Design of Experiments – Factorial Design MCQs With Answer

Introduction

Design of Experiments – Factorial Design MCQs With Answer is a focused question set aimed at M.Pharm students pursuing Pharmaceutical Formulation Development. This collection covers core factorial design principles—two-level and higher-level factorials, interactions, fractional factorials, confounding, resolution, blocking, randomization, and analysis strategies used in formulation optimization. Each MCQ emphasizes practical interpretation and decision-making in formulation studies such as identifying significant factors, planning efficient experimental runs, and designing screening versus optimization experiments. The questions target analytical thinking required in formulation development, helping students reinforce theory and apply factorial design methodology to real pharmaceutical problems.

Q1. What is the total number of experimental runs required for a full factorial design with four factors each at two levels (2-level factorial)?

• 8 runs
• 12 runs
• 16 runs
• 32 runs

Correct Answer: 16 runs

Q2. In a 2^3 factorial design, which term represents the interaction between factor A and factor B?

• A + B
• A*B
• A/B
• A^2B

Correct Answer: A*B

Q3. Which statement best defines a fractional factorial design?

• A design that examines only one factor at a time while keeping others constant
• A subset of runs from a full factorial used to reduce experiments while estimating selected effects
• A full replication of a factorial design with extra center points
• A design that uses only qualitative factors

Correct Answer: A subset of runs from a full factorial used to reduce experiments while estimating selected effects

Q4. In a 2^(k-p) fractional factorial design, what does the parameter p represent?

• The number of replicates performed
• The number of blocking variables
• The number of generators (fractional reduction exponent)
• The number of center points added

Correct Answer: The number of generators (fractional reduction exponent)

Q5. What is meant by the resolution of a fractional factorial design?

• The number of replicates needed to detect main effects
• The degree of confounding between main effects and interactions
• The measurement precision of the response variable
• The number of center points required

Correct Answer: The degree of confounding between main effects and interactions

Q6. Which resolution is necessary to ensure main effects are not aliased with two-factor interactions?

• Resolution II
• Resolution III
• Resolution IV
• Resolution V

Correct Answer: Resolution IV

Q7. In two-level coding, what are the conventional numeric levels used for the low and high settings?

• 0 and 1
• -1 and +1
• 1 and 2
• -2 and +2

Correct Answer: -1 and +1

Q8. Which of the following is a primary advantage of using factorial designs in formulation development?

• They require only qualitative data
• They allow simultaneous estimation of main effects and interactions efficiently
• They eliminate the need for statistical analysis
• They always require fewer runs than OFAT for any number of factors

Correct Answer: They allow simultaneous estimation of main effects and interactions efficiently

Q9. In a 2^5 full factorial study, how many degrees of freedom (excluding overall mean) are available for estimating effects?

• 5 degrees
• 31 degrees
• 32 degrees
• 25 degrees

Correct Answer: 31 degrees

Q10. Which method is commonly used to compute effect estimates for two-level factorials manually or in software, particularly when k is small?

• Yates’ algorithm
• Fisher’s LSD
• Principal Component Analysis
• Kruskal-Wallis test

Correct Answer: Yates’ algorithm

Q11. In a 2^(4-1) fractional factorial design with defining relation I = ABCD, which effect is aliased with main effect A?

• B
• BCD
• ABC
• ABD

Correct Answer: BCD

Q12. Which of the following best describes blocking in factorial experiments?

• Grouping experimental runs to remove variability due to nuisance factors
• Mixing different factor levels in the same run
• Adding more replicates to increase power
• Converting continuous factors to categorical factors

Correct Answer: Grouping experimental runs to remove variability due to nuisance factors

Q13. When conducting a screening experiment to identify the most influential formulation factors among many, which design is typically preferred?

• Full factorial 2^k with all interactions
• Fractional factorial (high resolution not required) or Plackett–Burman
• Central composite design
• Latin square design

Correct Answer: Fractional factorial (high resolution not required) or Plackett–Burman

Q14. What is the primary risk when using a fractional factorial design with low resolution for screening?

• Overfitting the response surface
• Aliasing important interactions with main effects leading to wrong conclusions
• Needing too many runs to interpret results
• Loss of randomization

Correct Answer: Aliasing important interactions with main effects leading to wrong conclusions

Q15. Which analysis tool is commonly used to visualize and rank standardized effect magnitudes in factorial experiments?

• Box-and-whisker plot
• Pareto chart of effects
• Kaplan-Meier curve
• Heatmap of correlations

Correct Answer: Pareto chart of effects

Q16. If a two-factor interaction AB is significant in a formulation study, what does this imply?

• The combined effect of A and B equals the sum of their individual effects
• The effect of factor A on the response depends on the level of factor B
• A and B have no influence on the response
• The factors A and B must be continuous variables

Correct Answer: The effect of factor A on the response depends on the level of factor B

Q17. In order to detect curvature in a two-level factorial region, which addition to the design is most appropriate?

• Add blocking
• Add center points
• Convert factors into three-levels randomly
• Increase replication only at the corners

Correct Answer: Add center points

Q18. Which principle supports the choice of coding factor levels to standardized values (like -1, +1) in factorial analysis?

• Orthogonality and simplifying effect estimation and interpretation
• To increase the number of runs required
• To eliminate the need for ANOVA
• To guarantee linearity of responses

Correct Answer: Orthogonality and simplifying effect estimation and interpretation

Q19. What is a fold-over design used for in fractional factorial experimentation?

• To split the experiment into blocks for convenience
• To resolve aliasing by augmenting the original fraction with another fraction having complementary generators
• To reduce the number of runs further
• To convert quantitative factors into qualitative factors

Correct Answer: To resolve aliasing by augmenting the original fraction with another fraction having complementary generators

Q20. In model-building from a 2-level factorial, which modeling strategy respects the hierarchy principle?

• Include only significant interactions and drop main effects even if non-significant
• Retain lower-order terms (main effects) that are part of significant interactions
• Exclude all interactions irrespective of significance
• Include only quadratic terms without main effects

Correct Answer: Retain lower-order terms (main effects) that are part of significant interactions

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