*2.4. Statistical Analysis*

Sample size calculation was conducted using three 1-β power values (0.80, 0.95, and 0.99), a significance threshold value of α equal to 0.05, and three effect size values (Cohen's f = 0.20, 0.25, and 0.30, respectively). Sample size was determined to be 40 participants (20 each group).

The effect of the treatments on the response variables (blood glucose and insulin) was assessed through a linear mixed model (LMM), where the treatment groups (group A and group B), the measurement times (i.e., immediately after the meal, t0; after 15 min, t1; 30 min, t2; 60 min, t3; 90 min, t4; and 120 min, t5), the order of treatment (first and second) and the age and sex of the subjects were entered into the model as fixed effects. The measurement × treatment and measurement × treatment order interactions were included among the independent variables. The measure × treatment interaction is the key variable for the primary endpoint, as it allows testing whether the trend over the course of the measurements differs for the two treatments.

With regards to the interaction measurement × treatment order, it is used to check whether trends during the measurement period differ according to the order of administration of the treatments (before or after wash-out). The identity of the subject was evaluated as a random effect, which provided a control for differences among the enrolled subjects.

Analyses were performed using the lme4 [29] packages in R ver. 4.0.1 [30] (R Foundation for Statistical Computing, Vienna, Austria) and unless otherwise stated, data are reported as means ± standard errors.

For each subject of groups 1 and 2, the glucose and insulin incremental areas under the curves (iAUCs) were calculated. The iAUCs were evaluated statistically using a *t*-test: two paired samples for means, with each subject being his or her own control. Differences resulting in *p*-values below 0.05 were considered significant.
