2, 22 Factorial design
3, 23 Factorial design
4, 2k Factorial design
Factorial designs are widely used in experiments involving several factors where
it is necessary to study the joint effect of factors on a response.
The most important of these special cases is that of k factors, each at only two levels.
These levels may be quantitative, such as two values of temperature, pressure, or
time; or they may be qualitative, such as two machines, two operators, the “high”
and “low” levels of a factor, or perhaps the presence and absence of a factor. A
complete replicate of such a design require 2*2*……*2=2k observations and is
called a 2k factorial design.