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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]

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]

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]

Psychometric functions for discrimination tests, which connect probabilities of correct response, pc, with Thurstonian discriminal distances, d′, are of theoretical and practical significance. This paper uses a computer-intensive approach to produce simulation-derived psychometric functions for the ' M + N' test, which is a generalization and can be considered as a framework of many forced-choice methods. The paper demonstrates and describes chance probabilities in different situations for the ' M + N' test. The paper compares the performances of the specified and unspecified ' M + N' test with the M = N test. The paper provides novel tables for pc and d′ for four specific versions of the ' M + N' test: the specified 'two-out-of-five' test (i.e., the ' M + N' test with M = 3 and N = 2); the unspecified 'one-out-of-four' test (i.e., the ' M + N' test with M = 3 and N = 1); the specified and unspecified octad tests (i.e., the ' M + N' test with M = N = 4). The corresponding B values, for calculation of the variances of d' for the tests, are also provided. The concept and practice of pseudo-correct response, i.e., forgiveness introduced by Ennis, are discussed and generalized. Practical Applications Considering the constraints imposed by the products and the circumstances of the business objective, different forms of various difference test method might be selected as the most suitable design. The proposed Thurstonian modeling approach using a simulation-derived psychometric function makes it possible to drive psychometric functions for any one of the more than 40 different versions of the ' M + N' test. This paper shows that a simulation-derived psychometric function is compatible with an exact psychometric function. R/ S-Plus codes for the simulation-derived psychometric functions are also developed and provided. Using this technique, various versions of commonly used sensory difference test methods, including the 2- AFC, triangle and tetrad, can be compared with many more versions of difference test methods. In addition, using the supplied R/ S-Plus codes, the Thurstonian sensory difference measure, d′, can be computed easily and quickly for various forms of the ' M + N' test. [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]

Ratings are widely and frequently used in sensory analysis. However, ratings from different methods cannot be treated equivalently because they represent different types of data generated from different cognitive mechanisms. Ignoring this fact may lead to misleading conclusions about true sensory difference or treatment effects obtained from the ratings data analysis. The receiver operating characteristic ( ROC) curve in signal detection theory is used in this paper to model the ratings of the A- Not A and the same-different methods. This paper comprehensively discusses statistical analysis of the ROC curves for the methods, including presentations of the ROC curve functions, estimations of d′s and their variances, goodness-of-fit tests, difference and similarity tests, testing powers and sample sizes, etc. The paper also discusses alternative indices of sensory difference derived from the ROC curve, including the R-index and Gini index. It is appealing to rethink the significance of the R-index, not only as a powerful test statistic but also as a useful sensory measure. R functions are provided for implementing all the analyses discussed in the paper. Practical Applications This paper provides a variety of approaches and R functions for statistical analysis for the ratings of the A- Not A, and the ratings of the same-different methods. The measures of d′s and other indices, which are method-independent measures of sensory differences and treatment effects, can be estimated from different types of ratings data. [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]

ABSTRACT This article attempts to deliver the following message to the researchers and practitioners in the sensory field. (1) Theoretically, drivers of consumer liking is based on relative importance of explanatory variables in a linear model. The problem is complicated when the variables involve linear dependence, which is the common situation in sensory and consumer data. (2) The commonly used methodologies, e.g., conjoint analysis, preference mapping and Kano's model, have serious limitations for determination of relative importance of correlated attributes and identification of drivers of consumer liking. (3) The conventional statistics, e.g., correlation coefficient, standard regression coefficient and P values of tests for regression parameters, etc., are inadequate and invalid measures of relative importance of correlated attributes. (4) There are three state-of-the-art methods for determination of relative importance of correlated attributes. They are the Lindeman, Merenda and Gold's method, Breiman's Random Forest and Johnson's relative weight. This article also provides statistical background and almost exhaustive main references on the topic of relative importance of variables scattered in various academic journals in different fields. The information will help the sensometricians and researchers with more statistical knowledge to embrace the mainstream of the research on the topic and to pursue advanced methods for drivers of consumer liking. PRACTICAL APPLICATIONS This article reviews some new methods for determination of relative importance of correlated explanatory variables to response variable in a regression model. The methods can be used for identification of drivers of consumer liking. The article also provides the sources of the corresponding computer packages and codes implementing the new methods. The packages and codes are freely available and easy to use. The R packages 'relaimpo' for the LMG method, 'randomForest' and 'party' for the original and modified Breiman's Random Forest method are available at . The R or S-Plus code 'johnson' for Johnson's relative weight is available from the online supplementary Appendix S1 of this article. [ABSTRACT FROM AUTHOR]

ABSTRACT Bayesian theory provides another philosophy of statistics and reasoning for data analysis. It offers an alternative to classical statistical inference. Bayesian approach is of theoretical and methodological significance to sensory discipline and has potentially wide application in sensory and consumer research. This paper discusses Bayesian approach to nonreplicated sensory preference, difference and equivalence tests based on proportions. Bayesian approach to the tests involves Bayesian inference for one proportion with and without background effect (i.e., guessing probability) and for two proportions. Thurstonian discriminal distance d′ is used for measure of sensory difference in Bayesian approach. A set of R and S-Plus codes implementing the Bayesian estimates and tests introduced in the paper is available from the supporting information in the online version of this paper. PRACTICAL APPLICATIONS Sensory preference, difference and equivalence tests are widely used in sensory analysis and consumer research. Bayesian approach provides an alternative to classical statistical inference for the tests. If sample size is large enough or prior distribution is less informative, the results from classical statistical inference and Bayesian approach may not differ greatly; while if sample size is small and prior distribution is more informative, the results may be dramatically different. [ABSTRACT FROM AUTHOR]

The table of critical values for significance tests for the R-index was updated and extended in the present article. A more accurate estimator of variance of the R-index, instead of the maximum variance of the R-index, was used in the calculations of the critical values of the table. Sample sizes were extended from 100 to 1,000. PRACTICAL APPLICATIONS Prior to this article, the significance of the R-index values could only be determined for sample sizes of 100 and less. This article enables significance to be determined for sample sizes as large as 1,000, which will be especially useful for the larger samples required for consumer testing. [ABSTRACT FROM AUTHOR]

R -index is an important statistic for testing and measuring product effects. The validation and merits of R-index are to a great extent due to the fact that it is closely related to the famous Mann–Whitney U statistic. Based on this fortunate relationship, statistical analyses for R-index are explored. The statistical analyses include estimations of R-index and its null and nonconditional variances with and without assuming continuity of data; difference and similarity tests using R-index; powers and sample sizes for the tests; linking R-index with Thurstonian δ (or d′). The new techniques developed in the paper extend greatly the original R-index analysis for categorical ratings data. It is expected that the recognition of the profound theoretical origin of R-index and the available statistical analyses for R-index will provide the impetus for the resurgence of interest in using R-index in sensory and consumer researches. [ABSTRACT FROM AUTHOR]