The use of analysis of variance and three-way factor analysis methods for studying the quality of a sensory panel

In sensory analysis a panel of assessors evaluate a collection of samples/products with respect to a number of sensory characteristics. Assessments are collected in a threeway data matrix crossing products, attributes and assessors. The main objective of the experiment is to evaluate products. However, the performance of each assessor and of the panel as a whole is of crucial importance for a successful analysis. At this aim univariate analysis for each sensory attribute as well as multi-way analysis considering all directions of information are usually performed. The present work studies the quality of a panel using both methods. The basic idea is to compare results and investigate relations between the two different analytical approaches

The statistical power of replications in difference tests

It has been argued that the binomial test with N=nk observations is a valid test when n assessors each perform k replicated difference tests, for instance triangular tests, see Various models and approaches to account for the replications have been suggested in the sensory literature. Ennis and Bi (1998) (and other papers by these authors) recommends the beta-binomial model, All these different approaches are compared theoretically and by applications on real data. A striking result is the similarity between beta-binomial models and generalized linear models: The beta-binomial model assumes that the true individual correct answer probabilities follow a beta-distribution. For the generalized linear model the corresponding density is deduced, and despite the apparent difference between the mathematical formulae, plots of the densities show that there is hardly any difference at all between the models induced by the two approaches, see It is shown how the statistical power of the binomial test can easily be computed for the various approaches using Monte Carlo methods and standard software. These power calculations show little difference between the three main approaches: beta-binomial models, generalized linear models and binomial mixture models. They also together with the theoretical comparison show how the simple extreme version of the binomial mixture model can be seen as the common extreme case for all three approaches. This common extreme case scenario corresponds to the situation where each individual is assumed to be either a discriminator (having probability one of correct answer) or a non-discriminator (having probability c of correct answer). Although this is not the proper description of the data generating process it does provide a lower limit of power for a given combination of n and k. Tables of these limit of power is provided for combinations of n=5,..,50 and k=1,..,5. It is shown how this lower limit is high enough to be of practical importance. For instance with n=12 assessors and k=4 replications for each assessor the power of the 0.05-level binomial test with N=48 for an effect size of 25% above chance is 77%. For the extreme case the (lower limit) power is 69%, hence only a moderate loss of power is seen. The power o

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Taking individual scaling differences into account by analyzing profile data with the Mixed Assessor Model

Scale range differences between individual assessors will often constitute a non-trivial part of the assessor-by-product interaction in sensory profile data (Brockhoff, 2003, 1998; Brockhoff and Skovgaard, 1994). We suggest a new mixed model ANOVA analysis approach, the Mixed Assessor Model (MAM) that properly takes this into account by a simple inclusion of the product averages as a covariate in the modeling and allowing the covariate regression coefficients to depend on the assessor. This gives a more powerful analysis by removing the scaling difference from the error term and proper confidence limits are deduced that include scaling difference in the error term to the proper extent. A meta study of 8619 sensory attributes from 369 sensory profile data sets from SensoBase (www.sensobase.fr) is conducted. In 45.3% of all attributes scaling heterogeneity is present (P-value <0.05). For the 33.9% of the attributes having a product difference P-value in an intermediate range by the traditional approach, the new approach resulted in a clearly more significant result for 42.3% of these cases. Overall, the new approach claimed significant product difference (P-value <0.05) for 66.1% of the attributes compared to the 60.3% of traditional approach. Still, the new, and non-symmetrical, confidence limits are more often wider than narrower compared to the classical ones: in 72.6% of all case

Application of replicated difference testing

International audienceIn a recent paper, Brockho and Schlich (1998, Handling replications in discrimination tests. Food Quality and Preference, 9(5), 303±312) proposed a statistically sound way of handling replications in dierence testing. In the present paper, this new test is applied to the data obtained in six experiments on non alcoholic beverages, where triangle tests were intensively replicated (between eight and 60 times) with groups of subjects composed of 12±61 students. The paper aims to estimate in these practical situations the extent to which a group of panelists is heterogeneous towards the ability of detecting a sensory dierence among two products. As the results indicate that group heterogeneity was lower than Brockho and Schlich ®rst guessed, the value of using replicates in dierence testing is emphasized. It seems that, average over experiments, at least 10 replicates were necessary to properly estimate the level of heterogeneity and that a single subject having done 10 replicates would bring to our test the same amount of informa- tion as ®ve subjects having done the test once only