of standard deviations away from the mean when sample sizes are restricted. So, if only 11 samples are used to determine uncertainty, 95% of samples will lie within 2.228 rather than 1.960 standard deviations of the experimentally determined mean. In many practical situations 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.. 2.2.6. REPORTING UNCERTAINTY. 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 implies that 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 number 3.27 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 to approximately 95% confidence in the analysis.. 2.3 2.3.1. ACCURACY AND BIAS DEFINITIONS. Accuracy relates to how close a result is to the true result (see Chapter 1 of The NIST Reference on Constants, Units, and Uncertainty9 and Chapter 2 of Caulcutt and Boddy11). For example, if a true concentration is 103.24 mg/kg and the measured concentration 105.61 mg/kg, there is a 2.37 mg/kg inaccuracy in the measurement process. The closer the measured concentration (which is usually the average of several individual measurements) is to the true concentration, the more accurate it is. Accuracy is different from precision or uncertainty in that the latter measures the spread 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 analyses might appear quite similar, in fact they are all in error by a given amount. This type of error is often called bias.. 2.3.2. DETERMINATION. OF. ACCURACY. It is often harder to determine accuracy than precision or uncertainty because this cannot easily be performed using replicates analysis. There are two principal approaches. The first is to use a certified reference material, whose properties are well established. Major national and international organizations are in the business of producing such standards. The second involves interlaboratory tests, in which one material is sent to several different laboratories (or to several analysts in one laboratory or to several instruments, if it suspected that there is an in-house bias), and the results compared..

(34) Statistical Assessment of Results of Food Analysis. 21. 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 measured quantity, such as a concentration, is obtained.. 2.3.3. SIGNIFICANCE. OF. DIFFERENCE. IN. MEANS. The main statistical technique consists of asking whether a mean measurement from one 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 difference between the means from both sources to their standard deviations. If the mean measurements 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 to the other. To do this, the first step is to calculate the pooled standard of the two procedures, defined by. s=. ( I A − 1) s A2 + ( I B − 1) sB2 ( I A + I B − 2). (2.6). where sA is the standard deviation obtained from procedure A, and IA the corresponding 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 t=. c A − cB s 1/ I A + 1/ IB. (2.7). which is normally presented as a positive number, so procedure A is the one that results in a higher average concentration estimate. The larger this number, the more likely it is that the two procedures differ. Consider an example as follows. For Reference Procedure A, we record 50 measurements, 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 standard deviation 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 (see Chapter 3 of The NIST Reference on Constants, Units, and Uncertainty,9 Appendix A.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 the more likely it is that there is a real difference between means. Many traditional statistical texts present critical values of this statistic in tabular form, so we can determine whether, for example, the likelihood this occurs by chance is less than.

(35) 22. Methods of Analysis of Food Components and Additives. 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 represents 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 variable 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.. 2.4.1. CLASSICAL CALIBRATION. There are several ways in which a calibration model can be formed between concentration (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 xˆ = a1c. (2.8). xˆ = a0 + a1c. (2.9). or. 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. ∑xc. i i. a1 =. i =1 I. ∑c. 2 i. i =1. where each measurement is denoted by i.. (2.10).

(36) Statistical Assessment of Results of Food Analysis. 23. For centered data, we have I. ∑ ( x − x )(c − c ) i. a1 =. i. i =1. I. ∑ (c − c ). (2.11). 2. i. i =1. and a0 = c − a1x where the “–” over the numbers refers to the mean. For the data set of Table 2.2, the best fit equations are xˆ = 2.576c or ˆx = 0.611 + 2.436c .. 2.4.2. INVERSE CALIBRATION. 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 cˆ = b1x. (2.12). or. TABLE 2.2 Sample Data for Univariate Calibration Concentration (mmol/L). Response. 1 1 2 3 3 4 4 5 6 6. 3.803 3.276 5.181 6.948 8.762 10.672 8.266 13.032 15.021 16.426.

(37) 24. Methods of Analysis of Food Components and Additives. cˆ = b0 + b1x. (2.13). is fitted to the data. For the data set of Table 2.2, the best fit equations are cˆ = 0.3847 x or cˆ = −0.0851 + 0.3923x . Note that the values of the coefficients for the 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.. 2.4.3. ERROR ANALYSIS. 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 P= ( x − xˆ ). (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 I. E=. ∑ ( x − xˆ ) /(I − P) 2. i. i =1. i. (2.15).

(38) Statistical Assessment of Results of Food Analysis. 25. 2.5 2 1.5 1 0.5 0 0. 1. 2. 3. 4. 5. 6. -0.5 -1 -1.5 -2 -2.5. FIGURE 2.1 Residual plot of the data of Table 2.2, after fitting to a two-parameter classical model.. 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, and can 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 (see Chapter 2 of Brereton10). In order to do this, it is usual to compare the replicate or experimental error to the lack of fit to the linear model. Provided there are sufficient replicates in the calibration, it is possible to obtain this information quite easily. In our 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 experimental uncertainty and should be used for guidance only; if it is important to achieve a more accurate estimate (e.g., for regulatory purposes), many more replicates are required. In order to perform this calculation, we need to calculate the average response at each concentration level, xi . 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 I. Srep =. ∑ (x − x ) i. i =1. equaling 5.665 in this example.. i. 2. (2.16).

(39) 26. Methods of Analysis of Food Components and Additives. However, the total sum of square residual error is given by I. Sresid =. ∑ (x − xˆ ) i. 2. i. (2.17). i =1. equaling 8.371 for the two-parameter classical model (the root mean square residual error is given by 8.371 / 8 or 1.0229 as above). A third sum of square error, called the lack-of-fit, can be calculated by subtracting the replicate error from the total residual error, C Sresid Srep 8.371 5.665 2.706. (2.18). This latter error indicates how well the linear model is obeyed. It is normal to compare the size of this error to the replicate error. To do this, one first divides each error by the associated number of degrees of freedom, to create an average sum of 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 in the model minus the number of replicates, or LNPR. (2.19). equaling 10 2 4 4 in the case of the two-parameter classical model. We then calculate a statistic called the F-ratio F (Slof /L)/(Srep /R). (2.20). or 0.478. Since the average lack-of-fit is less than the replicate error, it is not significant; this means that there is no evidence to say that the model is incorrect and 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 linear relationship expressed as a probability.. 2.4.4. CONFIDENCE INTERVALS. It is sometimes useful to determine the confidence limits for the calibration model.15 Earlier in this chapter we were primarily concerned with confidence in prediction of the concentration of a single reference standard. In the case of calibration, the confidence may vary according to the underlying concentration. For example, if a calibration were performed between 5 and 15 mmol/L, it is likely that there will be higher confidence in the predicted concentration at 10 mmol/L rather than at 5 mmol/L. It is also interesting to determine the confidence in prediction outside the.

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