Advantages and pharmaceutical applications of factorial design MCQs With Answer

Factorial design is a cornerstone of experimental design and DoE in pharmaceutical research, enabling simultaneous study of multiple formulation and process factors. By estimating main effects and interaction effects through 2^n and fractional factorial designs, it accelerates formulation optimization, process robustness, stability testing, and scale-up while conserving resources. Applications include tablet and capsule formulation, dissolution optimization, bioavailability studies, and process parameter screening within Quality by Design (QbD). Key advantages are efficient factor screening, detection of interactions, improved statistical power via replication, and integration with ANOVA and response surface methods for optimization. This focused MCQ set reinforces practical understanding of factorial design advantages and pharmaceutical applications. Now let’s test your knowledge with 30 MCQs on this topic.

Q1. What is the primary advantage of using a factorial design over one-factor-at-a-time (OFAT) experiments in formulation development?

• Requires fewer experimental runs than any other design
• Allows simultaneous estimation of main effects and interaction effects
• Eliminates the need for statistical analysis
• Only studies qualitative factors

Correct Answer: Allows simultaneous estimation of main effects and interaction effects

Q2. In a full 2^3 factorial design, how many experimental runs are required?

• 6
• 8
• 9
• 16

Correct Answer: 8

Q3. Which term describes the combined effect of two factors that is different from the sum of their individual effects?

• Main effect
• Interaction effect
• Blocking effect
• Random error

Correct Answer: Interaction effect

Q4. What is the main purpose of using a fractional factorial design in pharmaceutical experiments?

• To measure curvature in response surfaces
• To reduce the number of runs while screening many factors
• To remove the need for replication
• To always include all two-factor interactions

Correct Answer: To reduce the number of runs while screening many factors

Q5. In design terminology, what does a Resolution IV design imply?

• Main effects are aliased with other main effects
• Main effects are aliased with two-factor interactions but not with other main effects
• All interactions are fully estimable without aliasing
• It is equivalent to a full factorial

Correct Answer: Main effects are aliased with two-factor interactions but not with other main effects

Q6. Which statistical method is most commonly used to test significance of effects in factorial experiments?

• Chi-square test
• ANOVA (Analysis of Variance)
• Kaplan–Meier analysis
• Pearson correlation

Correct Answer: ANOVA (Analysis of Variance)

Q7. Why are center points included in some factorial experiments?

• To estimate curvature/non-linearity in the response
• To double the number of factors
• To replace blocking
• To eliminate the need for randomization

Correct Answer: To estimate curvature/non-linearity in the response

Q8. Which application is a typical pharmaceutical use of factorial design?

• Optimizing tablet formulation for hardness and dissolution
• Replacing clinical trials
• Measuring patient satisfaction surveys
• Performing molecular docking simulations

Correct Answer: Optimizing tablet formulation for hardness and dissolution

Q9. In a 2^4 full factorial design, how many two-factor interactions exist?

• 4
• 6
• 12
• 16

Correct Answer: 6

Q10. Which design is most suitable for initial screening of a large number of factors with minimal runs?

• Response Surface Methodology (RSM)
• Plackett-Burman or fractional factorial designs
• Full factorial 3^k design
• Latin square

Correct Answer: Plackett-Burman or fractional factorial designs

Q11. How does factorial design support Quality by Design (QbD) in pharmaceuticals?

• By eliminating analytical method validation
• By systematically identifying critical factors and interactions affecting product quality
• By reducing regulatory documentation requirements
• By replacing stability studies

Correct Answer: By systematically identifying critical factors and interactions affecting product quality

Q12. What is confounding in the context of factorial experiments?

• The deliberate blocking of treatments
• When two or more effects cannot be separately estimated because they are aliased
• The process of randomizing runs
• The addition of center points to detect curvature

Correct Answer: When two or more effects cannot be separately estimated because they are aliased

Q13. Which of the following is an advantage of replication in factorial designs?

• Reduces the number of factors needed
• Improves estimation of experimental error and increases statistical power
• Eliminates interactions
• Makes aliasing unavoidable

Correct Answer: Improves estimation of experimental error and increases statistical power

Q14. Which factor type can be included in a factorial design for pharmaceutical studies?

• Only numerical continuous factors
• Only categorical factors
• Both numerical (continuous) and categorical factors
• Neither categorical nor numerical factors

Correct Answer: Both numerical (continuous) and categorical factors

Q15. When optimizing a dissolution profile, which response would typically be used in a factorial experiment?

• Particle color
• Percent drug dissolved at a specified time
• Room temperature
• Manufacturer name

Correct Answer: Percent drug dissolved at a specified time

Q16. Which software is commonly used for factorial design analysis in pharmaceutical development?

• ImageJ
• Design-Expert, JMP or Minitab
• Microsoft Paint
• Notepad

Correct Answer: Design-Expert, JMP or Minitab

Q17. What is the role of blocking in factorial experiments?

• To increase the number of factors studied
• To account for known nuisance variability such as batch or day
• To measure interactions directly
• To replace randomization

Correct Answer: To account for known nuisance variability such as batch or day

Q18. Which design extension is recommended if significant curvature is detected after a factorial screening?

• Switch to Chi-square testing
• Apply Response Surface Methodology (e.g., Central Composite or Box-Behnken)
• Use a larger Plackett-Burman design
• Remove all interactions

Correct Answer: Apply Response Surface Methodology (e.g., Central Composite or Box-Behnken)

Q19. In pharmaceutical process optimization, detecting a significant interaction between compression force and lubricant concentration implies:

• Each factor can be optimized independently without impact on the other
• The effect of compression force depends on lubricant concentration and both should be considered together
• Both factors have no effect on tablet properties
• The data are invalid and experiment must be repeated

Correct Answer: The effect of compression force depends on lubricant concentration and both should be considered together

Q20. What does aliasing mean in a fractional factorial design?

• Complete independence of all effects
• When two or more effects are indistinguishable because of the reduced design
• Higher accuracy of main effect estimation
• Automatic detection of curvature

Correct Answer: When two or more effects are indistinguishable because of the reduced design

Q21. For a 2-level factorial experiment, what does the term “level” refer to?

• The number of replicates
• The specific settings or values of a factor (e.g., low and high)
• The significance level of a test
• The sample size per run

Correct Answer: The specific settings or values of a factor (e.g., low and high)

Q22. Which experimental design is often used for robustness testing of a formulation with a limited number of experiments?

• Full factorial 5^k
• Fractional factorial or Plackett-Burman screening
• Case-control study
• Randomized clinical trial

Correct Answer: Fractional factorial or Plackett-Burman screening

Q23. When scaling up a process, factorial designs help primarily by:

• Replacing process validation
• Identifying critical process parameters and their interactions affecting scale-up performance
• Only validating analytical methods
• Ensuring regulatory approval automatically

Correct Answer: Identifying critical process parameters and their interactions affecting scale-up performance

Q24. What purpose does randomization serve in factorial experiments?

• Guarantees zero experimental error
• Helps mitigate systematic bias due to uncontrolled variables
• Ensures all interactions are significant
• Allows merging of unrelated experiments

Correct Answer: Helps mitigate systematic bias due to uncontrolled variables

Q25. Which of the following is an example of a response variable in a formulation factorial study?

• API supplier name
• Tablet disintegration time
• Batch operator’s preference
• Company logo

Correct Answer: Tablet disintegration time

Q26. Which screening design is characterized by being efficient for many factors but does not estimate interactions well?

• Central Composite Design
• Plackett-Burman design
• Box-Behnken design
• Full 3-level factorial

Correct Answer: Plackett-Burman design

Q27. If an experimenter wants to study three factors at three levels each to map curvature fully, which design is appropriate?

• 2^3 factorial
• Full 3^3 factorial or a response surface design like Box-Behnken
• Plackett-Burman
• Latin square

Correct Answer: Full 3^3 factorial or a response surface design like Box-Behnken

Q28. Why is analysis of residuals important after fitting a factorial model?

• To confirm model assumptions such as normality and constant variance
• To increase the number of factors artificially
• To change the experimental design
• To avoid conducting ANOVA

Correct Answer: To confirm model assumptions such as normality and constant variance

Q29. In a 2-level factorial study, which strategy can help separate main effects from interactions when aliasing is present?

• Reduce the number of runs
• Add fold-over runs or additional experiments to unalias effects
• Ignore interactions entirely
• Change all factors to categorical

Correct Answer: Add fold-over runs or additional experiments to unalias effects

Q30. Which experimental outcome would indicate a significant interaction between excipient concentration and mixing time affecting dissolution?

• Dissolution changes uniformly with excipient regardless of mixing time
• The effect of excipient concentration on dissolution differs at short vs. long mixing times
• No change in dissolution with any factor
• Mixing time only affects color, not dissolution

Correct Answer: The effect of excipient concentration on dissolution differs at short vs. long mixing times

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