Introduction to Factorial ANOVA

Introduction to Factorial ANOVA

• Module five of ANNOVA series focuses on factorial ANOVA.

• Examination of both theoretical and practical aspects of factorial ANOVA.

• Recap of module three: discussion of one-factor ANOVA involving between and within designs.

  • One-factor ANOVA: Analysis of one independent variable with more than two levels.

Understanding Multiple Independent Variables

• Explore what happens when more than one independent variable is analyzed: 2, 3, or more independent variables.

• Example: Analysis of driving performance (dependent variable) with two independent variables.

  • Independent Variable 1: Alcohol intake (3 levels: low, medium, high).

  • Independent Variable 2: Age (2 levels: young, older).

• Resulting in a 2x3 factorial ANOVA design, referred to as an A by B design.

  • Example representation: 3 levels of alcohol and 2 levels of age results in a 3 by 2 design.

Second Example of Two-Factor ANOVA

• Example: Testing memory performance across different levels of noise and types of education students.

  • Independent Variable 1: Noise level (5 levels: quiet, slightly noisy, moderately noisy, noisy, very noisy).

  • Independent Variable 2: Type of student (4 levels: science, economics, arts, education).

• This example results in a 5 by 4 design.

  • Important Note: Each independent variable can be tested as either a between or within design depending on the study design.

Between vs Within Designs

• Age must be a between-level variable, as participants cannot fall into both age groups.

• Alcohol intake could be either:

  • Between design: Each participant experiences only one level of alcohol.

  • Within design: Each participant experiences all levels on different test occasions.

• Student type is typically a between factor due to diverse enrollment.

• Noise level could be both between and within, depending on the study design.

Higher Factorial ANOVA Designs

• Exploration of designs beyond two factors: 3-factor, 4-factor, etc.

  • Example: Gender, upbringing, noise level, and education level as independent variables.

• Understanding the basic two-factor design is fundamental for grasping more complex designs.

Main Effects in Factorial ANOVA

• Main Effects: Examining the effect of each independent variable separately on the dependent variable.

  • Referring back to the alcohol-age example:

    • Main Effect 1: Comparing driving performance between younger and older drivers across all alcohol levels.

    • Main Effect 2: Assessing the impact of alcohol level on driving performance across both age groups.

• Represented visually, averaged scores are analyzed to reveal differences.

Interactions in Factorial ANOVA

• Interactions: Examining whether the effect of one independent variable differs across levels of the other independent variable.

  • Example: Driving performance variations based on age across different alcohol levels.

• Graphical representation helps clarify interactions:

  • If interaction lines are similar, no interaction exists; if diverging, an interaction is present.

• Simple Effects: Examining the effect of one variable at a specific level of another variable.

  • Example: Analyzing alcohol's effect on young drivers specifically, and then on older drivers.

Higher Order Interactions

• In a 3-way design (e.g., 2 by 3 by 4), interactions become more complex.

  • First-order interactions involve pairs of the three factors.

  • Examples: Task vs Noise, Species vs Noise, Species vs Task.

• Second-order interactions involve the combination of all three variables.

Implications of Main Effects and Interactions

• Existence of significant main effects alongside interactions can complicate interpretations.

  • Importance in results writing: Always clarify specific differences, rather than general effects.

• Baseline Data Analysis: Critical for understanding complex factorial data outputs.

Practical Factorial ANOVA in SPSS

1. Introduction to setting up a factorial ANOVA in SPSS.

2. Utilizing a two-factor design (e.g., stress levels and handedness).

3. Data arrangement and entering into SPSS for analysis.

4. Concept of testing assumptions: normality, homogeneity of variance, and handling violations.

   • Levene's Test results are critical for interpreting validity of ANOVA results.

5. Review of output: looking at main effects and interaction effects.

SPSS Outputs Review

• Descriptive statistics to analyze the means across groups.

• Examination of interaction graphs for clearer understanding of relationships.

• Estimated Marginal Means (EM Means): Importance when group sizes are unequal.

Significance & Paired Comparisons

• Post Hoc Comparisons: Only makes meaningful group comparisons, avoiding unnecessary additional comparisons.

  • Example of paired comparisons emphasized: stress levels in different handedness groups to direct findings.