## 3 Results
### Statistical Data Analysis  
The ANOVA test with a single factor, also known as the unifactorial variation analysis, was the statistical method used to compare the means of the four independent groups represented by the concentration of the substance in the extract (polyphenols, protein content, vitamin C, carbohydrates) depending on the size of the particle size class, to determine if there are significant differences between them. The test results are presented in Table 4.  
The assumptions assumed to ensure the validity of the results were:  
* Null hypothesis (H\({}_{0}\)): there are no significant differences between group means (all means are equal).
* Alternative hypothesis (H\({}_{1}\)): there is at least one significant difference between the group means.  
The calculation of the F-statistic value, the ratio of the mean variance between groups to the mean variance within groups (F = 1936.07), suggests that the variance between groups is significantly greater than the variance within groups; the \(p\) value is less than 0.05 (\(p\) = 1.48\({}^{-32}\)), so we removed the null hypothesis and concluded that there are significant differences between the groups. This aspect can be observed in Table 5.  
Since the one-factor ANOVA method can tell whether there is a significant difference between groups, but does not indicate between which groups these differences exist, a post hoc test is needed to identify pairs of groups between which there are significant differences. The least significant difference (LSD) test can identify which groups differ significantly in terms of their means.  
The critical value named \"Least Significant Difference\" (LSD\({}_{\text{Crit one-tail}}\) = 23.17 and LSD\({}_{\text{Crit two-tail}}\) = 28.92) of the test was calculated based on the standard error of the difference between the group means and the critical coefficient derived from the t distribution (t\({}_{\text{Crit one-tail}}\) = 1.89 and t\({}_{\text{Crit two-tail}}\) = 2.36), corresponding to a level of significance \(p\) = 0.05 and the number n = 8 degrees of freedom. Through comparison of each pair of group means, it was found that the difference between the group means of protein content (777.44) and the other group means of vitamin C (11.86), carbohydrates (4.63), phenolic content (33.69) is greater than the LSD values, and then, we can consider that there is a significant difference between those pairs of two groups, protein versus vitamin C, carbohydrates and phenolic content.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Groups** & **Count** & **Sum** & **Average** & **Variance** \\ \hline Phenolic content [\(\mu\)g GAE/mL] & 8 & 269.59 & 33.69 & 23.79 \\ Protein content [\(\mu\)g/mL] & 8 & 6219.53 & 777.44 & 2350.78 \\ Vitamin C [\(\mu\)g/100 mL] & 8 & 94.94 & 11.86 & 18.74 \\ Carbohydrates [\(\mu\)g/mL] & 8 & 37.06 & 4.63 & 0.34 \\ \hline \hline \end{tabular}
\end{table}
Table 4: One-factor ANOVA test results.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source of Variation** & **SS** & **df** & **MS** & **F** & \(p\)**-Value** & **F Crit** \\ \hline Between Groups & 3,475,723.33 & 3 & 1,158,574 & 1936.07 & 1.48\({}^{-32}\) & 2.94 \\ Within Groups & 16,755.63 & 28 & 598.41 & / & / & / \\ Total & 3,492,478.97 & 31 & / & / & / & / \\ \hline \hline \end{tabular}
\end{table}
Table 5: ANOVA test results.