Design and analysis of experiments (DOE) is a systematic approach to planning, conducting, and analyzing experiments to identify factors, levels and interactions that influence a response variable. In pharmaceutical research and quality control, DOE helps optimize formulations, analytical methods, stability studies, and process validation by applying principles like randomization, replication, blocking, and factorial design. Key tools include ANOVA, regression, response surface methodology, factorial and fractional factorial designs, and sample size/power calculations. Understanding experimental layout, confounding, main effects versus interactions, and residual analysis is essential for reliable data interpretation and robust method development. Now let’s test your knowledge with 30 MCQs on this topic.
Q1. What is the primary goal of Design of Experiments (DOE) in pharmaceutical research?
- To document standard operating procedures
- To identify factors affecting a response and optimize processes
- To increase production speed without analysis
- To perform routine quality checks only
Correct Answer: To identify factors affecting a response and optimize processes
Q2. Which of the following is NOT a basic principle of DOE?
- Randomization
- Replication
- Blocking
- Bias maximization
Correct Answer: Bias maximization
Q3. In DOE terminology, what is a ‘factor’?
- The response measured in an experiment
- An experimental error component
- An independent variable that is controlled during the experiment
- A statistical test used after the experiment
Correct Answer: An independent variable that is controlled during the experiment
Q4. What does ‘level’ refer to in an experimental design?
- The number of replicates in an experiment
- The specific values or categories of a factor
- The response variable magnitude
- The blocking strategy used
Correct Answer: The specific values or categories of a factor
Q5. Which design is most appropriate when studying two or more factors and their interactions?
- Completely randomized design with single factor
- Factorial design
- Sequential single-variable testing
- Descriptive observational study
Correct Answer: Factorial design
Q6. What advantage does a factorial design have over one-factor-at-a-time experiments?
- It ignores interactions
- It assesses main effects and interactions simultaneously
- It requires no replication
- It only works for qualitative factors
Correct Answer: It assesses main effects and interactions simultaneously
Q7. What is ‘confounding’ in experimental design?
- A method to increase sample size
- The mixing of effects of two factors so their individual effects cannot be separated
- A plotting technique for residuals
- A type of replication
Correct Answer: The mixing of effects of two factors so their individual effects cannot be separated
Q8. Which analysis method is commonly used to test factor effects in DOE?
- ANOVA (Analysis of Variance)
- Chi-square test only
- Kaplan-Meier survival analysis
- Fick’s diffusion equation
Correct Answer: ANOVA (Analysis of Variance)
Q9. In a 2^3 factorial design, how many experimental runs are required without replication?
- 3
- 6
- 8
- 12
Correct Answer: 8
Q10. What does ‘replication’ provide in an experiment?
- Reduction of experimental cost
- An estimate of experimental error and improved precision
- Elimination of the need for randomization
- Guaranteed detection of interactions
Correct Answer: An estimate of experimental error and improved precision
Q11. Why is randomization important in DOE?
- To increase confounding intentionally
- To ensure results are biased
- To protect against unknown sources of variation and reduce bias
- To fix factor levels permanently
Correct Answer: To protect against unknown sources of variation and reduce bias
Q12. What is a ‘blocking’ strategy used for?
- To increase the number of factors tested
- To group experimental units with similar nuisance variability to reduce error
- To maximize the main effects’ confounding
- To avoid replication
Correct Answer: To group experimental units with similar nuisance variability to reduce error
Q13. Which design is efficient when many factors exist but only a few are expected to be important?
- Full factorial design
- Fractional factorial design
- Single-run pilot study
- Cross-sectional survey
Correct Answer: Fractional factorial design
Q14. What does ‘resolution’ indicate in a fractional factorial design?
- The precision of measurement instruments
- The degree to which main effects are confounded with interactions
- The number of levels per factor
- The number of replicates required
Correct Answer: The degree to which main effects are confounded with interactions
Q15. Which response surface method is commonly used for optimization in formulation development?
- Cox proportional hazards model
- Central Composite Design (CCD)
- Latin square with one factor
- Descriptive statistics only
Correct Answer: Central Composite Design (CCD)
Q16. What is an interaction effect?
- Effect of a single factor regardless of others
- When the effect of one factor depends on the level of another factor
- A random error term in ANOVA
- A blocking variable
Correct Answer: When the effect of one factor depends on the level of another factor
Q17. Which assumption is NOT required for ANOVA?
- Independence of observations
- Normality of residuals
- Equal variances (homoscedasticity)
- Exact equality of group means before the experiment
Correct Answer: Exact equality of group means before the experiment
Q18. In pharmaceutical method validation, DOE can be used to assess:
- Only stability under one condition
- Robustness, ruggedness, and critical method parameters
- Marketing strategies
- Patient adherence exclusively
Correct Answer: Robustness, ruggedness, and critical method parameters
Q19. What is the purpose of residual analysis after fitting an experimental model?
- To increase sample size
- To verify model assumptions and detect outliers or non-linearity
- To select factors for blocking
- To compute confidence intervals only
Correct Answer: To verify model assumptions and detect outliers or non-linearity
Q20. Which plot is useful to visualize interactions between factors?
- Main effects plot only
- Interaction plot
- Histogram of raw data only
- Kaplan-Meier curve
Correct Answer: Interaction plot
Q21. Type I error in hypothesis testing corresponds to:
- Failing to detect a true effect
- Incorrectly concluding there is an effect when there is none (false positive)
- Random sampling error only
- Confusing factor levels
Correct Answer: Incorrectly concluding there is an effect when there is none (false positive)
Q22. Power of an experiment is:
- The probability to detect an effect when a true effect exists
- The probability of a Type I error
- The number of experimental runs
- The magnitude of random error
Correct Answer: The probability to detect an effect when a true effect exists
Q23. Which design is commonly used for screening many formulation factors quickly?
- Full response surface design
- Plackett-Burman or fractional factorial screening designs
- Matched-pairs clinical trial
- Case-control observational design
Correct Answer: Plackett-Burman or fractional factorial screening designs
Q24. What is ‘orthogonality’ in the context of experimental design?
- When factor effects are correlated
- When estimates of factor effects are independent and uncorrelated
- When factors have only one level
- When randomization is not applied
Correct Answer: When estimates of factor effects are independent and uncorrelated
Q25. Which DOE technique reduces runs while preserving information about main effects for many factors?
- Full factorial with high replication
- Fractional factorial design
- Single-subject design
- Descriptive cross-sectional survey
Correct Answer: Fractional factorial design
Q26. When optimizing dissolution with two continuous factors, which approach is most suitable?
- Two-level factorial only without follow-up
- Response surface methodology with central composite or Box-Behnken design
- Time-series analysis
- Non-statistical trial-and-error
Correct Answer: Response surface methodology with central composite or Box-Behnken design
Q27. Which statistic in ANOVA compares variance between groups to variance within groups?
- p-value directly
- F-statistic
- Median
- Standard deviation only
Correct Answer: F-statistic
Q28. In a DOE report, which information is essential to reproduce the experiment?
- Only the conclusions
- Factor definitions, levels, experimental layout, randomization, replication, and analysis methods
- Only the final optimized settings
- Only the brand names used in materials
Correct Answer: Factor definitions, levels, experimental layout, randomization, replication, and analysis methods
Q29. Which design is useful when curvature is expected in the response and one wants to fit a quadratic model?
- 2-level full factorial without center points
- Central Composite Design with axial points
- Completely randomized design without replicates
- Single-run screening
Correct Answer: Central Composite Design with axial points
Q30. How can DOE contribute to Quality by Design (QbD) in pharmaceutical development?
- By replacing process understanding with trial-and-error
- By systematically identifying critical factors, establishing design space, and supporting robust processes
- By focusing only on marketing and regulatory paperwork
- By eliminating the need for analytical validation
Correct Answer: By systematically identifying critical factors, establishing design space, and supporting robust processes
