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The Two‐Out‐of‐Five method is one of the basic sensory discrimination methods. It is a special case of the 'M+N' method with M = 3 and N = 2. Three variants of the method are discussed in the paper: specified, unspecified, and unspecified with forgiveness. Analytical and simulation‐derived psychometric functions for all three variants of the Two‐Out‐of‐Five method are derived and produced. The performance of the method in both difference and similarity/equivalence tests are explored. It is shown that both difference and similarity/equivalence testing powers for the specified Two‐Out‐of‐Five are larger than those for the 2‐AFC and 3‐AFC. Both difference and similarity/equivalence testing powers for the unspecified Two‐Out‐of‐Five are larger than those for the Triangle and Duo‐trio. Both difference and similarity/equivalence testing powers for the unspecified with forgiveness Two‐Out‐of‐Five are larger than those for the conventional unspecified Two‐Out‐of‐Five and unspecified Tetrads. Tables and R codes are presented and provided for estimations of the probability of correct response, Pc, Thurstonian discriminal distance δ or d', and the B value for estimating the variance of d' for the three variants of the Two‐Out‐of‐Five method. Practical Applications: The Two‐Out‐of‐Five method is a powerful sensory discrimination method. However, this method has not been used widely in sensory and consumer research, partly since the method has not been explored adequately in the literature. This paper explores the Two‐Out‐of‐Five method and shows that the method has potential for wide application. The Two‐Out‐of‐Five method involves a larger number of samples (5) and sensory fatigue may be of concern. Hence, the method may not be suitable for taste and smell tests with strong stimuli. The method is particularly suitable for manual and visual inspection testing where sensory fatigue is of a lesser concern. [ABSTRACT FROM AUTHOR]

A 12‐week longitudinal study with 247 US menopausal women was undertaken to investigate the perceptual efficacy of a tablet formulated with an extract of Siberian rhubarb to provide relief from menopausal symptoms. The 5‐point menopause rating scale (MRS) (0 = none; 1 = mild; 2 = moderate; 3 = severe; 4 = extremely severe) was used to measure symptom intensity. The MRS scale, an ordinal categorical scale, was transformed into an R‐index, a ratio scale, using the frequencies of the MRS categories. Symptom relief was compared to an initial week baseline measure; defined as R‐index = 0.5. An index, A.RDEX, which is based on area under the R‐index curve (AUC) in the range of 0–84 days was used to measure percentage efficacy of symptom relief. Results show that symptom relief occurs through the first 17 days in terms of R‐index = 0.64 for the total score and improves with continued use, reaching an A.RDEX = 0.42 by 84 days, suggesting about 42% relief considering all 11 MRS attributes. Practical Applications: MRS ratings data can be transformed into an R‐index using MRS category frequencies at an initial week and a subsequent week. Functional data analysis for R‐index values provides an advanced statistical model for analysis of perceptual differences throughout longitudinal studies that can examine MRS attribute effects over time. R codes are developed and provided in the paper to transform MRS data into R‐index measures and to conduct functional data analysis for R‐index measures obtained from different time points (weeks or days). [ABSTRACT FROM AUTHOR]

The sparse hierarchical clustering (SHC) method and the R package "sparcl" are used for consumer segmentation with 247 perimenopausal and postmenopausal US women. The data includes 11 menopause rating scale (MRS) attributes measuring severity of symptoms collected in the first week of a 12‐week extended use menopause tablet perceptual efficacy study. SHC is one of the advanced statistical clustering approaches for high‐dimensional data with potential noise variables. Sparse clustering is an important topic of the actively developing field of statistical learning with sparsity. An advantage of the SHC method is that it simultaneously finds the clusters of subjects and the important clustering variables. It allows clustering the data in low‐dimensional subspaces without dimension reduction of the data before clustering. The SHC method is particularly applicable to consumer segmentation based on high‐dimensional consumer data. Practical Applications: Sparse hierarchical clustering (SHC) provides advantages in consumer segmentation based on high‐dimensional consumer data with potential noise variables. This advanced clustering method finds the relative importance of attributes in clustering, helping to identify homogeneous clusters and enhance understanding of how consumer responses/needs vary among clusters. [ABSTRACT FROM AUTHOR]

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This article explores the two‐interval, two‐alternative forced‐choice (2I2AFC) paradigm in signal detection theory (SDT), which can also be called the paired A‐Not A with AB and BA pairs in the sensory and consumer fields. The article describes how to estimate the parameters and their variances from the psychometric function of the method. Tables and R codes were developed and are provided for the estimations. The performance of the method is evaluated. It shows that the paired A‐Not A with AB and BA pairs is more effective and powerful than the conventional A‐Not A and the A‐Not A with reminder (A‐Not AR) tests. An extension of the method, that is, the ratings of the paired A‐Not A with AB and BA pairs is also explored. A facial shine case study applying this method is provided. Practical applications: As one of the paired versions of sensory discrimination methods, the paired A‐Not A with AB and BA pairs has wide potential applications to detect and measure sensory difference, especially to detect and measure before‐after treatment effects of products. The method can be used to detect both product effects and serving order effects. [ABSTRACT FROM AUTHOR]

The unspecified tetrad is a powerful non‐attribute‐specified sensory discrimination method widely used for sensory analysis and consumer research. A paired version of the method is proposed and explored in this article. It is the paired unspecified tetrad with different order (AB and BA) pairs. An analytical and a simulation‐derived psychometric function of the new method are produced. The paired unspecified tetrad with AB and BA pairs is more powerful than the conventional unspecified tetrad and the paired versions of the triangle and duo‐trio methods. A weakness of the paired version of the unspecified tetrad versus the conventional unspecified tetrad is that the new method involves in more adaption, fatigue, or memory factors. Practical Applications: The paired unspecified tetrad with different order (AB and BA) pairs has wide potential applications, especially for visual or manual inspection of food or nonfood products to detect before–after treatment effects, but may not be suitable for food tasting considering the adaption, fatigue, or memory factors. [ABSTRACT FROM AUTHOR]

There are two main objectives of this paper. One is to review the current Thurstonian models for the conventional and modified triangle and duo‐trio methods. Another objective is to develop Thurstonian models for, and assess the performances of the paired triangle and paired duo‐trio methods with AB and BA pairs. Bradley's models based on the noncentral F distribution for the triangle and duo‐trio methods are revisited and are used to derive the psychometric functions for the paired versions of the triangle and duo‐trio methods. The simulation‐derived psychometric functions for the new methods are also produced. The performances of the new methods in both difference and similarity/equivalence tests are explored and show that the new methods are more powerful than most of the conventional unspecified forced‐choice methods and are similar to the unspecified tetrad. Practical applications: The triangle and the duo‐trio methods are popular sensory discrimination methods used widely in sensory and consumer research. One weakness of the methods is relatively lower testing power. The paired triangle and paired duo‐trio methods proposed and explored in this paper overcome this weakness of the conventional methods. The paired versions of the methods are more powerful than most of the conventional unspecified discrimination methods in difference and similarity tests for products. The new methods are particularly suitable for assessment of before–after treatment effects of products. The methods have wide potential application for visual and manual inspection testing of food or non‐food products where less sensory fatigue is of concern. R codes were developed and provided in the paper for the Thurstonian models of both the conventional versions and the paired versions of the triangle and the duo‐trio methods. [ABSTRACT FROM AUTHOR]

In recent sensory literature, Bi and Kuesten (2015a. Food Quality and Preference, 43, 47-52; 2015b. Journal of Sensory Studies, 30, 461-471) have proposed the 'M + N' classification method with larger M and N (>3) for discrimination testing based on Fisher's exact test. Industry studies using the method are shared in this article to illustrate application of the method. The tests and measures are taken for non-fatiguing visual and manual inspections conducted across a variety of product categories. Further, within the examples provided, a validation between labs is documented and results of the method are compared to results from other methods (2-Alternative Choice and 2-Alternative Forced Choice) based on common conventional sensory measurement Thurstonian d′. Estimations are given of Intraclass Correlation Coefficient and Cronbach's coefficient alpha for evaluation of panel performance in the test using the 'M + N' classification method with larger M and N (only for M = N > 3). Practical applications Sorting methods are popular and often used for rapid investigation of product quality, product differences, or consumer perception and are used to help guide product maintenance and/or development efforts. The 'M + N' classification method with larger M and N, a type of sorting technique, can be applied for sensory discrimination and perceptual tests with generation of various indices, including Thurstonian discriminal distance delta (or d′) thereby offering the ability to compare results with other sensory discrimination methods. [ABSTRACT FROM AUTHOR]

The m-Alternative Forced Choice ( mAFC), including the 2AFC, 3AFC, and mAFC where m > 3, are a type of widely used sensory discrimination method. This article offers an interesting finding for the psychometric function for the mAFC. The conventional general psychometric function for the mAFC, which is based on m independent normal distributions with one signal and m−1 noise observations, can be expressed as an elegant simplified form, i.e., a single cumulative distribution function (cdf) of the standard ( m−1)-variate normal distribution. This finding provides not only an alternative approach to calculate the probability of correct responses ( Pc) and Thurstonian discriminal distance ( δ) for the mAFC, but also an intuitive geometric interpretation for Pc in the mAFC. Moreover, the simplified form of the psychometric function for the mAFC may provide some insight for the decision strategies used in the mAFC. Practical Applications The simplified form of the psychometric function for the mAFC derived originally in this paper can be expressed in a built-in S-Plus program ' pmvnorm' (for 3AFC) and R program ' pmvnorm' (for mAFC where m > 2) in the R package 'mvtnorm.' Two R codes 'mAFCp' and 'mAFCq,' which are based on the simplified form and the R package, were developed in the article. The codes can be used for calculations of Pc and δ for the mAFC easily. A table for Pc values in the mAFC is produced for m = 2 to 8, and δ from 0 to 4 with a step of 0.1. A table for δ values in the mAFC is produced for m = 2 to 8, and Pc from 0.01 to 0.99 with a step of 0.01. A table for the B values for calculation of variance of d-prime obtained from the mAFC is also produced. [ABSTRACT FROM AUTHOR]

In a recent paper in the sensory literature, the method of "M + N" with larger M and N is proposed to be a new kind of sensory discrimination method. Fisher's exact test is used for the method for discrimination testing. The current article focuses on sensory measurements for the method. Five indices for sensory measurements and effect-sizes are derived, estimated, and proposed. The indices include log odds ratio, R-index, Thurstonian discriminal distance δ (or d'), Cohen's D (or d) and Gini-index. Variances of the estimators of the indices are also produced. With the proposed indices, the method of "M + N" with larger M and N can be connected to and compared with the conventional sensory discrimination methods based on common sensory measurements. [ABSTRACT FROM AUTHOR]

The Benchmark Dose ( BMD) methodology is a statistical tool for quantitative risk assessment. It has been developed as an alternative to the approach of 'no observed adverse effect level' or 'lowest observed adverse effect level' during the last decades in many scientific fields for risk assessment. Because risk is various and ubiquitous, the BMD methodology has potential applications in the food science field for risk assessment of negative sensory effects in product development and sensory and consumer research. This paper discusses the BMD analysis in a product development effort using ratings data and Thurstonian discriminal d′ data. Practical Applications Risk assessment of negative sensory effects in product development using the Benchmark Dose ( BMD) methodology has two major objectives. One objective is to determine an appropriate change of ingredient for a product at an allowed risk. The second objective is to assess the risk of negative sensory effects associated with a particular change. The well-developed U. S. Environmental Protection Agency's ( EPA) Benchmark Dose Modeling Software ( BMDS) and the R/ S-Plus codes developed and provided in the paper can be used for BMD analysis. [ABSTRACT FROM AUTHOR]

Torgerson's complete method of triads is a famous and useful method for com-parison of multiple samples. However, this method has not been used widely in the sensory field. One possible reason is that the Thurstonian model of the method is complicated and there is no published tables and available computer software for applications of the method. This paper discusses a Thurstonian model for a special case of the method with one control sample and two test samples. A table for Thurstonian discriminal distances and proportions of responses is produced. A set of R/S-Plus codes was developed and provided for applications of the method including estimations of parameters and covariance matrix, difference and similarity tests. A case study is provided for illustration of applications of the methods. The main novel contributions of this paper to the method are (1) using a computer-intensive approach to produce a simulation-based psychological function for the special case of the method and (2) using a delta method to derive a covariance matrix of the estimators of the two Thurstonian discriminal distances. [ABSTRACT FROM AUTHOR]

Measuring and analyzing time-intensity ( T- I) of sensory attributes is an important subject of sensory analysis. This paper proposes using functional data analysis ( FDA), an emerging field in statistical research, as a new strategy and framework for sensory T- I data analysis. This paper discusses and illustrates how to apply the well-developed FDA techniques and use the available R package 'fda' to analyze sensory T- I data. The analyses include data smoothing, descriptions of functional data, functional regression analysis, functional analysis of variance and permutation tests of functional hypotheses (functional F-tests and t-tests). Some conclusions about applications of FDA to sensory T- I data are reached. Practical Applications The currently used statistical analysis for sensory T- I data is not well developed. There are some limitations of using univariate and multivariate data analyses for sensory T- I data. FDA is a promising alternative. This paper shows some advantages using FDA and the R package 'fda' for the analysis of sensory T- I data. It is expected that the introduction and application of FDA in the sensory field will dramatically improve data analysis for T- I evaluation of sensory attributes. [ABSTRACT FROM AUTHOR]

Sensory measurement underlies sensory science. Sensory analysis and decision-making heavily depend on the quality of sensory data, which is determined by the performance of trained sensory panels and panelists. Various methods have been proposed for monitoring and assessing the performance. A weakness of the currently used methods is lack of a unified framework for various criteria and a variety of experiments with different types of data. This paper proposes to use accuracy, validity and reliability as general terminologies to describe sensory measurement and to apply the intraclass correlation coefficient ( ICC) as a framework for monitoring and assessing performance. ICC can measure both similarity among panelists and sensitivity of panels and panelists. Hence, ICC can handle the problems of both reliability and validity. ICC can be obtained from different types of data for diverse experiments. This paper provides the equations and R and S- Plus functions for estimations of ICCs from continuous data (ratings), multivariate continuous data, ordinal data, ranking data, binary-choice data, multiple-choice data and forced-choice data. Confidence intervals, variances of the estimators, comparison with a fixed value and difference and similarity tests for multiple ICCs are also provided. The relationship between Cronbach's coefficient alpha and ICC is discussed. Practical Applications Intraclass correlation coefficient ( ICC) may play a framework role in monitoring and assessing performance of trained sensory panels and panelists. It can be used as an index of the quality of sensory data. The larger the ICC or Cronbach's coefficient alpha value, the better the performance of panels and panelists. If and only if an ICC is significantly larger than a specified value, can the quality of the data for that attribute be regarded as acceptable. A statistical test that fails to show that an ICC or Cronbach's coefficient alpha is significantly larger than a specified lowest limit, e.g., 0.1, suggests that the products are undiscriminating, or the sensory data, at least for that attribute, might not be valid and reliable. We should use that data with caution. [ABSTRACT FROM AUTHOR]