2.6. Statistical Analysis

Data were fitted to second-order polynomial equations (Equation (2)) for each dependent Y variable (L*, firmness, TPC, WL), as a function of independent variables X_j (T, t, and Sp), through a stepwise multiple regression analysis using Statistica version 8.0 software (Tulsa, OK, USA) [36]:

Where Y is the predicted response, X_j is the independent variable, b₀ is the intercept coefficient, b_j is the linear terms, b_jj is the squared terms, and b_ij is the interaction terms.

The stepwise regression procedure was performed using the backward elimination method in order to remove non-significant interaction terms from the initial response surface model step by step. In each subsequent step, the least significant variable in the model was removed until all remaining variables had individual p-values smaller than 0.05 [37]. The criteria for eliminating a variable from the full regression equation was based on R² values, standard error (SE) estimate, and the significance of the F-test and derived p values. The lack-of-fit and significance of the effects of each of the three independent factors was determined by analysis of variance. Three-dimensional response surface plots were generated by using plotting software [36].

To verify the accuracy of the predictive equations for the color, texture, and TPC, a total of 10 randomly selected treatment experiments, within the experimental range conditions, were replicated.

Data from untreated (Ctr) and optimum TS-treated conditions, such as mean and standard deviation (SD) of multiple measurements, was subjected to analysis of variance [36] at p < 0.05 with mean separation by Tukey’s Honestly Significant Difference (HSD) test to determine thermosonication effects on tomato quality attributes for different storage days.