Design of experiments – basic concepts and objectives MCQs With Answer

Design of experiments (DOE) introduces systematic planning and analysis of tests to understand how factors and their levels influence responses in pharmaceutical research. For B.Pharm students, DOE covers key concepts — factors, levels, treatments, experimental units, randomization, replication, blocking, factorial and fractional designs, interactions, ANOVA and response-surface methods — with practical objectives: identify critical process variables, quantify effects, detect interactions, reduce variability and optimize formulations or processes. Mastery of DOE improves study efficiency, robustness and reproducibility in formulation development, stability studies and process optimization. Now let’s test your knowledge with 30 MCQs on this topic.

Q1. What is the primary objective of Design of Experiments (DOE) in pharmaceutical studies?

• To conduct single uncontrolled trials to collect observations
• To systematically study factors and interactions to optimize responses
• To replace statistical analysis with expert judgment
• To minimize documentation during formulation

Correct Answer: To systematically study factors and interactions to optimize responses

Q2. In DOE terminology, what is a “factor”?

• The measured outcome or response from an experiment
• A background noise source affecting results
• An experimental variable deliberately changed during the study
• The number of replicates used in the study

Correct Answer: An experimental variable deliberately changed during the study

Q3. What does “level” mean in the context of DOE?

• The number of responses measured
• A specific value or setting of a factor
• The statistical power of the experiment
• The randomization sequence number

Correct Answer: A specific value or setting of a factor

Q4. Which term best describes the measured outcome in an experiment?

• Factor
• Level
• Response (or dependent variable)
• Block

Correct Answer: Response (or dependent variable)

Q5. What is a “treatment” in an experimental design?

• A method of randomization
• A specific combination of factor levels applied to experimental units
• An error term in ANOVA
• The baseline control only

Correct Answer: A specific combination of factor levels applied to experimental units

Q6. What is an experimental unit?

• The replicate number assigned to each run
• The smallest physical entity to which a treatment is applied
• The statistical test used for analysis
• The overall mean of all observations

Correct Answer: The smallest physical entity to which a treatment is applied

Q7. Why is randomization important in DOE?

• To ensure the same treatment is always applied first
• To eliminate the need for replication
• To reduce systematic bias by randomly assigning treatments to experimental units
• To guarantee normality of data

Correct Answer: To reduce systematic bias by randomly assigning treatments to experimental units

Q8. What is the purpose of replication in experiments?

• To increase the number of factors
• To estimate experimental error and improve precision
• To eliminate interactions
• To reduce the number of required runs

Correct Answer: To estimate experimental error and improve precision

Q9. How does blocking help an experiment?

• By increasing the number of factors tested
• By grouping similar experimental units to reduce variability due to known nuisance factors
• By eliminating the need for randomization
• By guaranteeing orthogonality of factors

Correct Answer: By grouping similar experimental units to reduce variability due to known nuisance factors

Q10. What is a main effect in factorial experiments?

• The combined effect of all factors together
• The effect of changing one factor averaged over levels of other factors
• An unimportant interaction term
• The residual error after fitting the model

Correct Answer: The effect of changing one factor averaged over levels of other factors

Q11. What defines an interaction between two factors?

• When the combined effect equals the sum of individual effects
• When one factor has no effect at any level
• When the effect of one factor depends on the level of another factor
• When randomization is not performed

Correct Answer: When the effect of one factor depends on the level of another factor

Q12. How many runs are required for a full two-level factorial design with 4 factors?

• 4
• 8
• 16
• 32

Correct Answer: 16

Q13. What is a fractional factorial design used for?

• To increase experimental runs beyond full factorial
• To reduce the number of runs while estimating main effects and some interactions
• To remove all interactions from the model
• To guarantee normal distribution of responses

Correct Answer: To reduce the number of runs while estimating main effects and some interactions

Q14. What does “aliasing” or “confounding” refer to in fractional factorials?

• When factorial design is random
• When two or more effects cannot be separately estimated and are mixed together
• When responses are measured with perfect accuracy
• When replication is maximal

Correct Answer: When two or more effects cannot be separately estimated and are mixed together

Q15. Which property defines an orthogonal design?

• Factors are non-independent
• Factor effects can be estimated independently with uncorrelated estimates
• No replication is allowed
• Only one factor is studied at a time

Correct Answer: Factor effects can be estimated independently with uncorrelated estimates

Q16. What is the main purpose of ANOVA in DOE?

• To calculate medians only
• To compare means across multiple treatments and partition variance
• To randomize assignments
• To design the experimental runs

Correct Answer: To compare means across multiple treatments and partition variance

Q17. Which of the following is NOT an assumption of one-way ANOVA?

• Independence of observations
• Normal distribution of residuals
• Homogeneity of variances across groups
• All factors must have only two levels

Correct Answer: All factors must have only two levels

Q18. What is the primary use of a Central Composite Design (CCD)?

• Screening a large number of variables with minimal runs
• Estimating main effects only
• Fitting a quadratic (second-order) model for response surface optimization
• Ensuring orthogonality in fractional designs

Correct Answer: Fitting a quadratic (second-order) model for response surface optimization

Q19. What does a Latin square design control for?

• Only one blocking factor
• Two blocking factors (rows and columns) while testing treatments
• All possible interactions automatically
• No need for randomization

Correct Answer: Two blocking factors (rows and columns) while testing treatments

Q20. What is the Taguchi method mainly focused on?

• Maximizing run count for detailed estimates
• Robust parameter design to reduce variability and improve quality
• Replacing ANOVA with graphical methods only
• Eliminating the need for blocking

Correct Answer: Robust parameter design to reduce variability and improve quality

Q21. What is the role of center points in factorial experiments?

• To estimate interactions exclusively
• To detect curvature and assess nonlinearity in responses
• To increase aliasing intentionally
• To avoid randomization

Correct Answer: To detect curvature and assess nonlinearity in responses

Q22. What does a Resolution III fractional factorial design imply?

• Main effects are unconfounded with any interactions
• Main effects may be aliased with two-factor interactions
• All two-factor interactions are estimable
• No aliasing exists between any effects

Correct Answer: Main effects may be aliased with two-factor interactions

Q23. When is a split-plot design typically used?

• When all factors are easy to change between runs
• When some factors are hard or expensive to change and require whole-plot randomization
• Only for single-factor experiments
• To remove the need for error estimation

Correct Answer: When some factors are hard or expensive to change and require whole-plot randomization

Q24. In hypothesis testing, what does “power” refer to?

• The probability of rejecting the null hypothesis when it is true
• The probability of failing to detect an effect
• The probability of correctly rejecting the null hypothesis when a true effect exists
• The significance level chosen by the researcher

Correct Answer: The probability of correctly rejecting the null hypothesis when a true effect exists

Q25. What is a Type I error (alpha) in the context of DOE?

• Failing to reject a false null hypothesis
• Incorrectly accepting an alternative hypothesis
• Rejecting a true null hypothesis (false positive)
• The variability due to blocking factors

Correct Answer: Rejecting a true null hypothesis (false positive)

Q26. How does a randomized block design (RBD) improve experiments?

• By ignoring nuisance variability
• By reducing within-treatment variability through blocking similar units
• By increasing the number of factors studied
• By eliminating the need for replication

Correct Answer: By reducing within-treatment variability through blocking similar units

Q27. When is a nested design appropriate?

• When all factor levels are crossed with each other
• When levels of one factor exist only within specific levels of another factor
• When there is only one experimental unit
• When interactions are impossible

Correct Answer: When levels of one factor exist only within specific levels of another factor

Q28. In a Latin square of order n, how many treatments and levels are there?

• n treatments and n levels for rows and columns
• n^2 treatments only
• 2n treatments and n levels only
• One treatment repeated n times

Correct Answer: n treatments and n levels for rows and columns

Q29. What is an orthogonal array commonly used for in Taguchi experiments?

• To ensure non-randomized assignment of runs
• To provide a balanced and reduced set of runs that assess factor effects independently
• To maximize aliasing between factors
• To eliminate the need for statistical analysis

Correct Answer: To provide a balanced and reduced set of runs that assess factor effects independently

Q30. What is the main goal of screening designs such as Plackett-Burman?

• To precisely estimate quadratic response surfaces
• To identify the few important factors among many potential variables with minimal runs
• To provide full interaction estimation for all factors
• To completely randomize across multiple blocks

Correct Answer: To identify the few important factors among many potential variables with minimal runs

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