Ordinal Analysis of Variation of Sensory Responses in Combination with Multinomial Ordered Logistic Regression vs. Chemical Composition: A Case Study of the Quality of a Sausage from Different Producers

Abstract

The newly developed statistical technique of two-way ordinal analysis of variation (ORDANOVA) was applied for the first time to sensory responses in combination with multinomial ordered logistic regression of a response category vs. chemical composition. A corresponding tutorial is provided. As a case study, samples of a sausage from different producers, purchased at the same time from a market, were compared based on sensory responses of experienced experts. A decomposition of total variation of the ordinal data and simulation of the multinomial distribution of the relative frequencies of the responses in different categories showed a statistically significant difference between the producers’ samples, and an insignificant difference between the experts’ responses related to the same sample. The capabilities of experts were also evaluated. The influence of chemical composition of a sausage sample on the probability of a response category was modeled using multinomial ordered logistic regression of the response on mass fractions of the main sausage components. This statistical technique can be helpful for understanding sources of variation of sensory responses on food quality properties. It is also promising for a revision of specification limits for chemical composition, as well as for the prediction of sensory properties when the chemical composition of the product is subject to quality control.

Power of a test for assessing interlaboratory consensus of nominal and ordinal characteristics of a substance, material, or object

“…In practice, responses to a categorical property of an object may be correlated with the quantitative parameters, for example of the object's chemical composition [22]. Moreover, responses to different properties of the same object may be correlated between them [23].…”

“…Such decomposition may include a component related to the possible interaction between the two factors. In addition, decomposition by response categories was discussed in papers [20][21][22]. Note that the sample estimators by equations ( 2)-( 9) are biased from the corresponding population variations [41,43].…”

“…can belong to the same or different categories. However, intensity of water odor or the taste of a sausage from very bad to excellent [22,23], which are able to be 'equal/unequal' or 'greater than'/'less than', relate to ordinal variables. Since categories may be expressed verbally, and no algebraic operations and mathematical functions exist among them, a consensus numerical value (the equivalent of a mean) in an interlaboratory comparison or meta-analysis of categorical properties cannot be formulated.…”

“…Consensus of responses of different laboratories participating in an interlaboratory comparison, classifying a substance, material, or object according to its nominal and ordinal characteristics, could be also interpreted as cohesiveness. The recently developed two-way factorial analysis of variation of nominal variables CATANOVA and of ordinal variables ORDANOVA, applied first in [20] and [21][22][23], respectively, answers the question' is a consensus among participating laboratories achieved?' The answer is based on testing hypotheses about homogeneity of the between-laboratory and within-laboratory variation components, as well as the components caused by other factors under study.…”