Understanding Factorial Designs and Interactions
A factorial design involves studying the effects of multiple factors simultaneously. The notation $4 \times 3 \times 3$ indicates a factorial design with three factors.
- Factor 1 has 4 levels.
- Factor 2 has 3 levels.
- Factor 3 has 3 levels.
The total number of factors in this design is 3.
Identifying Three-Way Interactions
A 'three-way interaction' examines how the effects of three factors combine or influence each other.
In any factorial design, the number of possible interactions of a specific order is determined by the number of ways to select that number of factors from the total available factors.
For a three-way interaction, we need to select 3 factors.
Calculating Interactions for the $4 \times 3 \times 3$ Design
In this specific design, there are 3 factors in total.
The number of ways to choose 3 factors from the 3 available factors is calculated using combinations:
$ \binom{\text{Total Factors}}{\text{Factors in Interaction}} = \binom{3}{3} $Calculating the combination:
$ \binom{3}{3} = \frac{3!}{3!(3-3)!} = \frac{3!}{3!0!} = \frac{6}{6 \times 1} = 1 $Therefore, there is only 1 possible three-way interaction that can be studied in a $4 \times 3 \times 3$ factorial design. This interaction involves all three factors.
Important Questions from Research Design
Design used in experimental research in which groups are randomly formed and that controls most sources of invalidity is known as
‘Which of the following are the complete experimental research designs?
(A) Factorial design
(B) One group after-only design
(C) Before-after design with one experiment and two control groups
(D) Latin square design
(E) One-group before-after design
Choose the correct answer from the options given below:
The 'Age' of a respondent is an example of
The internal validity factor in research is related to the issue of
The post-test only control group design avoids:
