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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]

• Functional data analysis (FDA) for Rating Scale (RS) Time-Intensity (T-I) data. • The mean RS functional curves and their 1st and 2nd derivative curves. • The index of efficiency (A.RS) based on area under curve for percentage (%) relief. • Functional analysis of variance (FANOVA) for detection of group effects. A longitudinal study was undertaken recently in the USA to investigate the perceptual efficacy of a supplement tablet. Efficacy was assessed using an 11-attribute 5-point Rating Scale (RS). The RS diary time-intensity data were analyzed using functional data analysis (FDA). The mean RS functional curves and their 1st and 2nd derivative curves are produced. Attribute intensities (symptom relief) are compared to baseline measures. Two indices of efficacy were used to measure reduction in symptom severity. Results show symptoms decreased over the 12-week study with use of the tablet. The focus of this paper is on applied use of FDA and the new index A.RS which shows advantages by providing examination of the full range of longitudinal data (0–84 days) and a percentage efficacy index versus a traditional efficacy index that is based on the difference between just two time points (day 0 and day 84). The analytic methods in this paper have relevancy for sensory and consumer time-intensity research and longitudinal study. [ABSTRACT FROM AUTHOR]

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]

We propose objective, image-based techniques for quantitative evaluation of facial skin gloss that is consistent with human judgments. We use polarization photography to obtain separate images of surface and subsurface reflections, and rely on psychophysical studies to uncover and separate the influence of the two components on skin gloss perception. We capture images of facial skin at two levels, macro-scale (whole face) and meso-scale (skin patch), before and after cleansing. To generate a broad range of skin appearances for each subject, we apply photometric image transformations to the surface and subsurface reflection images. We then use linear regression to link statistics of the surface and subsurface reflections to the perceived gloss obtained in our empirical studies. The focus of this paper is on within-subject gloss perception, that is, on visual differences among images of the same subject. Our analysis shows that the contrast of the surface reflection has a strong positive influence on skin gloss perception, while the darkness of the subsurface reflection (skin tone) has a weaker positive effect on perceived gloss. We show that a regression model based on the concatenation of statistics from the two reflection images can successfully predict relative gloss differences. [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]

Highlights • The 4I2AFC is a paired 2-AFC with AB and BA pairs. • The 4I2AFC can be used to detect small changes of stimuli. • The 4I2AFC can be used to identify direction of stimuli changes. • The 4I2AFC is more powerful than the tetrads in both difference and similarity testing. • The 4I2AFC is particularly suitable for visual or manual evaluations with less sensory fatigue. Abstract The four-interval, two-alternative forced-choice (4I2AFC) is a paired version of the 2-AFC with AB and BA pairs as two alternatives, where A is a signal or a stronger stimulus and B is a noise or a weaker stimulus. The task of the subject in 4I2AFC is to select the pair (AB) with decreasing stimuli change. The 4I2AFC is a powerful sensory discrimination forced-choice method to detect small, directional changes of stimuli particularly suitable for visual or manual evaluations with less sensory fatigue. This paper explores the 4I2AFC method and includes an applied illustrative case study for measuring facial skin smoothness visually using the method. An analytical psychometric function is derived. The performances of the 4I2AFC in both difference testing and similarity/equivalence testing are compared with those of the conventional sensory discrimination forced-choice methods. The 4I2AFC is theoretically more powerful than any of the published conventional methods including the tetrads. [ABSTRACT FROM AUTHOR]

This paper proposes a new type of sensory discrimination methods, i.e., paired versions of various sensory discrimination forced-choice methods, which can be regarded as modified versions of the same-different method. The new type of methods possesses the advantage of the same-different test for measuring overall sensory difference, but overcomes its weaknesses of large variations of response bias and lower testing power. An important finding is that this type of methods is closely related to the same-different area theorem and its extension. The same-different area theorem establishes an equivalence between the area under the receiver operating characteristic (ROC) curve of the same-different method and the proportion of correct responses ( P c ) in the dual-pair method. This paper re-demonstrates and extends the same-different area theorem. An analytical expression of a general psychometric function for the new type of methods is derived. Performances of the new type of methods are evaluated with testing power and sample size in both difference and similarity/equivalence tests. R codes are provided for the new type of methods for P c , Thurstonian discriminal distance δ, and variance of d′ , where d′ is an estimator of δ. [ABSTRACT FROM AUTHOR]

Consumers’ affective states associated with product development are hot topics and an important area of consumer research. The Profile of Mood States 2nd Edition TM – Adult (POMS 2-A™) with 65 items and 5 negative scales can be used to assess adult consumers’ affect. Consumer POMS data collected in the US for the NUTRILITE™ brand multivitamin multimineral supplement product are analyzed using an advanced statistical model and the R package ‘repolr’. This proportional odds model (POM) fitted with generalized estimating equations (GEE) is more appropriate for repeated ordinal categorical data than conventional ANOVA. Analysis of the data collected before product testing show that there are significant user group effects for each of the 7 POMS scales and significant gender and age group effects for some scales. Product users, females and age group 45–55 show larger scores for positive scales and smaller scores for the negative scales than non-users, males and other age groups. Analysis of the data collected after product testing shows that there are significant product effects for some scales of POMS (Depression-Dejection, Anger-Hostility, and Total Mood Disturbance). The estimated effect parameters in the model, i.e., log odds ratio values, can be transformed into Thurstonian discriminal distance δ or d -prime and other sensory measures, offering all the advantages of Thurstonian modeling and ease of interpretation of the results. Further analysis shows that although the results using conventional ANOVA are consistent with the results using the advanced POM model, the POM model for the POMS data is more valid and powerful than conventional ANOVA. [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]

• Simulated Type I errors rates of ANOVA based on GLM and LM models for CATA data. • Simulated testing powers of ANOVA based on the GLM and LM models for CATA data. • Predicted precisions using GLM and LM models for CATA data. • The claim that logistic regressions violate Type I error rates is not generally true. • Liberty or conservativeness is not a criterion of validity or invalidity of a test. Some discussions about statistical models used for analysis of CATA data appear in recent issues of this journal. This paper is a further discussion on the topic, following Bi and Kuesten (2022) (Food Quality and Preference , 95), related to Meyners and Hasted (2021, 2022) (Food Quality and Preference , 92, 95). This paper presents some statistical analyses for a real consumer CATA dataset using a generalized linear model (GLM) and a linear model (LM), respectively. The main objectives are to simulate Type I error levels of ANOVA; to simulate the empirical testing powers of ANOVA; and to compare testing results and predicted precisions based on different models. Meyners and Hasted (2022) claim that logistic regressions violate Type I error rates. The simulation results show that the claim is not generally true and suggest that violating Type I error rates is due to two-way ANOVA with a special type of Sums of Squares (Type2SS), not due to the GLM. Meyners and Hasted (2022) conclude that the GLM or logistic regression is invalid and flawed for analysis of CATA data. We disagree with the conclusion because we cannot find any convincing reasoning supporting the conclusion. It is true that the test of two-way ANOVA with Type2SS based on the GLM is more liberal than that with Type1SS and that based on the LM. Liberty and conservativeness are a characteristic of a test, not a criterion to judge validity or invalidity of a test. Meyners and Hasted (2022) advocate that GLM should be precluded for the use of CATA data. Our position is that the GLM deserves to be a standard and first selected practice, at least one of the useful and valid methods for analysis of CATA data. The advocacy of precluding the GLM for analysis of CATA data is unacceptable. [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]

Psychographics data were collected from three global consumer studies for phytonutrient supplements products. The objective of this paper was to explore the usage of the psychographics and other consumer data for sensory causal inference, i.e., cause-and-effect inference, rather than conventional statistical associational inference. In this work, three case studies are presented for different key measures from each study with different resulting outcomes. For each case study, propensity score analysis (PSA) was applied to account for consumer covariates after down-selection of the many scales included in each study to those of relevant importance. Causal effects are shown to be not significant in two of the three case studies, but larger than the associational effects; and importantly, one of these studies shows direction of the effects changed. The third case study shares a situation where the associational effect is not significant, however significant causal effects were found. These findings suggest accounting for consumer psychographic and other covariates is prudent for researchers to consider, especially for observational studies where many important covariates exist that may confound results and interpretations. Results show the PSA methodology using psychographics and other data for causal inference provides useful insights that may lead to implications for business decision-making. [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]

• General self-efficacy measures are collected from Japanese consumers. • Agglomerative hierarchical clustering is applied for consumer segmentation. • Clusters formed from general self-efficacy ratings are reviewed. • Clusters are compared/contrasted with selected psychographics and hedonics. • The implications of general self-efficacy cluster differences are discussed. Segmentation based on psychographics data is a relatively new topic and one of the current trends of consumer research within the sensory and consumer research fields. In this paper, Japanese consumer segmentation was conducted based on General self-efficacy (GSE) self-assessment collected in a phytonutrient supplement study. The aim of this study was to understand the influence of GSE on self-reported health behaviors, well-being, and product involvement and liking. The product tested was a 3-tablet phytonutrient supplement, 2 of each to be taken twice daily for 5 days; n = 206 vitamin mineral supplement (VMS) users participated in the study. The agglomerative hierarchical clustering method was used in the segmentation. Two clusters were identified that distinguished those with higher vs lower GSE. Results indicate those with higher GSE have a higher overall sense of well-being , are more actively looking for products and services that help them live a healthy lifestyle and are more involved with the product (phytonutrient tablets). Those with higher GSE also tend to rate the product more favorably on Overall Liking. These findings extend our understanding of GSE and the influential role of psychographics on responses for the phytonutrient supplement category. Further, these results suggest future efforts to increase GSE may help increase involvement and engagement with the category toward quality-of-life improvement. [ABSTRACT FROM AUTHOR]

The Lady Tasting Tea is a famous real story in the history of development of statistics, related to R.A. Fisher, one of the greatest statisticians and founders of modern statistics. The main learning and insight offered by this paper from revisiting the story are that the methodology of conventional sensory difference tests can be and should be expanded to cover the ‘ M + N ’ method with larger M and N . Unlike the conventional discrimination tests, which use multiple sets of ‘ M + N ’ samples with small M and N based on a binomial model, the ‘ M + N ’ tests with larger M and N can reach a statistical significance in a single trial using only one set of ‘ M + N ’ samples based on a hypergeometric distribution in Fisher’s exact test. This paper explores the applications of the new methods particularly in assessing performance of trained sensory panels and panelists. The connection of the odds ratio or common odds ratio with Cohen’s standardized mean difference d is also discussed. [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]

Highlights: [•] PANAS emotions associated with aromas of phytonutrient supplements were measured. [•] PANAS scales are valid measurements of consumer emotion of phytonutrient aromas. [•] Long (20-item) and short (10-item) PANAS scales are consistent but not equivalent. [•] Aroma discrimination was demonstrated using PANAS positive and negative dimensions. [•] Consumer hedonic, sensory, and emotional attributes represent different dimensions. [ABSTRACT FROM AUTHOR]

Highlights: [•] Classical time-intensity is extended with MATI (multi-attribute time-intensity). [•] Data was collected with descriptive and consumer panels on taffy chews. [•] MATI offers concurrent evaluation of multiple intensity and hedonic attributes. [•] Some analytics are novel and avoid limitations in other time–intensity analytics. [•] MATI statistical methods offer panel and panelist performance assessment. [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]

• GLM is more appropriate for testing product difference with CATA data. • Multiple comparisons based on GLM with a binomial distribution for CATA data. • Cochran's Q test and normal approximation for CATA data have historical importance. • There is no sound reason nowadays to use these methods for CATA data analyses. ANOVA and multiple comparisons based on generalized linear model (GLM) with a binomial distribution are proposed to be used for testing product differences with CATA data. The methods of Cochran's Q test and ANOVA based on a normal distribution for CATA data analyses have only historical significance. There is no sound reason nowadays to insist on using these methods for CATA data analyses from both a theoretical and a practical perspective. [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]

• TURF (Total Unduplicated Reach and Frequency) is proposed for analyzing CATA data. • CATA examples from a women's multi-vitamin/mineral gummy survey are shared. • R code 'turfcata' is provided and used with the R package 'turfR'. CATA (Check All That Apply) questions are one of the most popular approaches used widely in sensory and consumer fields. This paper proposes to apply the TURF (Total Unduplicated Reach and Frequency) technique to summarize and analyze CATA data. Numerical examples from a women's multi-vitamin/mineral gummy survey conducted online recently in the US are provided to show the TURF analysis for CATA data. The R package 'turfR' was used in the analysis of the CATA data. An R code ('turfcata') was developed and is provided for the analysis using the R package 'turfR'. [ABSTRACT FROM AUTHOR]

• Performance reliability of sensory descriptive panels is critical to sensory analysis. • Intraclass correlation coefficient (ICC) and Cronbach's coefficient alpha can be used to measure performance reliability (PR). • Thurstonian d-prime and R-index can be used to measure Effect Size (ES). • Performance Reliability versus Effect Size (PR-ES) can be used as a framework for analysis of sensory descriptive panel data. • An historical protein powder case study is shared using the PR-ES framework. Performance reliability of sensory descriptive panels is critical to sensory analysis. Treatment effect size (ES) of products is a main objective of sensory analysis. The intraclass correlation coefficient (ICC) and Cronbach's coefficient alpha can be used to measure performance reliability, while Thurstonian d-prime and R-index can be used to measure ES. In this paper, an industry case study with a full historical database spanning 10 years of protein studies is shared. This case study uses the analysis framework of Performance Reliability versus Effect Size (PR-ES). R codes for the analysis are developed, used, and provided in the paper. [ABSTRACT FROM AUTHOR]

Objectives: Translucent skin is an attribute widely appreciated by people in East Asian countries. There have been studies in the literature to describe the phenomenon by means of clinical grading, instrumental measurement and image analysis. However, due to its subjective and complex nature, skin translucency has not been comprehensively and rigorously characterized and modelled, particularly in the Chinese population. This study is to develop a mathematical model that quantitatively describes skin translucency from visual cues objectively measured from the skin. Materials and Methods: The study was designed to characterize and model skin translucency by incorporating expert evaluation, panel perception and image analysis of multiple skin visual attributes in one analysis. Faces of 36 Chinese females aged 18–65 years old were evaluated by a dermatologist to obtain clinical translucency scores. Subject pairs were formed with a relatively high and low translucency score in each pair. Their faces were judged in person by 9 panellists in paired‐comparison (2‐AFC) fashion to pick a 'more translucent skin' from each subject pair. Front‐view facial images of the subjects were taken, and multiple colour and other visually perceivable skin attributes were measured using image analysis. Bradley‐Terry analysis and multiple regressions were performed to correlate the panel choices of 'more translucent skin' with the objectively measured skin parameters. Results: Multiple skin colour properties affected the panel choices towards translucent skin. Among them skin tone lightness and skin glossiness had positive effects on skin translucency while the hue, colour unevenness, severity of red and dark spots affected it negatively. Subsurface light reflection and skin visual smoothness had some effect but were not statistically significant. A mathematical model was constructed to predict a person's skin translucency from objectively measured skin attributes. Conclusion: The subjective property of skin translucency can be characterized and quantified via a comprehensive modelling process involving clinical grading, panel evaluation, image‐based measurement of skin attributes and statistical analysis. A novel skin parameter, Skin Translucency Index (STI) was established, which provides a way to measure skin translucency, making it possible to assess treatment efficacy before and after product application. [ABSTRACT FROM AUTHOR]