*3.3. Statistical Analysis*

The data collected were processed in four distinct phases, using the STATA 15.0 (Budapest, Hungary) integrated statistical software. In the first phase, the socio-demographic characteristics of the sample were defined, through descriptive analyses; in the second phase, the psycho-attitudinal scales were interpreted, checking their internal consistency (alpha-coe fficient) and calculating the average of each item. In the third part, a description of the WTPs detected for the three types of fruit juices was made; in addition, by means of parametric (t-test) and non-parametric tests (Wilcoxon tests), it was verified whether the three WTPs were significantly di fferent, and therefore, two deltas (premium prices) were calculated. The two premium prices were obtained, one at a time, by first calculating the di fference between the WTP for natural and conventional fruit juices and then the di fference between WTP for enriched and conventional fruit juice:

$$
\begin{array}{c}
\Delta WTP\_{NAT} = \left(WTP\_{NAT} - WTP\_{CONV}\right) \\
\Delta WTP\_{ENR} = \left(WTP\_{ENR} - WTP\_{CONV}\right)
\end{array}
$$

Later, the seemingly unrelated regressions (SUR) [50] were presented, together the Breusch-Pagan test of independence, to measure how the price premium of the two fruit juices can be influenced and, at the same time, to verify whether the price premium of the two types of juices is explained by common attributes.

This stochastic model may be expressed by the following relationship:

$$y = X\beta + u$$

where *y* and *u* are vectors with n elements, *X* is a matrix with n rows and *k* + 1 columns (with *k* the explanatory variables + 1 for the constant) and β is the vector containing *k* + 1 unknown coe fficients.
