## 2 Materials and Methods
### The Analysis of Variance  
The ANOVA test is a statistical analysis method used to compare means between at least three groups. In the analysis phase, there must be a categorical variable that has at least three groups and whose observations are independent. There also needs to be a quantitative variable consisting of numerical data [38; 39]. Although there are different ANOVA tests, the one-way ANOVA test was applied, since evaluation was made on a single factor in this study. One-way ANOVA is a tool used to test whether there is a statistically significant difference between the means of independent groups. Table 3 specifies the different factors, \(\alpha\), and n observations at each level for the specified factor. Levels of the factor are sometimes referred to as treatments. In this study, there are six observations or levels for each factor, as indicated in Table 2. The runs are performed in random order. In inferential statistics, the null hypothesis is a general statement that assumes that there is nothing beyond what is expected, for example, that there is no relationship between groups or variables or that there is no difference between two measured phenomena. Therefore, changing the factor treatment does not affect the mean response if the null hypothesis is confirmed. We can describe the observations in Table 3 with a linear statistical model, as specified in Equation (1):  
\[y_{ij}=\mu+\tau_{i}+e_{ij} \begin{cases}i=1,2,\cdots,\alpha\\ j=1,2,\cdots,n\end{cases}  \tag{1}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Factor** & & **Observations** & & **Totals** & **Averages** \\ \hline
1 & \(y_{11}\) & \(y_{12}\) & \(\cdots\) & \(y_{1n}\) & \(y_{1}\). & \(\overline{y}_{1}\). \\
2 & \(y_{21}\) & \(y_{22}\) & \(\cdots\) & \(y_{2n}\) & \(y_{2}\). & \(\overline{y}_{2}\). \\
3 & \(y_{31}\) & \(y_{32}\) & \(\cdots\) & \(y_{3n}\) & \(y_{3}\). & \(\overline{y}_{3}\). \\ � & � & � & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) \\ \(\alpha\) & \(y_{a1}\) & \(y_{a2}\) & \(\cdots\) & \(y_{an}\) & \(y_{a}\). & \(\overline{y}_{a}\). \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Typical data for a one-factor experiment. Figure 2: (a) Technical drawing of ISO527–type1A standard specimen. (b) Specimens after tensile tests. Factor effects are generally defined as deviations from the overall mean. Thus, the effect of \(\tau_{\text{i}}\) can be written as zero. Equation (1) can be expressed as follows:  
\[y_{ij}=\mu+\epsilon_{ij} \begin{cases}i=1,2,\cdots,\alpha\\ j=1,2,\cdots,n\end{cases}  \tag{2}\]  
The ANOVA test examines the variability of samples in two ways. These are the variance corresponding to each transaction and the overall variance. Thus, \(y_{\text{i}}\) is the representation of the total observations within the ith factor, and \(y_{\text{i}}\) is the representation of the mean of the observations within the ith factor. \[y_{i\cdot}=\sum\limits_{j=1}^{n}y_{ij},\qquad\overline{y}_{i\cdot}=\frac{y_{ i\cdot}}{n},\qquad i=1,2,\cdots,\alpha \tag{3}\]  
Overall, \(y_{\cdot\cdot}\) represents the total of all observations, \(N=n*\alpha\), and \(\overline{y}_{\cdot\cdot}\) is the average of all observations. \[y_{\cdot\cdot}=\sum\limits_{i=1}^{\alpha}\sum\limits_{j=1}^{n}y_{ij},\qquad \overline{y}_{\cdot\cdot}=\frac{y_{\cdot\cdot}}{N} \tag{4}\]  
The sum of squares identity is specified below in Equation (5). Thus, the total sum of squares is the sum of squares of the treatments and the sum of squares of the errors:  
\[