**4. Conclusions and final remarks**

the tasters, since the difference *P[X > q0.025] - P[X > q0.975]* is the largest among the

Therefore, in the evaluation of the four specialty coffees, given the low probabilities, it can be said that a sensory experiment carried out with the objective of discriminating the specialty coffees, is done with consumers who present more

**Figure 3** shows graphically the agreement between the scores given by trained (blue hatched) and untrained (black hatched) tasters, according to the results

The importance of using bootstrap procedures in the analysis of responses that

*Graphical representation of the probability distributions adjusted for the notes attributed by untrained (black) and trained (blue) tasters and the respective 95% confidence intervals for the maximum scores modes attributed*

corroborate with these scores is relevant for statistically validating the scores obtained in international competitions, since it assumes that subjective and / or unknown factors, related to the different sensory perceptions of the tasters may suggest violations in the sample distribution, and as a consequence, the estimates of the probabilistic model are distorted. Thus, through successive resampling, an empirical distribution for each parameter is generated in connection with the assumed probabilistic model, and inferences will be made with better precision and accuracy. The amplitude of the confidence interval in **Figure 3** reflects the precision

analyzed coffees.

*Recent Advances in Numerical Simulations*

improved training.

shown in **Table 3**.

**Figure 3.**

**186**

*to each special coffee.*

The GEV distribution can be applied to the sensory analysis of specialty coffees, whose sensorial panel presents an heterogeneity among consumers.

The probabilities obtained by this distribution show that the sensory analysis of specialty coffees performed by untrained consumers indicates that they are able to differentiate specialty coffees and provide similar scores to the sensory analysis performed by consumers with prior training.

The proposed inference made it possible to attribute some degree of uncertainty regarding the occurrence of sensory scores in the different types of specialty coffees studied and to indicate which group each coffee belongs to with high probability according to the Specialty Grade.

It can be recommended that more intensive training with tasters or the application of the proposed methodology with tasters with international certification should be considered with a view to assessing specialty coffees against a reference score of 9 points, since for the present study, only coffee D has a high probability of presenting this note. It should be noted that according to the analysis protocol provided by Specialty Coffee Association of America, the results of the sensory evaluation vary according to a scale where the grades upper to 9 correspond to exceptional coffee.

The study has some limitations that provide directions for future research, although the GEV distribution is specific for analyzing maximum values, the data generating mechanism truncates the maximum score at 10. This characteristic could be taken into account, fitting the model to truncated data. Some proposals have appeared in the literature to consider truncation in the estimation process by maximum likelihood, but there is no consolidated methodology yet. Therefore, it is a possibility for further studies that may be the subject of future research.

### **Acknowledgements**

The authors are grateful to the National Council for Scientific and Technological Development (CNPq—Conselho Nacional de Desenvolvimento Científico e Tecnológico), the Minas Gerais State Research Support Foundation (FAPEMIG— Fundação de Amparo para Pesquisa do Estado de Minas Gerais), the Coordination for the Improvement of Higher Education Personnel (CAPES—Coordenação de Aperfeiçoamento de Pessoal de Nível Superior), and the National Coffee Science and Technology Institute (INCT/Café—Instituto Nacional de Ciência e Tecnologia do Café).

### **Conflict of interest**

The authors declare no conflict of interest.
