# Sensory Panel Performance Evaluation--Comprehensive Review of Practical Approaches
## 4 Methods, Models and Frameworks in Sensory Panel Evaluation
### Structure and Models of Sensory Data  
Sensory data are typically available as a four-way data structure: numbers of assessors, products, attributes and replicates are the four data modes. This structure determines what types of models can be used. Linear models are routinely used to analyze data (Figure 2). Mostly ANOVA models are used on mean sensory data with the design of experiment (DoE) parameters as factors. Sensory data are first averaged across panelists and replicates, then with the help of DoE parameters (fixed effects) ANOVA models are run on these data. Mixed models on raw sensory data have the subject as a random effect and DoE parameters as fixed effects. In the case of panel performance examinations, significant effects and interactions are chosen [52]. For panel performance tests, only the full factorial design is used. However, balanced incomplete block design (BIBD) is also applied in tests with a high number of samples [53]. The commonly used experimental design is often named Randomized Complete Block Design, within-assessors design or a repeated measures design. In the case of  
Figure 2: Classical four-way data structure of sensory data (based on [13]). replications, the design is named the Randomized Complete Block Design with more than one observation per experimental unit, then the ANOVA model is as follows [45]:  
\[Y_{ijk}=\mu+\alpha_{l}+v_{j}+c_{ij}+\epsilon_{ijk} \tag{4}\]  
where \(\mu\) is the grand mean for attributes, with \(\alpha_{1}\) as the assessor effect, \(v_{j}\) is the product effect, \(c_{ij}\) is the interaction effect (panelist \(\times\) product) and \(\epsilon_{ijk}\) N(0, \(\sigma^{2}\)) is the random replicate error. Instead of the commonly used ANOVA model, [PERSON] and coworkers [48] propose a mixed assessor model (MAM). In the mixed assessor model, the interaction in commonly used ANOVA tests is broken down into a scaling coefficient and a clear disagreement effect. As a result, the products are better separated and the agreement of the assessors is also improved. The MAM model breaks down the interaction into the sum of the scaling coefficient (\(\beta_{i}x_{j}\)) and the pure disagreement (\(d_{ij}\)). Thus, the following mixed assessment model is:  
\[Y_{ijk}=\mu+\alpha_{l}+v_{j}+\beta_{i}x_{j}+d_{ij}+\epsilon_{ijk} \tag{5}\]  
where \(i\) is the number of assessors, \(j\) is the number of products, \(k\) is the number of repetitions, \(\alpha_{i}\) is the assessor effect, \(v_{j}\) is the product effect, \(\beta_{i}\) is the scaling coefficient resulting from the different use of scales by the assessors and \(d_{ij}\) is the clear disagreement. The scaling coefficient \(\beta_{i}\) is obtained from the linear regression. If the assessor uses the scale in the same way as the panel, then \(\beta_{i}=1\), if the assessor's scale is larger than the panel, then \(\beta_{i}>1\), if the assessor's scale is smaller than the panel, then \(0<\beta_{i}<1\). If a negative value is given, the scale is misunderstood by \(\beta_{i}<0\). In summary, the advantage of the mixed assessor model is that it takes into account the scaling differences, as product averages are incorporated into the modeling as covariates and allows the covariance regression coefficients to depend on the assessors [54]. [PERSON] and co-workers implemented the generalization of the CAP (Control of Assessor Performances) system developed by [PERSON] to evaluate assessors and panel using the MAM-CAP table (Mixed Assessor Model-Control of Assessment Performances). The main purpose of the MAM-CAP table is to help the panel leader to make decisions concerning the individual assessors and the panel: discrimination (F-_Prod_), agreement (F-_Disa_), repeatability (RMSE) and scale usage (F-_Scal_). The MAM-CAP table is a fast and synthetic diagnostic tool, and each row corresponds to a sensory attribute. One part of the table summarizes the performance of the panelist, and the other part corresponds to the panel.