The correct answer is: A. To know the relationship between two variables.
Factorial analysis is a statistical method that is used to understand the relationship between two or more variables. It can be used to determine if there is a relationship between the variables, and if so, how strong the relationship is. Factorial analysis can also be used to identify the factors that are most important in determining the relationship between the variables.
Option B is incorrect because factorial analysis is not used to test hypotheses. Hypothesis testing is a statistical method that is used to determine if there is a statistically significant difference between two groups. Factorial analysis is not used to determine if there is a difference between two groups, but rather to determine if there is a relationship between two variables.
Option C is incorrect because factorial analysis is not used to know the difference between two variables. Factorial analysis is used to determine if there is a relationship between two variables, not to determine the difference between the variables.
Option D is incorrect because factorial analysis is not used to know the difference among the many variables. Factorial analysis is used to determine the relationship between two or more variables, not to determine the difference between the variables.