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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]

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]

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]

The present article discusses the replicated similarity testing using a paired comparison method. The “two one-sided tests” (TOST) combined with a beta-binomial model are proposed for this testing. Simulation studies provide evidence that the proposed testing is valid and reliable. [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]

Similarity testing is an important methodology in sensory and consumer research. It is of practical and theoretical significance. In many comparative experiments in sensory and consumer field, the objective is not to demonstrate difference but to demonstrate equivalence or similarity between treatments. It is widely acknowledged that the conventional hypothesis test with the null hypothesis of “no difference” between two treatments is appropriate for difference testing but inappropriate for similarity testing. Schuirmann [Biometrics 37 (1981) 617] introduced the use of interval hypotheses testing in the context of bioequivalence. For the interval hypotheses testing, the null hypothesis is that the difference between two treatments is larger than a specified non-zero value defining equivalence or similarity and the alternative hypothesis is that the difference is smaller than the specified value. If the null hypothesis is rejected, equivalence or similarity is then concluded. Based on this concept and approach, the present paper discusses some statistical procedures of similarity testing used for different situations in sensory and consumer research. The procedures include similarity testing for hedonic or intensity rating means, similarity testing using conventional discrimination methods (forced choice methods and the methods with response bias) and similarity testing for preference proportions. [Copyright &y& Elsevier]