Skip to main content

Factorial Design — Previous Year Questions

📊 Topic Overview​

MetricValue
Papers Appeared17 of 28 (60.7%)
Priority🔴 HIGH
Section DistributionSec A: 10
Most RepeatedTypes and definition of factorial design (11 times)
ProbabilityExtremely High

🎯 Must-Know Concepts​

  1. Definition of factorial design and key terms (factor, level, cell)
  2. Types: between-subjects, within-subjects, mixed factorial
  3. 2×2 factorial design with example
  4. Main effects and interaction effects
  5. Advantages and limitations

🔥 Most Repeated Question: Define Factorial Design and Explain Its Types (11 appearances)​

Answer (Section A — ~450 words):​

A factorial design is an experimental design in which two or more independent variables (factors) are simultaneously manipulated to examine their individual effects (main effects) and their combined effect (interaction effect) on a dependent variable. The term "factorial" reflects the fact that all factors are crossed — every level of one factor is combined with every level of every other factor.

Key Terms: Factor: An independent variable in a factorial design. Example: Type of instruction (lecture vs discussion). Level: The number of values a factor takes. Example: Gender has 2 levels (male, female). Cell: A unique combination of factor levels. In a 2×2 design, there are 4 cells. Main effect: The overall effect of one factor, averaged across all levels of the other factor(s). Interaction effect: When the effect of one factor differs depending on the level of another factor. Interactions make factorial designs especially powerful.

Types of Factorial Design:

1. Independent Groups (Between-Subjects) Factorial Design Different participants are assigned to each cell. Requires large samples. Eliminates carryover effects but is less statistically powerful. Example: A 2×2 design with Factor A (stress: high/low) and Factor B (sleep deprivation: yes/no); each of 4 groups receives a different combination.

2. Repeated Measures (Within-Subjects) Factorial Design The same participants experience all cells. Requires fewer participants, more statistically powerful, but susceptible to order effects (counterbalancing required). Example: Each participant responds to all four stress×sleep combinations at different times.

3. Mixed Factorial Design At least one factor is between-subjects and at least one is within-subjects. Common in psychology — e.g., Group (clinical vs control) as between-subjects, Time (pre/post) as within-subjects.

2×2 Factorial Design — Illustrated:

Consider a 2×2 design studying anxiety (low, high) × difficulty (easy, hard) on test performance:

Easy TaskHard Task
Low AnxietyGroup 1Group 2
High AnxietyGroup 3Group 4

Main effect of Anxiety: difference in performance between low and high anxiety, averaged across difficulty. Main effect of Difficulty: difference between easy and hard, averaged across anxiety. Interaction: Does the effect of anxiety on performance depend on task difficulty? (e.g., high anxiety hurts only on hard tasks).

Advantages: Economical — tests multiple factors and their interactions in a single study. Ecological validity — real-world behaviour is multiply determined; factorial designs reflect this. Provides interaction information unavailable from single-factor designs.

Limitations: Complexity increases rapidly with additional factors (a 3×3×3 design has 27 cells). Interpretation of higher-order interactions becomes difficult. Large sample requirements for between-subjects designs.

📝 Other Questions​

Main effects vs interaction effects (Section B — ~250 words)​

A main effect is the effect of one independent variable on the dependent variable, collapsing across (averaging over) all levels of the other independent variable(s). In a 2×2 design with factors A and B, the main effect of A is determined by comparing rows; the main effect of B by comparing columns.

An interaction effect occurs when the effect of one factor on the dependent variable is not the same at every level of another factor — the factors "interact." Interactions reveal that the combined effect of two factors is more than (or different from) the sum of their individual effects.

Example: A study examines caffeine (yes/no) and time of day (morning/evening) on alertness:

  • Main effect of caffeine: caffeine drinkers are more alert overall.
  • Main effect of time: people are more alert in the morning overall.
  • Interaction: caffeine may only improve alertness in the evening (when alertness is otherwise low) but not in the morning (when alertness is already high).

Interaction effects are identified by examining whether the lines in a graph are parallel (no interaction) or non-parallel/crossing (interaction present). Significant interactions require that main effects be interpreted cautiously — they may be misleading if the interaction is present.

🧠 Memory Aids​

Design Types (IBM): Independent groups, Between-within (Mixed), Measures (Repeated)

2×2 has 4 cells, 2×2×2 has 8 cells — multiply levels: 2×2=4, 2×3=6, 3×3=9

📚 Related Content​

✅ Self-Assessment​

  1. What is the difference between a main effect and an interaction effect?
  2. How many cells does a 2×3 factorial design have? A 3×3?
  3. When would you choose a within-subjects over a between-subjects factorial design?
  4. What does a non-parallel line graph in a factorial design indicate?
  5. Why do interaction effects make main effects potentially misleading?

💡 Exam Tips​

  • Section A: Define → Key terms (factor, level, cell, main effect, interaction) → Types (3) → 2×2 example with table → Advantages/Limitations.
  • Always draw the 2×2 table — it earns marks and demonstrates understanding.
  • The distinction between main effect and interaction is the conceptual core — must be explained clearly with a concrete example.