## 3 Materials and Methods
### Phase#3: Analysis
#### 3.3.2 Step#3.2: Processing Data Using Statistical Tool  
For the section on sustainability, a more in-depth statistical analysis was applied using the chi-square test. The test was used to verify the possible existence of significant associations between the geographical location of the companies and the adoption of sustainable practices, with the aim of determining whether the observed differences were statistically significant or due to chance [34].  
Since the survey responses were categorical in nature, the chi-square test was deemed the most appropriate statistical method for analyzing the distribution of these variables. This test allows for the evaluation of potential associations between categorical variables, specifically assessing whether the frequency of responses differs in relation to the geographical location of the companies. The chi-square test is particularly well suited for examining the relationships between discrete events, such as the number of companies adopting sustainability practices, as it compares the observed distribution of responses to what would be expected under the null hypothesis of independence [35]. By applying this test, it is possible to observe variations in sustainability practices across regions are statistically significant, thereby providing insights into the influence of geographical factors on corporate sustainability behavior.  
The process considered the following considerations:  
1. Formulation of hypotheses. The null hypothesis states that there is no relationship between the variables, while the alternative hypothesis suggests that there is a significant relationship.
2. Level of significance. The test is conducted with a significance level of 5% (0.05), which indicates the acceptable probability of error in rejecting the null hypothesis;
3. Organization of data: The data are presented in a contingency table, which shows the distribution of the variables being tested.
4. Calculation of expected frequencies: Under the null hypothesis, the expected frequencies for each cell in the table are calculated, based on the overall proportions.
5. Calculating the chi-square. The chi-square value is calculated by comparing the observed frequencies with the expected frequencies, using the formula (Equation (1)):  
\[x^{2}=\sum\frac{(Oi-Ei)^{2}}{Ei} \tag{1}\]  
where  
_Oi_: Observed frequency for each category.  
_E_: Expected frequency, calculated as \((\text{R}_{\text{i}}\cdot\text{C}_{\text{j}})/\text{N}\) in which \(\text{R}_{\text{i}}\) is the sum of the rows, \(\text{C}_{\text{j}}\) the sum of the columns, and e N is the grand total.  
The degrees of freedom are calculated as defined in Equation (2):  
\[Df=(\text{r}-1)(\text{c}-1) \tag{2}\]  
where r is the number of rows and c is the number of columns in the contingency table.  
The calculated \(\chi^{2}\) value is compared against a critical value from the chi-square distribution table at a chosen significance level (\(\alpha=0.05\)). If the calculated value exceeds the critical value, the null hypothesis (H0)--stating no association between variables--is rejected.  
The significant relationships identified through the chi-square test provide actionable insights, guiding regional policies to target specific barriers and promote sustainable practices more effectively.  
6. Comparing with the critical value. The calculated value is compared with the tabulated value. If the calculated chi-square is greater than the critical value, the null hypothesis is rejected, indicating a significant relationship between the variables. If it is less, the null hypothesis is accepted, indicating that there is no significant relationship. In this case, the chi-square test on proportions was used to verify the presence of a relationship between the geographical location of the companies and the adoption of sustainability practices.