Advanced Experimental Designs

The Basics of Factorial Designs

Basic Characteristics of Factorial Designs

A factorial design is a research design that investigates the influence of two or more independent variables (IVs) on an outcome of interest. This allows researchers to understand how multiple variables interact and contribute to changes in the dependent variable (DV).

• Purpose: To efficiently investigate the effects of multiple independent variables, providing insights into how they independently and collectively affect the outcome.

• Factors are referred to by letters (e.g., Factor A, Factor B, Factor C), and each factor can consist of different levels, which are the variations of the independent variable.

• Levels: Each factor in a factorial design can have two or more levels; for example, temperature can be tested at low, medium, and high levels.

Why Can’t We Pick A Single Name for Independent Variables?

The term Independent Variable (IV) refers to the variable manipulated in research and is typically plotted on the X-axis of a graph because it potentially influences another variable, known as the dependent variable (DV).

• X serves as a placeholder in graphs to represent various independent variables, facilitating comparisons across different studies.

• Factor: This term describes independent variables that may interact with one another, jointly impacting the outcome variable while allowing for more complex analyses.

• Design: This represents a 2 x 2 factorial design; it involves two independent variables (Humidity and Temperature) and one dependent variable (Score on the memory task).

A factorial research design is used when researchers want to study two or more independent variables (factors) at the same time and see not only their individual effects but also how they interact with each other.

🔹 1. What are “levels” in a factorial design?

A level is simply the number of conditions or variations within a factor.

• If a factor is “Medication Type”:

  • Level 1 = Lithium

  • Level 2 = Ketamine

• If another factor is “Time”:

  • Level 1 = Week 1

  • Level 2 = Week 6

  • Level 3 = Week 12

👉 This would be a 2 × 3 factorial design (2 levels × 3 levels).

🔹 2. How many groups (conditions) are there?

To find total experimental conditions:

Example:

• 2 (medications) × 3 (time points) = 6 total conditions

Each combination is a unique group:

• Lithium at Week 1

• Lithium at Week 6

• Lithium at Week 12

• Ketamine at Week 1

• Ketamine at Week 6

• Ketamine at Week 12

🔹 3. Types of outcomes in factorial designs

Factorial designs produce three main types of results:

✅ A. Main Effects

This is the effect of one independent variable on the dependent variable, ignoring the other factor.

• Example:

  • Does medication type affect symptom improvement overall?

  • Does time affect symptom improvement overall?

👉 You can have a main effect for each factor.

✅ B. Interaction Effects (the most important part)

This happens when the effect of one factor depends on the level of another factor.

• Example:

  • Ketamine might work faster early (weeks 1–6) but plateau later

  • Lithium might show slow, steady improvement over time

👉 That difference in patterns = interaction effect

If lines on a graph are:

• Parallel → No interaction

• Non-parallel or crossing → Interaction present

✅ C. Simple Effects

These break down an interaction to look more closely.

• Example:

  • Compare Lithium vs Ketamine only at Week 6

  • Compare Week 1 vs Week 12 only for Ketamine

Graphical Representation of Results

Graphical representation includes various forms, which can illustrate the data succinctly.

• Two graphs might depict the same information but vary in clarity; choosing the right graph depends on which version accurately communicates the findings to the audience.

• Y-axis: Memory Task Score

• X-axis: Humidity levels, with distinct points representing the temperature conditions.

PROS of Factorial Designs

• Main Effects:
      - Occurs when one IV alone significantly influences the DV, allowing for clearer interpretations. This facilitates the understanding of factors like temperature or humidity influencing task performance independently.

    - It allows researchers to isolate the main effects of each IV while controlling for other variables, enhancing the reliability of the findings.

Factorial Design Example #2: Driving Experience and Cell Phone Use

• Research Question: Examining the impact of driving experience and cell phone use on accident rates among drivers.

• Conditions:
      - Inexperienced drivers reported 6 accidents, while experienced drivers reported 3 accidents under varying cell phone use conditions—15 accidents with phone use versus 5 without.

• Design: This represents a 2 x 2 factorial design with independent variables (Driving Experience and Cell Phone Use) and one dependent variable (Number of Accidents over 10 years).

Rationale for Using Factorial Designs

• Factorial designs are beneficial because they evaluate the interaction of multiple experimental factors, overcoming limitations present when conducting separate experiments on the same subjects.

• Interaction: The term refers to the situation where the effect of one independent variable on the DV changes depending on the level of another independent variable.

    - Example: The effects of cell phone use on driving may differ significantly between inexperienced and experienced drivers.

Interaction in Factorial Designs

• Visual graphical analysis is critical for detecting interaction effects:

    - If the plotted lines on a graph intersect, it indicates that there is an interaction between the factors being studied.

    - Conversely, if the lines remain parallel, it suggests there is no interaction between the factors.

CONS of Factorial Designs

• The complexity of factorial designs increases as more IVs and levels are included in the design, leading to an unmanageable rise in experimental conditions.

    - Example: A design featuring 5 experience levels and 5 levels of cell phone use results in 25 unique experimental conditions, complicating recruitment efforts and data analysis.

    - An overabundance of factors can complicate visualizations, making it difficult to interpret complex graphs clearly.

Main Effects and Interactions Analysis

• A factorial design typically results in as many main effects as there are factors:
      - For 2 factors, it will yield 1 interaction (AB).     - For 3 factors, it will yield 4 interactions (AB, AC, BC, ABC).

Example: Main Effect of Cell Phone Use

• Analyzing the accident data illustrates the overall impact of cell phone use across differing driver experiences:

    - Inexperienced drivers: 6 accidents (No Use) + 15 (Use) = 21 total Accidents.
    - Experienced drivers: 3 accidents (No Use) + 5 (Use) = 8 total Accidents.

Main Effect of Driving Experience

• The impact of driving experience can be observed through the marginal totals of accidents, emphasizing the differences among driver groups:
      - Inexperienced Drivers: 21 Total Accidents
      - Experienced Drivers: 8 Total Accidents.

Factorial Design Options

• Between-Subjects Factorial Design: In this design, each participant is exposed to only one condition of the experiment, enhancing focus on the effect of that condition.

• Within-Subjects Factorial Design: In this approach, each participant experiences every condition, which allows for the control of individual differences in responses.

• Mixed-Factorial Design: Incorporates aspects of both the between-subjects and within-subjects designs, offering flexibility and robustness in research methodology.

Study by Dahl & Price (2012) - 2x3 Design

• Research Question: Explore participants’ belief in a witness's alibi regarding a robbery, examining how witness characteristics influence perception.

• Conditions: The study analyzed relationships and the age of the alibi witness, providing varied categorizations:
      - Witness categories included children aged 6 and adults aged 25 as potential witnesses, aimed at assessing age-related biases.

The Power of Factorial Designs

• Key Questions Addressed:
      - What is the main effect of witness age?
      - What is the main effect of the witness-suspect relationship?
      - Is there an interaction between witness age and relationship to suspect?

Demonstration of Main Effects and Interactions

• Response levels in percentage for belief in the suspect's guilt based on the type of witness:
      - Child witness (30%, 40%, 50% corresponding to different relationships) vs. Adult witness (75%, 60%, 45% with the same relationships).

Marginal Means Calculation

• Calculating average belief probabilities allows for the marginal means to be presented for ease of interpretation in analysis:
      - Children: 40% average belief
      - Adults: 60% average belief.

Graphing Main Effects and Interactions

• Utilizing graphical representations effectively illustrates the possible relationships between witness characteristics and their perceived trustworthiness based on age and relationship to the suspect.

Findings on Main Effects

• The Marginal Means Analysis reveals:
      - A significant main effect of witness age: Children display a belief level of 40%, while adults exhibit a higher average of 60%.
      - The relationship of the witness to the suspect shows negligible impact, suggesting no significant independent effect.
      - Noteworthy interactions have been observed between age and relationship status, influencing perception of guilt.

Interpreting the Interaction

• The influence of the witness's relationship with the suspect significantly fluctuates according to the age of the witness presented.
      - Children serving as witnesses tended to increase perceived suspect guilt, whereas adult witnesses’ relationships may diminish the belief in the suspect's guilt.

Mixed-Factorial Design Overview

• Mixed-factorial designs encompass at least one between-subjects variable and one within-subjects variable, amplifying the variability and depth of the study.

Example of Transitioning to a Mixed-Subjects Design

• Employing a previously defined memory task (Humidity and Temperature) while transitioning into a mixed-factorial design could involve testing different temperature conditions as between-subjects and humidity levels as within-subjects conditions.

Quasi-Independent Variables in Mixed-Factorial Designs

• Quasi-independent variables can be embraced as factors in mixed-factorial designs, permitting their inclusion for analysis without direct manipulation.

• Examples of quasi-independent variables (IVs) could consist of age, sex, or religion as between-subjects variables, while distraction categories during observation serve as within-subjects variables.

PROS of Mixed-Factorial Designs

• Mixed-factorial designs capitalize on the strengths found in both within-subjects and between-subjects setups, enabling researchers to reduce random error through repeated measures tracked on individual participants.

CONS of Mixed-Factorial Designs

• Despite their strengths, mixed-factorial designs may not be suitable for every type of inquiry, especially where one extensive variable encompasses numerous values, ensuing complications in data collection and analysis.