In: Statistics and Probability
Suppose there are two treatments for diabetes patient in a hospital namely X and Y.
Let both have two levels of dosage as low and high.
Hence we are interested in finding whether the change in the dosage level of a treatment independently affects the diabetes level differently or not, that is, is the treatment significantly affecting the patient and is there any interaction between the two treatments.
As we will get 4 different dosages as :
Low X and low Y
Low X and high Y
High X adn low Y
High X and high Y
This is 2^2 factorial design.
Similarly if there are 3 treatments under study as X, Y and Z then it will become 2^3 factorial design.
And here we will check effect of different dosage level of each treatment that is whether a treatment is significantly affecting the patient or not.
We will also check interaction between X,Y and Y, Z and X, Z and lastly X, Y, Z.