Comparison of ANOVA with the Tobit model for analysing sensory data

The data of sensory trials often contain a large number of zeroes, due to the limited scale used. It therefore is clear that the data are not normal. Out of concern that this might lead to problems with the application of ANOVA, Guillet et al. [Guillet, M., Methot, S., & Rodrigue, N. (2001). Application of Tobit models to handle zero-valued attribute intensities. Presented at the Pangborn conference in Dijon] proposed to use the Tobit model for the analysis of sensory trials. They demonstrated with a data set for a workshop at the fourth Pangborn Sensory Science Symposium that this model generally detects more significant differences between products than ANOVA does.It should be noted, however, that randomization theory provides a justification to use ANOVA for designed experiments, even for non-normal data. On the other hand, the Tobit model has strict model assumptions itself, and the usual proof of the consistency of the maximum likelihood estimate in the Tobit model does not work for sensory trials.Using the same data set as Guillet et al. [Guillet, M., Methot, S., & Rodrigue, N. (2001). Application of Tobit models to handle zero-valued attribute intensities. Presented at the Pangborn conference in Dijon], we compare the two models with the help of permutation tests. Our results indicate that ANOVA allows to test without violating the nominal level, while the Tobit model rejects the null hypothesis too often.