Complex Factorial Designs
Factorial Designs
 Studies with a complex design explore the effects of more
than one factors on the dependent variable.
 Specially important in several economic and social
phenomena.
 Two types: 1) Simple factorial designs (two-factor-factorial
design)
2) Complex factorial designs (multi-factorfactorial design)
Complex Factorial Designs
 A design in which the effects of varying more than two
factors is considered.
 Considers three or more independent variables
simultaneously.
 Extraneous variables to be controlled by homogeneity are
called control variable and the independent variables are
called the experimental variables.
2x2x2 Complex Factorial Design
•Used in the case of three factors with one experimental
variable having two treatments and two control
variables, each having two levels.
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Cont.
 Possible to determine the main effects of three variables.
 The interactions between each possible pair of variables can also
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be determined, which are called First Order Interactions (two
variables are considered at a time and one is ignored).
The interaction between variable triplets can also be determined,
which are called Second Order Interactions (Complex factorial
analysis).
The combined mean of data in cells 1,2,3,4 for treatment A is
compared with combined mean of data in cells 5,6,7,8 for
treatment B to determine the main effects of the experimental
variable.
Similar can be done to determine the effects of control variable 1
and control variable 2.
Complex factorial design can be generalized to any number and
combination of experimental and control independent variables.
Advantages and disadvantages
 Provide equivalent accuracy as happens in case of
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experiments with only one factor with less labour.
Effects of two or more variables can be determined in a
single experiment, there it can utilise researcher’s limited
resources.
The interaction effects can be determined.
One challenge in factorial designs is that interactions can
make it hard to interpret main effects if the interaction is
large enough to mask the main effect.
It can be time-confusing.
Example
 If we want to determine the effects of sleeping less than 6
hours a day on performance in exam, with attention to IQ
score and preparedness for exams, the complex factorial
design can be utilized.
 8 group of subjects will be made, with each group having a
different combination of treatment A or B, IQ low or high
and preparedness level high or low.
 The combined mean of data in selected groups will be
compared with groups in respect to the effect of which
variable we want to determine.
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