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SENSORY EVALUATION T ECHNIQUES T HIRD EDITION Morten Meilgaard, D.Sc. Senior Technical Advisor The Stroh Brewery Company Detroit, Michigan Gail Vance Civille, B.S. President Sensory Spectrum, Inc. Chatham, New Jersey B. Thomas Carr, M.S. Principal Carr Consulting Wilmette, Illinois Boca Raton New York CRC Press © 1999 by CRC Press LLC
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SENSORY EVALUATION TECHNIQUESTHIRD EDITION

Morten Meilgaard, D.Sc.Senior Technical AdvisorThe Stroh Brewery CompanyDetroit, Michigan

Gail Vance Civille, B.S.PresidentSensory Spectrum, Inc.Chatham, New Jersey

B. Thomas Carr, M.S.PrincipalCarr ConsultingWilmette, Illinois

Boca Raton New York

CRC Press

9 by CRC Press LLCC Press LLC

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This book contains information obtained from authentic and highly regarded sources. Reprinted materialis quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonableefforts have been made to publish reliable data and information, but the author and the publisher cannotassume responsibility for the validity of all materials or for the consequences of their use.

Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronicor mechanical, including photocopying, microfilming, and recording, or by any information storage orretrieval system, without prior permission in writing from the publisher.

The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, forcreating new works, or for resale. Specific permission must be obtained in writing from CRC Press LLCfor such copying.

Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431.

Trademark Notice:

Product or corporate names may be trademarks or registered trademarks, and areused only for identification and explanation, without intent to infringe.

Visit the CRC Press Web site at www.crcpress.com

© 1999 by CRC Press LLC

No claim to original U.S. Government worksInternational Standard Book Number 0-84930-276-5

Printed in the United States of America 1 2 3 4 5 6 7 8 9 0Printed on acid-free paper

Library of Congress Cataloging-in-Publication Data

Meilgaard, Morten and Civille, Gail VanceSensory Evaluation Techniques: Third Edition / Morten Meilgaard, D.Sc. and

p. cm.Includes bibliographical references.ISBN 0-84930-276-5

Catalog record is available from the Library of Congress

disclaimer Page 1 Tuesday, May 29, 2001 9:21 AM

Gail Vance Civille, B.S.

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Preface to the Third Edition

How does one plan, execute, complete, analyze, interpret, and report sensory tests? Hopefully, the practices and recommendations in this book cover all of those phases of sensory evaluation. The text is meant as a personal reference volume for food scientists, research and development scientists, cereal chemists, perfumers, and other professionals working in industry, academia, or government, who need to conduct good sensory evaluation. The book should also supply useful background to marketing research, advertising, and legal professionals who need to understand the results of sensory evaluation. It could also give a sophisticated general reader the same understanding.

Because the first edition was used as a textbook at the university and professional level, partly in courses taught by the authors, the second and third editions incorporate a growing number of ideas and improvements arising out of questions from students. The objective of the book is now twofold. First, as a “how to” text for professionals, it aims for a clear and concise presentation of practical solutions, accepted methods, and standard practices. Second, as a textbook for courses at the academic level, it aims to provide just enough theoretical background to enable the student to understand which sensory methods are best suited to particular research problems and situations, and how tests can best be implemented.

The authors do not intend to devote text and readers’ time to resolving controversial issues, but a few had to be tackled. We take a fresh look at all statistical methods used for sensory tests, and we hope you like our straightforward approach. The second edition was the first book to provide an adequate solution to the problem of similarity testing. This was adopted and further developed by ISO TC34/SC12 on Sensory Evaluation, resulting in the current “unified” procedure (Chapter 6, Section II, p. 60) in which the user’s choice of α- and β-risks defines whether difference or similarity is tested for. Another “first” is the unified treatment of all ranking tests with the Friedman statistic, in preference to Kramer’s tables.

Chapter 11 on the Spectrum™ method of descriptive sensory analysis, developed by Civille, has been expanded. The philosophy behind Spectrum is threefold: (1) the test should be tailored to suit the objective of the study (and not to suit a prescribed format); (2) the choice of terminology and reference standards should make use not only of the senses and imagination of the panelists, but also of the accumulated experience of the sensory profession as recorded in the literature; and (3) a set of calibrated intensity scales is provided which permits different panels at different times and locations to obtain comparable and reproducible profiles. The chapter now contains full descriptive lexicons suitable for descriptive analysis of a number of products, e.g., cheese, mayon-naise, spaghetti sauce, white bread, cookies, and toothpaste. Also new is a set of revised flavor intensity scales for attributes such as crispness, juiciness, and some common aromatics, and two training exercises.

The authors wish the book to be cohesive and readable; we have tried to substantiate our directions and organize each section so as to be meaningful. We do not want the book to be a turgid set of tables, lists, and figures. We hope we have provided structure to the methods, reason to the procedures, and coherence to the outcomes. Although our aim is to describe all tests in current use, we want this to be a reference book that can be read for understanding as well as a handbook that can serve to describe all major sensory evaluation practices.

The organization of the chapters and sections is also straightforward. Chapter 1 lists the steps involved in a sensory evaluation project, and Chapter 2 briefly reviews the workings of our senses. In Chapter 3, we list what is required of the equipment, the tasters, and the samples, while in Chapter 4, we have collected a list of those psychological pitfalls that invalidate many otherwise

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good studies. Chapter 5 discusses how sensory responses can be measured in quantitative terms. In Chapter 6, we describe all the common sensory tests for difference, the Triangle, Duo-trio, etc., and, in Chapter 7, the various attribute tests, such as ranking and numerical intensity scaling. Thresholds and just-noticeable differences are briefly discussed in Chapter 8, followed by what we consider the main chapters: Chapter 9 on selection and training of tasters, Chapters 10 and 11 on descriptive testing, and Chapter 12 on affective tests (consumer tests).

The body of text on statistical procedures is found in Chapters 13 and 14, but, in addition, each method (Triangle, Duo-trio, etc.) in Chapters 6 and 7 is followed by a number of examples showing how statistics are used in the interpretation of each. Basic concepts for tabular and graphical summaries, hypothesis testing, and the design of sensory panels are presented in Chapter 13. We refrain from detailed discussion of statistical theory, preferring instead to give examples. Chapter 14 discusses multifactor experiments that can be used, for example, to screen for variables that have large effects on a product, to identify variables that interact with each other in how they affect product characteristics, or to identify the combination of variables that maximize some desirable product characteristic, such as consumer acceptability. Chapter 14 also contains a discussion of multivariate techniques that can be used to summarize large numbers of responses with fewer, meaningful ones, to identify relationships among responses that might otherwise go unnoticed, and to group respondents of samples that exhibit similar patterns of behavior. New in the third edition is a detailed discussion of data-relationship techniques used to link data from diverse sources collected on the same set of samples. The techniques are used to identify relationships, for example, between instrumental and sensory data or between sensory and consumer data.

At the end of the book, the reader will find guidelines for the choice of techniques and for reporting results, plus the usual glossaries, indexes, and statistical tables.

With regard to terminology, the terms “assessor,” “judge,” “panelist,” “respondent,” “subject,” and “taster” are used interchangeably, as are ‘‘he,” “she,” and “(s)he” for the sensory analyst (the sensory professional, the panel leader) and for individual panel members.

Morten MeilgaardGail Vance Civille

B. Thomas Carr

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The Authors

Morten C. Meilgaard, M.Sc., D.Sc., F.I. Brew, is Visiting Professor (emeritus) of Sensory Science at the Agricultural University of Denmark and Vice President of Research (also emeritus) at the Stroh Brewery Co., Detroit, MI. He studied biochemistry and engineering at the Technical Univer-sity of Denmark, to which he returned in 1982 to receive a doctorate for a dissertation on beer flavor compounds and their interactions. After 6 years as a chemist at the Carlsberg Breweries, he worked from 1957 to 1967 and again from 1989 as a worldwide consultant on brewing and sensory testing. He served for 6 years as Director of Research for Cervecería Cuauhtémoc in Monterrey, Mexico, and for 25 years with Stroh. At the Agricultural University of Denmark his task was to establish Sensory Science as an academic discipline for research and teaching.

Dr. Meilgaard’s professional interest is the biochemical and physiological basis of flavor, and more specifically the flavor compounds of hops and beer and the methods by which they can be identified, namely, chemical analysis coupled with sensory evaluation techniques. He has published over 70 papers. He is the recipient of the Schwarz Award and the Master Brewers Association Award of Merit for studies of compounds that affect beer flavor. He is founder and past president of the Hop Research Council of the U.S., and is past chairman of the Scientific Advisory Committee of the U.S. Brewers Association. For 14 years he was chairman of the Subcommittee on Sensory Analysis of the American Society of Brewing Chemists. He has chaired the U.S. delegation to the ISO TC34/SC12 Subcommittee on Sensory Evaluation.

Gail Vance Civille is President of Sensory Spectrum, Inc., a management consulting firm involved in the field of sensory evaluation of foods, beverages, pharmaceuticals, paper, fabrics, personal care, and other consumer products. Sensory Spectrum provides guidance in the selection, imple-mentation, and analysis of test methods for solving problems in quality control, research, develop -ment, production, and marketing. She has trained several flavor and texture descriptive profile panels in her work with industry, universities, and government.

As a Course Director for the Center for Professional Advancement and Sensory Spectrum, Ms. Civille has conducted several workshops and courses in basic sensory evaluation methods as well as advanced methods and theory. In addition, she has been invited to speak to several professional organizations on different facets of sensory evaluation.

Ms. Civille has published several articles on general sensory methods, as well as sophisticated descriptive flavor and texture techniques. A graduate of the College of Mount Saint Vincent, New York with a B.S. degree in Chemistry, Ms. Civille began her career as a product evaluation analyst with the General Foods Corporation.

B. Thomas Carr is Principal of Carr Consulting, a research consulting firm that provides project management, product evaluation, and statistical support services to the food, beverage, personal care, and home care industries. He has over 18 years of experience in applying statistical techniques to all phases of research on consumer products. Prior to founding Carr Consulting, Mr. Carr held a variety of business and technical positions in the food and food ingredient industries. As Director of Contract Research for NSC Technologies/NutraSweet, he identified and coordinated outside research projects that leveraged the technical capabilities of all the groups within NutraSweet R&D, particularly in the areas of product development, analytical services and sensory evaluation. Prior to that, as Manager of Statistical Services at both NutraSweet and Best Foods, Inc., he worked closely with the sensory,

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analytical, and product development groups on the design and analysis of a full range of research studies in support of product development, QA/QC, and research guidance consumer tests.

Mr. Carr is a member of the U.S. delegation to the ISO TC34/SC12. He is actively involved in the statistical training of scientists and has been an invited speaker to several professional organizations on the topics of statistical methods and statistical consulting in industry. Since 1979, Mr. Carr has supported the development of new food ingredients, consumer food products, and OTC drugs by integrating the statistical and sensory evaluation functions into the mainstream of the product development effort. This has been accomplished through the application of a wide variety of statistical techniques including design of experiments, response surface methodology, mixture designs, sensory/instrumental correlation, and multivariate analysis.

Mr. Carr received his B.A. degree in Mathematics from the University of Dayton, and his Master’s degree in Statistics from Colorado State University.

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Acknowledgments

The authors wish to thank our associates at work and our families at home for thoughts and ideas, for material assistance with typing and editing, and for emotional support. Many people have helped with suggestions and discussion over the years. Contributors at the concept stage were Andrew Dravnieks, Jean Eggert, Roland Harper, Derek Land, Elizabeth Larmond, Ann Noble, Rosemarie Pangborn, John J. Powers, Patricia Prell, and Elaine Skinner. Improvements in later editions were often suggested by readers and were given form with help from our colleagues from two Subcom-mittees on Sensory Evaluation, ASTM E-18 and ISO TC34/SC12, of whom we would like to single out Louise Aust, Donna Carlton, Sylvie Issanchou, Sandy MacRae, Magni Martens, Suzanne Pecore, Rick Schifferstein, and Pascal Schlich. We also thank our colleagues Clare Dus, Kathy Foley, Kernon Gibes, Stephen Goodfellow, Dan Grabowski, Marie Rudolph, and Barbara Pirmann for help with illustrations and ideas, and The Stroh Brewery Company, Sensory Spectrum, Inc., and The NutraSweet Co. for permission to publish and for the use of their facilities and equipment.

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Dedication

to Manon, Frank, and Cathy

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Table of Contents

CHAPTER 1Introduction to Sensory Techniques

I. IntroductionII. Development of Sensory Testing

III. Human Subjects as InstrumentsIV. Conducting a Sensory Study

References

CHAPTER 2Sensory Attributes and the Way We Perceive Them

I. IntroductionII. Sensory Attributes

A. AppearanceB. Odor/Aroma/FragranceC. Consistency and TextureD. FlavorE. Noise

III. The Human SensesA. VisionB. TouchC. OlfactionD. Chemical/Trigeminal FactorsE. GustationF. Hearing

IV. Perception at Threshold and AboveReferences

CHAPTER 3Controls for Test Room, Product, and Panel

I. IntroductionII. Test Controls

A. Development of Test Room DesignB. LocationC. Test Room Design

1. The Booth2. Descriptive Evaluation and Training Area3. Preparation Area4. Office Facilities5. Entrance and Exit Areas6. Storage

D. General Design Factors1. Color and Lighting

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2. Air Circulation, Temperature, and Humidity3. Construction Materials

III. Product ControlsA. General EquipmentB. Sample Preparation

1. Supplies and Equipment2. Materials3. Preparation Procedures

C. Sample Presentation1. Container, Sample Size, and Other Particulars2. Order, Coding, and Number of Samples

D. Product SamplingIV. Panelist Controls

A. Panel Training or OrientationB. Product/Time of DayC. Panelists/Environment

References

CHAPTER 4Factors Influencing Sensory Verdicts

I. IntroductionII. Physiological Factors

A. AdaptationB. Enhancement or Suppression

III. Psychological FactorsA. Expectation ErrorB. Error of HabituationC. Stimulus ErrorD. Logical ErrorE. Halo EffectF. Order of Presentation of SamplesG. Mutual SuggestionH. Lack of MotivationI. Capriciousness vs. Timidity

IV. Poor Physical ConditionReferences

CHAPTER 5Measuring Responses

I. IntroductionII. Psychophysical Theory

A. Fechner’s LawB. Stevens’ LawC. The Beidler Model

III. ClassificationIV. Grading

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V. RankingVI. Scaling

A. Category ScalingB. Line ScalesC. Magnitude Estimation Scaling

References

CHAPTER 6Overall Difference Tests: Does a Sensory Difference Exist Between Samples?

I. IntroductionII. The Unified Approach to Difference and Similiarity Testing

III. Triangle TestIV. Duo-Trio TestV. Two-out-of-Five Test

VI. Same/Different Test (or Simple Difference Test)VII. “A” – not “A” Test

VIII. Difference-from-Control TestIX. Sequential Tests

References

CHAPTER 7Attribute Difference Tests: How Does Attribute X Differ Between Samples?

I. Introduction: Paired Comparison DesignsII. Directional Difference Test: Comparing Two Samples

III. Pairwise Ranking Test: Friedman Analysis—Comparing Several Samples in All Possible Pairs

IV. Introduction: Multisample Difference Tests — Block DesignsV. Simple Ranking Test: Friedman Analysis — Randomized (Complete)

Block DesignVI. Multisample Difference Test: Rating Approach — Evaluation by Analysis

of Variance (ANOVA)VII. Multisample Difference Test: BIB Ranking Test

(Balanced Incomplete Block Design) — Friedman AnalysisVIII. Multisample Difference Test: BIB Rating Test (Balanced Incomplete Block Design) —

Evaluation by Analysis of VarianceReferences

CHAPTER 8Determining Thresholds

I. IntroductionII. Definitions

III. Applications of Threshold DeterminationsA. Example 8.1: Threshold of Sunstruck Flavor Compound Added to BeerB. Example 8.2: Threshold of Isovaleric Acid in Air

References

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CHAPTER 9Selection and Training of Panel Members

I. IntroductionII. Panel Development

III. Selection and Training for Difference TestsA. Selection

1. Matching Tests2. Detection/Discrimination Tests3. Ranking/Rating Tests for Intensity4. Interpretation of Results of Screening Tests

B. TrainingIV. Selection and Training of Panelists for Descriptive Testing

A. Selection for Descriptive Testing1. Prescreening Questionnaires2. Acuity Tests3. Ranking/Rating Screening Tests for Descriptive Analysis4. Personal Interview

B. Training for Descriptive Testing1. Terminology Development2. Introduction to Descriptive Scaling3. Initial Practice4. Small Product Differences5. Final Practice

V. Panel Performance and MotivationA. PerformanceB. Panelist Maintenance, Feedback, Rewards, and Motivation

ReferencesAppendix 9.1 Prescreening Questionnaires

A. Prescreening Questionnaire for a Tactile Panel (Skinfeel or Fabric Feel)B. Prescreening Questionnaire for a Flavor PanelC. Prescreening Questionnaire for an Oral Texture PanelD. Prescreening Questionnaire for a Fragrance Panel E. Scaling Exercises

CHAPTER 10Descriptive Analysis Techniques

I. DefinitionII. Field of Application

III. Components of Descriptive AnalysisA. Characteristics: the Qualitative AspectB. Intensity: the Quantitative AspectC. Order of Appearance: the Time AspectD. Overall Impression: the Integrated Aspect

IV. Commonly Used Descriptive Test MethodsA. The Flavor Profile MethodB. The Texture Profile MethodC. The Quantitative Descriptive Analysis (QDA®) MethodD. The Spectrum™ Descriptive Analysis MethodE. Time-Intensity Descriptive AnalysisF. Free-Choice Profiling

References

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CHAPTER 11The Spectrum™ Descriptive Analysis Method

I. Designing a Descriptive ProcedureII. Terminology

III. IntensityIV. Other OptionsV. Modified Short-Version Spectrum Descriptive Procedures for Quality Assurance,

Shelf-Life Studies, etc.ReferencesAppendix 11.1 Spectrum Terminology for Descriptive Analysis

A. Terms Used to Describe AppearanceB. Terms Used to Describe Flavor (General and Baked Goods)

Example: Flavor Terminology of Baked GoodsC. Terms Used to Describe Semisolid Oral Texture

Example: Semisolid Texture Terminology — Oral Texture of Peanut ButterD. Terms Used to Describe Solid Oral Texture

Example: Solid Texture Terminology of Oral Texture of CookiesE. Terms Used to Describe Skinfeel of Lotions and CreamsF. Terms Used to Describe Handfeel of Fabric and PaperG. Terms Used to Describe the Feel of Hair (Wet and Dry)H. Terms Used to Describe the Lather and Skinfeel of Bar SoapI. Terms Used to Describe the Skinfeel of Antiperspirants

Appendix 11.2 Spectrum Intensity Scales for Descriptive AnalysisA. Intensity Scale Values (0 to 15) for Some Common AromaticsB. Intensity Scale Values (0 to 15) for the Four Basic TastesC. Intensity Scale Values (0 to 15) for Semisolid Oral Texture AttributesD. Intensity Scale Values (0 to 15) for Solid Oral Texture AttributesE. Intensity Scale Values (0 to 15) for Skinfeel Texture AttributesF. Intensity Scale Values (0 to 15) for Fabricfeel Attributes

Appendix 11.3 Spectrum Descriptive Analysis Product LexiconsAppendix 11.4 Spectrum Descriptive Analysis Full Product Descriptions

A. White BreadB. ToothpasteC. Peanut ButterD. MayonnaiseE. Marinara Sauce

Appendix 11.5 Spectrum Descriptive Analysis Training ExercisesA. Basic Taste Combinations ExerciseB. Cookie Variation Exercise

CHAPTER 12Affective Tests: Consumer Tests and In-House Panel Acceptance Tests

I. Purpose and ApplicationsA. Product MaintenanceB. Product Improvement/OptimizationC. Development of New ProductsD. Assessment of Market PotentialE. Category ReviewF. Support for Advertising Claims

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II. The Subjects/Consumers in Affective TestsA. Sampling and DemographicsB. Source of Test Subjects: Employees, Local Residents, the General Population

III. Choice of Test LocationA. Laboratory TestB. Central Location TestsC. Home Use Tests

IV. Affective Methods: QualitativeA. ApplicationsB. Types of Qualitative Affective Tests

1. Focus Groups2. Focus Panels3. One-on-One Interviews

V. Affective Methods: QuantitativeA. ApplicationsB. Types of Quantitative Affective Tests

1. Preference Tests2. Acceptance Tests

C. Assessment of Individual Attributes (Attribute Diagnostics)VI. Design of Quantitative Affective Tests

A. Questionnaire DesignB. Protocol Design

VII. Using Other Sensory Methods to Supplement Affective TestingA. Relating Affective and Descriptive DataB. Using Affective Data to Define Shelf-Life or Quality Limits

1. Example 12.3: Shelf Life of Sesame CrackerReferencesAppendix 12.1 Questionnaire for Consumer Studies

A. Candy Bar Questionnaire1. Candy Bar Liking Questions2. Candy Bar Specific Evaluation

B. Paper Table Napkins Questionnaire1. Paper Table Napkins Liking Questions2. Paper Table Napkins Specific Evaluation

Appendix 12.2 Protocol Design for Consumer StudiesA. Protocol Design Format Worksheets

1. Product Screening2. Sample Information3. Sample Preparation4. Sample Presentation5. Subjects

B. Protocol Design Example: Candy Bars1. Product Screening2. Sample Information3. Sample Preparation4. Sample Presentation5. Subjects

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CHAPTER 13Basic Statistical Methods

I. IntroductionII. Summarizing Sensory Data

A. Summary Analysis of Data in the Form of RatingsB. Estimating the Proportion of a Population that Possesses a Particular

CharacteristicC. Confidence Intervals on µ and pD. Other Interval EstimatesE. Data Transformations

III. Statistical Hypothesis TestingA. Statistical HypothesesB. One-Sided and Two-Sided HypothesesC. Type I and Type II ErrorsD. Examples: Tests on Means, Standard Deviations, and Proportions

1. Example 13.1: Testing that the Mean of a Distribution is Equal to a Specified Value

2. Example 13.2: Comparing Two Means — Paired-Sample Case3. Example 13.3: Comparing Two Means — Independent (or Two-Sample) Case4. Example 13.4: Comparing Standard Deviations from Two Normal Populations5. Example 13.5: Testing that the Population Proportion is Equal to a

Specified Value6. Example 13.6: Comparing Two Population Proportions

E. Calculating Sample Sizes in Discrimination TestsIV. The Statistical Design of Sensory Panel Studies

A. Sampling: Replication vs. Multiple ObservationsB. Blocking an Experimental Design

1. Completely Randomized DesignsC. Randomized (Complete) Block Designs

1. Randomized Block Analysis of Ratings2. Randomized Block Analysis of Rank Data

D. Balanced Incomplete Block Designs1. BIB Analysis of Ratings2. BIB Analysis of Rank Data

E. Latin Square DesignsF. Split-Plot Designs

1. Split-Plot Analysis of RatingsG. A Simultaneous Multiple Comparison Procedure

V. Appendix on ProbabilityA. The Normal Distribution

1. Example 13.7: Calculating Normal Probabilities on an Interval2. Example 13.8: Calculating Normal Tail Probabilities

B. The Binomial Distribution1. Example 13.9: Calculating Exact Binomial Probabilities2. Example 13.10: The Normal Approximation to the Binomial

References

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CHAPTER 14Advanced Statistical Methods

I. IntroductionII. Data Relationships

A. All Independent Variables1. Correlation Analysis2. Principal Components Analysis3. Cluster Analysis

B. Dependent and Independent Variables1. Regression Analysis

a. Simple Linear Regressionb. Multiple Linear Regression

2. Principal Component Regression3. Partial Least Squares Regression4. Discriminant Analysis

III. The Treatment Structure of an Experimental DesignA. Factorial Treatment StructuresB. Fractional Factorials and Screening Studies

1. Constructing Fractional Factorials2. Plackett-Burman Experiments3. Analysis of Screening Studies

C. Response Surface MethodologyReferences

CHAPTER 15Guidelines for Choice of Technique

I. IntroductionA. Define the Project ObjectiveB. Define the Test ObjectiveC. Reissue Project Objective and Test Objectives — Revise Test Design

Table 15.1. Types of Problems Encountered in Sensory AnalysisTable 15.2. Area of Application of Difference Tests:

Does a Sensory Difference Exist Between Samples?Table 15.3. Area of Application of Attribute Difference Tests:

How Does Attribute X Differ Between Samples?Table 15.4. Area of Application of Affective Tests Used in Consumer Tests and

Employee Acceptance TestsTable 15.5. Area of Application of Descriptive TestsReference

CHAPTER 16Guidelines for Reporting Results

I. IntroductionII. Summary

III. ObjectiveIV. ExperimentalV. Results and Discussion

References

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STATISTICAL TABLESTable T1. Random Orders of the Digits 1 to 9: Arranged in Groups of Three ColumnsTable T2. The Standard Normal DistributionTable T3. Upper-α Probability Points of Student’s t-DistributionTable T4. Percentage Points of the Studentized Range: Upper-α Probability Points

for Tukey’s HSD Multiple Comparison ProcedureTable T5. Upper-α Probability Points of χ2 DistributionTable T6. Upper-α Probability Points of F-DistributionTable T7. Minimum Number of Assessments in a Triangle TestTable T8. Critical Number of Correct Responses in a Triangle TestTable T9. Minimum Number of Assessments in a Duo-Trio or One-Sided Directional

Difference TestTable T10. Critical Number of Correct Responses in a Duo-Trio or

One-Sided Directional Difference TestTable T11. Minimum Number of Assessments in a Two-Sided Directional

Difference TestTable T12. Critical Number of Correct Responses in a Two-Sided Directional

Difference TestTable T13. Minimum Number of Assessments in a Two-out-of-Five TestTable T14. Critical Number of Correct Responses in a Two-out-of-Five Test

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