Explain the factorial design with the help of a suitable example

What is Factorial Design:--

Now let us come to the term factorial design. Factorial design is an aspect of experimental design. As explained in the above part of the blog, many experiments require two or more variables for the research conduct. 

In practical form, it becomes hard for the researchers to find all the possible combinations of the levels of the variables and factors for the investigation process.

Thus, researchers employ a technique named Factorial Design. Factorial design helps to complete the trial and replication of an experiment. It also investigates all possible combinations of the variables and functions. Thus, factorial design makes the tasks of researchers easier and reliable.

How does Factorial Design Work:--

A factorial design simply works by replicating the levels of factors or variables. Let us consider a simple example to understand this process more clearly. For a particular experiment, there are two variables used A and B. Variable A has a levels, while the other variable B has b levels.

The factorial design will form a replicate that contains all possible ab combinations. In literal terms, factorial design will investigate the influence of all the experimental variables, factors and integration effects on the response. If the variable or factor consists of k factors. 

The total of 2k experiments will be performed. Or, if the 2 variables are involved in the research a total of 4 experiments would be performed, if 8 variables are ________ ________ ___ _____ ___ ________ __________ _______.
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