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
- Assertion (A): Due to the experiment of Time, Motion and Fatigue studies, a factory does not remain a factory, it is converted into a laboratory
Reason (R): Management succeeds or fails as human relations in business are intelligently or unintelligently handled Given below are two statements
Statement I An explanatory correlational design explains the degree of association among two or more. variables
Statement II In prediction correlational design, the investigator identifies variables that will positively predict an out come
Choose the correct answer.- Select the option based on the Assertion (A) and Reason (R) :
Assertion (A): Extraneous Variables can influence the results of a research study.
Reason (R): Extraneous variables are not controlled by the researcher. - ____________ is to explore the data without prior hypthesis.
- An experimental research design incorporates
(i) Random assignment of participants to treatment conditions
(ii) Effect on a dependent variable recorded
(iii) Observe placebo effect
(iv) Manipulation of independent variable
(v) Increase attrition
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